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Social Network Analysis 101: Ultimate Guide

Comprehensive introduction for beginners.

Social network analysis is a powerful tool for visualizing, understanding, and harnessing the power of networks and relationships. At Visible Network Labs, we use our network science and mapping tools and expertise to track collaborative ecosystems and strengthen systems change initiatives. In this Comprehensive Guide, we’ll introduce key principles, theories, terms, and tools for practitioners framed around social impact, systems change, and community health improvement. Let’s dig in!

Learn more and get started with the tools below in our complete Guide.

Table of Contents

You can read this guide from start-to-finish or use the table of contents to fast forward to a topic or section of interest to you. The guide is yours to use as you see fit.

Introduction

Let’s start by reviewing the basics, like a definition, why SNA is important, and the history of the practice. If you want a quick intro to this methodology, download our Social Network Analysis Brief .

Definition of Social Network Analysis (SNA)

Social Network Analysis , or SNA, is a research method used to visualize and analyze relationships and connections between entities or individuals within a network. Imagine mapping the relationships between different departments in a corporation. The outcome would be a vivid picture of how each department interacts with others, allowing us to see communication patterns, influential entities, and bottlenecks

The Importance of SNA

SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.

This methodology also helps demonstrate the impact of relationship-building and systems change efforts by documenting the changes in the quality and quantity of relationships before and after the initiative. The maps and visualizations produced by SNA are an engaging way to share your progress and impact with stakeholders, donors, and the community at large.

Brief Historical Overview of SNA

The concept of SNA emerged in the 1930s within the field of sociology. Its roots, however, trace back to graph theory in mathematics. It was not until the advent of computers and digital data in the 1980s and 1990s that SNA became widely used, revealing new insights about organizational dynamics, community structures, and social phenomena.

While it originated as an academic research tool, it is increasingly used to inform real-world practice. Today, it is used in a broad variety of industries, fields, and sectors, including business, web development, public health, foundations and philanthropy , telecommunications, law enforcement, academia, and systems change initiatives, to name a few.

Fundamentals of SNA

SNA is a broad topic, but these are some of the essential terms, concepts, and theories you need to know to understand how it works.

Nodes and Edges

In SNA, nodes represent individuals or entities while edges symbolize the relationships between them. For example, in an inter-organizational network, nodes might be companies, and edges could represent communication, collaboration, or competition.

Network Types

Different types of networks serve different purposes. ‘Ego Networks’ focus on one node and its direct connections, revealing its immediate network. ‘Whole Networks’, on the other hand, capture a broader picture, encompassing an entire organization or system. Open networks are loosely connected, with many opportunities to build new connections, ideal for innovation and idea generation – while closed networks are densely interconnected, better for refining ideas amongst a group who all know each other.

Network Properties

Properties such as density (the proportion of potential connections that are actual connections), diameter (the longest distance between two nodes), and centrality (the importance of a node within the network) allow us to understand the network’s structure and function. Metrics also can measure relationship quality across the network, like our validated trust and value scores.

Dyadic and Triadic Relationships

Dyadic relationships involve two nodes, like a partnership between two companies. Triadic relationships, involving three nodes, are more complex but can offer richer insights. For instance, it might show how a third company influences the relationship between two others, or which members of your network are the best at building new relationships between their peers.

Homophily and Heterophily

Homophily refers to the tendency of similar nodes to connect, while heterophily is the opposite. In a business context, we might see homophily between companies in the same industry and heterophily when seeking diversity in a supply chain. Many networks aim to be diverse but get stuck talking to the same, similar partners. These network concepts underly many strategies promoting network innovation to avoid group-think among likeminded partners.

Network Topologies

Lastly, the layout or pattern of a network, its topology, can reveal much about its function. For instance, a centralized topology, where one node is connected to all others, may indicate a hierarchical organization, while a decentralized topology suggests a more collaborative and flexible environment. This is also referred to as the structure of the network. Read more.

Theoretical Background of SNA

Many different theories have developed to explain how certain network properties, like their topology, centrality, or type, lead to different outcomes. Here are several key theories relevant to SNA.

Strength of Weak Ties Theory

This theory postulates that weak ties or connections often provide more novel information and resources compared to strong ties. These “weak” relationships, which may seem less important, can serve as important bridges between different clusters within a network. Read more.

Structural Hole Theory

This theory posits that individuals who span the structural holes, or gaps, in a network—acting as a bridge between different groups—hold a strategic advantage. They can control and manipulate information and resources flowing between the groups, making their position more influential. Read more

Small World Network Theory

This theory emphasizes the interconnectedness of nodes within a network. It suggests that most nodes can be reached from any other node through a relatively short path of connections. This property leads to the famous phenomenon of “six degrees of separation,” indicating efficient information transfer and connectivity in a network.

Barabási–Albert (Scale-Free Network) Model

This model suggests that networks evolve over time through the process of preferential attachment, where new nodes are more likely to connect to already well-connected nodes. This results in “scale-free” networks, where a few nodes (“hubs”) have many connections while the majority of nodes have few.

Data Collection and Preparation

Every network mapping begins by collecting and preparing data before it can be analyzed. This data varies widely, but at a basic level, they must include data on nodes (the entities in the network) and data on edges (the lines between nodes representing a relationship or connection). Additional data on the attributes of the nodes or edges add more levels of analysis and insight but are not strictly necessary.

Primary Methods for Collecting SNA Data

This can be as simple as conducting interviews or surveys within an organization. The more complex the network, the more difficult it is to collect good primary data: If you have more than 5-10 partners, interviews and surveys are hard to conduct by hand.

Network survey tools like PARTNER collect relational data by asking respondents who they are connected to, and then asking them about aspects of their relationships to provide trust, value, and network structure scores. This is impossible to do using most survey software like Google Forms without hours of cleaning by hand.

Response rates are an important consideration if using surveys for data collection. Unlike a typical survey where a small sample is representative, a network survey requires a high response rate – 80% and above are considered the gold standard.

In an inter-organizational context where surveys are impossible, or you cannot achieve a valid response rate, one might gather data through business reports, contracts, or publicly available data on partnerships and affiliations. For example, you could visit an organization’s website to note who they list as a partner – and do the same for others – to generate a basic SNA map.

Secondary Sources of SNA Data

Secondary sources include data that was already collected but can be used again, often to complement your use of primary data you collect yourself. This might include academic databases, industry reports, or social media data. It’s important to ensure the accuracy and reliability of these sources.

You can also conduct interviews or focus groups with network members to add a qualitative perspective to your results. These mixed-method SNA projects provide a great deal more depth to their network maps through their conversations with numerous network representatives to explore deeper themes and perspectives.

Ethical Considerations in Data Collection

When collecting data, it’s crucial to ensure privacy, obtain necessary permissions, and anonymize data where necessary. Respecting these ethical boundaries is critical for maintaining trust and integrity in your work.

Consider also how your SNA results will be used. For example, network analysis can help assess how isolated an individual is to target them for interventions. Still, it could also be abused by insurance companies to charge these individuals a higher rate (loneliness increases your risk of death).

Lastly, consider ways to involve the communities with stake in your SNA using approaches like community-based participatory research. Bring in representatives from target populations to help co-design your initiative or innovation as partners, rather than patients or research subjects.

Preparing Data for Analysis

Data needs to be formatted correctly for analysis, often as adjacency matrices or edgelists. Depending on the size and complexity of your network, this can be a complex process but is crucial for meaningful analysis.

If you are new to SNA, you can start by laying out your data in tables. For example, the table below shows a relational data set for a set of partners within a public health coalition. The first column shows the survey respondent (Partner 1), the second shows who they reported as a partner, the third shows their reported level of trust, and the fourth their reported level of collaboration intensity. This is just one of many ways to lay out and organize network data.

Depending on which analysis tool you choose, a varying degree of data preparation and cleaning will be required. Usually, free tools require the most work, while software with subscriptions do a lot of it for you.

Network Analysis Methods & Techniques

There are many ways to analyze a network or set of entities using SNA. Here are some of basic and advanced techniques, along with info on network visualization – a major component and common output of SNA projects.

Basic Technique: Network Centrality

One of the most common ways to analyze a network is to look at the centrality of various nodes to identify key players, information hubs, and gatekeepers across the network. There are three types of centrality, each corresponding to a different aspect of connectivity and centrality. Degree, Betweenness, and Closeness Centrality are measures of a node’s importance.

Degree Centrality  

Can be used to identify the most connected actors in the network. These actors are considered “popular” or “active” and they often have a strong influence within the network due to their numerous direct connections. In a coalition or network, these nodes could be the organizations or individuals that are most active in participating or the most engaged in the network activities. They may be the ‘go-to’ people for information or resources and have a significant impact on shaping the group’s agenda.

Betweenness Centrality

A useful for identifying the “brokers” or “gatekeepers” in the network. These actors have a unique position where they connect different parts of the network, facilitating or controlling the flow of information between others. In a coalition context, these could be the organizations or individuals who have influence over how information, resources, or support flow within the network, by virtue of their position between other key actors. These actors could play crucial roles in collaboration, negotiation, and conflict resolution within the network.

Closeness Centrality

A measure of how quickly a node can reach every other node in the network via the shortest paths. In a coalition, these nodes can disseminate information or exert influence quickly due to their close proximity to all other nodes. These ‘efficient connectors’ are beneficial for the rapid spread of information, resources, or innovations across the network. They could play a vital role during times of rapid change or when swift collective action is required.

Advanced Techniques: Clusters and Equivalence

Clustering Coefficients

The Clustering Coefficient provides insights into the “cliquishness” or local cohesion of the network around specific nodes. In a coalition or inter-organizational network, a high clustering coefficient may indicate that a node’s connections are also directly connected to each other, forming tight-knit groups or sub-communities within the larger network. These groups often share common interests or objectives, and they might collaborate or share resources more intensively. Understanding these clusters can be crucial for coalition management as it can highlight potential subgroups that may need to be engaged differently, or that might possess different levels of influence or commitment to the coalition’s overarching goals.

Structural Equivalence

Structural Equivalence is used to identify nodes that have similar patterns of connections, even if they do not share a direct link. In a coalition context, structurally equivalent organizations or individuals often occupy similar roles or positions within the network, and thus may have similar interests, influence, or responsibilities. They may be competing or collaborating entities within the same sectors or areas of work. Understanding structural equivalence can provide insights into the dynamics of the network, such as potential redundancies, competition, or opportunities for collaboration. It can also reveal how changes in one part of the network may impact other, structurally equivalent parts of the network.

Visualizing Networks

Network visualization is a key tool in Social Network Analysis (SNA) that allows researchers and stakeholders to see the ‘big picture’ of the network structure, as well as discern patterns and details that may not be immediately evident from numerical data. Here are some key aspects and benefits of network visualization in the context of a coalition or inter-organizational network:

Overview of Network Structure: Visualizations provide a snapshot of the entire network structure, including nodes (individuals or organizations) and edges (relationships or interactions). This helps to comprehend the overall size, density, and complexity of the network. Seeing these relationships mapped out can often make the network’s structure more tangible and easier to understand.

Identification of Key Actors: Centrality measures can be represented visually, making it easier to identify key actors or organizations within the network. High degree nodes, gatekeepers, and efficient connectors will stand out visually, which can assist in identifying who holds influence or power within the network.

Detecting Subgroups and Communities: Visualization can also highlight clusters or subgroups within the network. These might be based on shared interests, common goals, or frequent interaction. Understanding these subgroups is crucial for coalition management and strategic planning, as different groups might have unique needs, concerns, or levels of engagement.

Identifying Outliers and Peripheral Nodes: Network visualizations can also help in identifying outliers or peripheral nodes – those who are less engaged or connected within the network. These actors might represent opportunities for further engagement or potential risks for network cohesion.

Highlighting Network Dynamics: Visualizations can be used to show changes in the network over time, such as the formation or dissolution of ties, the entry or exit of nodes, or changes in nodes’ centrality. These dynamics can provide valuable insights into the evolution of the coalition or network and the impact of various interventions or events.

Software and Tools for SNA

SNA software helps you collect, clean, analyze, and visualize network data to simplify the process of of analyzing social networks. Some tools are free with limited functionality and support, while others require a subscription but are easier to use and come with support. Here are some popular s tools used across many application

Introduction to Popular SNA Tools

Tools like UCINet, Gephi, and Pajek are popular for SNA. They offer a variety of functions for analyzing and visualizing networks, accommodating users of varying skill levels. Here are ten tools for use in different contexts and applications.

• UCINet: A comprehensive software package for the analysis of social network data as well as other 1-mode and 2-mode data.
• NetDraw: A tool usually used in tandem with UCINet to visualize networks.
• Gephi: An open-source network analysis and visualization software package written in Java.
• NodeXL: A free and open-source network analysis and visualization software package for Microsoft Excel.
• Kumu: A powerful visualization platform for mapping systems and better understanding relationships.
• Pajek: Software for analysis and visualization of large networks, it’s particularly good for handling large network datasets.
• SocNetV (Social Networks Visualizer): A user-friendly, free and open-source tool.
• Cytoscape: A bioinformatics software platform for visualizing molecular interaction networks.
• Graph-tool: An efficient Python module for manipulation and statistical analysis of graphs.
• Polinode: Tools for network analysis, both for analyzing your own network data and for collecting new network data.

Choosing the Right Tool for Your Analysis:

The right tool depends on your needs. For beginners, a user-friendly interface might be a priority, while experienced analysts may prefer more advanced functions. The size and complexity of your network, as well as your budget, are also important considerations.

PARTNER CPRM: A Community Partner Relationship Management System for Network Mapping

For example, we created PARTNER CPRM, a Community Partner Relationship Management System, to replace the CRMs used by most organizations to manage their relationships with their network of strategic partners. Incorporating data collecting, analysis, and visualization features alongside CRM tools like contact management and email tracking, the result is a powerful and easy-to-use network mapping tool.

SNA Case Studies

Looking for a real-world example of a social network analysis project? Here are three examples from recent projects here at Visible Network Labs.

Case Study 1: Leveraging SNA for Program Evaluation

SNA is increasingly becoming a vital tool for program evaluation across various sectors including public health, psychology, early childhood, education, and philanthropy. Its potency is particularly pronounced in initiatives centered around network-building.

Take for instance the Networks for School Improvement Portfolio by the Gates Foundation. The Foundation employed PARTNER, an SNA tool, to assess the growth and development of their educator communities over time. The SNA revealed robust networks that offer valuable benefits to members by fostering information exchange and relationship development. By repeating the SNA process at different stages, they could verify their ongoing success and evaluate the effectiveness of their actions and adjustments.

Read the Complete Case Study Here

Case Study 2: Empowering Coalition-building

In the realm of policy change, building a coalition of partners who share a common goal can be pivotal in overturning the status quo. SNA serves as a strategic tool for developing a coalition structure and optimizing pre-existing relationships among the members.

The Fix CRUS Coalition in Colorado, formulated in response to the closure of five major peaks to public access, is a prime example of this. With the aim of strengthening state liability protections for landowners, the coalition employed PARTNER to evaluate their network and identify key players. Their future plans involve mapping connections to important legislators as their bill progresses through the state legislature. Additionally, their network maps and reports will prove instrumental in acquiring grants and funding.

Case Study 3: Boosting Employee Engagement

In the private sector, businesses are increasingly harnessing SNA to optimize their employee networks, both formal and informal, with the goal of enhancing engagement, productivity, and morale.

Consider the case of Acuity Insurance. In response to a transition to a Hybrid-model amid the COVID-19 pandemic, the company started using PARTNER to gather network data from their employees. Their aim was to maintain their organizational culture and keep employee engagement intact despite the model change. Their ongoing SNA will reveal the level of connectedness within their team, identify employees who are over-networked (and hence at risk of burnout), and pinpoint those who are under-networked and could be missing crucial information or opportunities.

Read More About the Project Here

Challenges and Future Directions in Network Analysis

Like all fields and practices, social network analysis faces certain limitations. Practitioners are constantly innovating to find better ways to conduct projects. Here are some barriers in the field and current trends and predictions about the future of SNA.

The Limitations of SNA

SNA is a powerful tool, but it’s not without limitations. It can be time-consuming and complex, particularly with larger networks. Response rates are important to ensure accuracy, which makes data collection more difficult and time-consuming. SNA also requires quality, validated data, and the interpretation of results can be subjective. Software that helps to address these problems requires a significant investment, but the results are often worth it.

Lastly, SNA is a skill that takes time and effort to learn. If you do not have someone in-house with network analysis skills, you may need to hire someone to carry out the analysis or spend time training an employee to build the capacity internally.

Current Trends and Future Predictions

One emerging trend is the increased application of SNA in mapping inter-organizational networks such as strategic partnerships, community health ecosystems, or policy change coalitions. Organizations are realizing the power of these networks and using SNA to navigate them more strategically. With SNA, they can identify key players, assess the strength of relationships, and strategize on how to optimize their network for maximum benefit.

In line with the rise of data science, another trend is the integration of advanced analytics and machine learning with SNA. This fusion allows for the prediction of network behaviors, identification of influential nodes, and discovery of previously unnoticed patterns, significantly boosting the value derived from network data.

The future of SNA is likely to see a greater emphasis on dynamic networks – those that change and evolve over time. With increasingly sophisticated tools and methods, analysts will be better equipped to track network changes and adapt strategies accordingly.

In addition, there is a growing focus on inter-organizational network resilience. As global challenges such as pandemics and climate change underscore the need for collaborative solutions, understanding how these networks can withstand shocks and adapt becomes crucial. SNA will play an instrumental role in identifying weak spots and strengthening the resilience of these networks.

Conclusion: Social Network Analysis 101

SNA offers a unique way to visualize and analyze relationships within a network, be it within an organization or between organizations. It provides valuable insights that can enhance communication, improve efficiency, and inform strategic decisions.

This guide provides an overview of SNA, but there is much more to learn. Whether you’re interested in the theoretical underpinnings, advanced techniques, or the latest developments, we encourage you to delve deeper into this fascinating field.

Resources and Further Reading

For those who want to build more SNA skills and learn more about network science, check out these recommendations for further reading and exploration from the Visible Network Labs team of network science experts.

Recommended Books on SNA

• “Network Science” by Albert-László Barabási – A comprehensive introduction to the theory and applications of network science from a leading expert in the field.
• “Analyzing Social Networks” by Steve Borgatti, Martin Everett, and Jeffrey Johnson – An accessible introduction, complete with software instructions for carrying out analyses.
• “Social Network Analysis: Methods and Applications” by Stanley Wasserman and Katherine Faust – A more advanced, methodological book for those interested in a deep dive into the methods of SNA.
• “Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives” by Nicholas Christakis and James Fowler – An engaging exploration of how social networks influence everything from our health to our political views.
• “The Network Imperative: How to Survive and Grow in the Age of Digital Business Models” by Barry Libert, Megan Beck, and Jerry Wind – An excellent book for those interested in applying network science in a business context.
• “Networks, Crowds, and Markets: Reasoning About a Highly Connected World” by David Easley and Jon Kleinberg – An interdisciplinary approach to understanding networks in social and economic systems. This book combines graph theory, game theory, and market models.

Online Resources and Courses

Here are some online learning opportunities, including online courses, communities, resources hubs, and other places to learn about social network analysis.

• Social Network Analysis  by Lada Adamic from the University of Michigan
• Social and Economic Networks: Models and Analysis  by Matthew O. Jackson from Stanford University
• Introduction to Social Network Analysis  by Dr. Jennifer Golbeck from the University of Maryland, College Park
• Statistics.com :   Statistics.com offers a free online course called  Introduction to SNA  taught by Dr. Jennifer Golbeck.
• The Social Network Analysis Network:  This website provides a directory of resources on network methods, including courses, books, articles, and software.
• The SNA Society:  This organization provides a forum for social network analysts to share ideas and collaborate on research. They also offer a number of resources on their website, including a list of online courses.

Journals and Research Papers on SNA

These are a few of the most influential cornerstone research papers in network science and analysis methods:

• “The Strength of Weak Ties” by Mark Granovetter (1973)
• “Structural Holes and Good Ideas” by Ronald Burt (2004)
• “ Collective dynamics of ‘small-world’ networks” by Duncan Watts & Steven Strogatz (1998)
• “The structure and function of complex networks.” by M.E. Newman (2003).
• “Emergence of scaling in random networks” by A. Barabasi (1999).

Check out these peer-reviewed journals for lots of network science content and information:

• Social Networks : This is an interdisciplinary and international quarterly journal dedicated to the development and application of network analysis.
• Network Science : A cross-disciplinary journal providing a unified platform for both theorists and practitioners working on network-centric problems.
• Journal of Social Structure (JoSS) : An electronic journal dedicated to the publication of network analysis research and theory.
• Connections : Published by the International Network for Social Network Analysis (INSNA), this journal covers a wide range of social network topics.
• Journal of Complex Networks : This journal covers theoretical and computational aspects of complex networks across diverse fields, including sociology.

Frequently Asked Questions about SNA

A: SNA is a research method used to visualize and analyze relationships and connections within a network. In an organizational context, SNA can be used to explore the structure and dynamics of an organization, such as the informal connections that drive formal processes. It can reveal patterns of communication, identify influential entities, and detect potential bottlenecks or gaps.

A: The primary purpose of SNA is to uncover and visualize the relationships between entities within a network. By doing so, it allows us to understand the network’s structure and dynamics. This insight can inform strategic decision-making, facilitate change management, and enhance overall efficiency within an organization.

A: SNA allows researchers to examine the relationships between entities, the overall structure of the network, and the roles and importance of individual entities within it. This can involve studying patterns of communication, collaboration, competition, or any other type of relationship that exists within the network.

A: SNA has a wide range of applications across various fields. In business, it’s used to analyze organizational structures, supply chains, and market dynamics. In public health, it can map the spread of diseases. In sociology and anthropology, SNA is used to study social structures and relationships. Online, SNA is used to study social media dynamics and digital marketing strategies.

A: Key concepts in SNA include nodes (entities) and edges (relationships), network properties like density and centrality, and theories such as the Strength of Weak Ties and Structural Hole Theory. It also encompasses concepts like homophily and heterophily, which describe the tendency for similar or dissimilar nodes to connect.

A: An example of SNA could be a study of communication within a corporation. By treating departments as nodes and communication channels as edges, analysts could visualize the communication network, identify key players, detect potential bottlenecks, and suggest improvements.

A: Social Network Analysis refers to the method of studying the relationships and interactions between entities within a network. It involves mapping out these relationships and applying various analytical techniques to understand the structure, dynamics, and implications of the network.

A: In psychology, SNA can be used to study the social relationships between individuals or groups. It might be used to understand the spread of information, the formation of social groups, the dynamics of social influence, or the impact of social networks on individual behavior and well-being.

A: SNA can be conducted at different levels, depending on the focus of the study. The individual level focuses on a single node and its direct connections (ego networks). The dyadic level looks at the relationship between pairs of nodes, while the triadic level involves three nodes. The global level (whole network) considers the entire network.

A: There are several types of networks in SNA, including ego networks (focused on a single node), dyadic and triadic networks (focused on pairs or trios of nodes), and whole networks. Networks can also be categorized by their structure (like centralized or decentralized), by the type of relationships they represent, or by their application domain (such as organizational, social, or online networks).

A: SNA is used to visualize and analyze the relationships within a network. Its insights can inform strategic decisions, identify influential entities, detect potential weaknesses or vulnerabilities, and enhance the efficiency of communication or processes within an organization or system. It’s also an essential tool for research in fields like sociology, anthropology, business, public health, and digital marketing.

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A Guide to Social Network Analysis and its Use Cases

• Last Updated on April 23, 2021

In today’s world of limitless connectivity, multiple devices, unlimited choices, several individual personas, there is something sublime unifying all of the above. There is an invisible thread connecting all the dots despite the digital growth happening every day. According to the Chaos Theory, something as small as the flutter of a butterfly’s wing can ultimately cause a typhoon halfway around the world.

In other words, we are a part of a network in all stages of our lives, be it a social network like friends or family, an organization network like an educational institution or workplace. The networks we are a part of also include a social media network where we connect with people across the world or even a consumer network as users of various brands. Thus, networks are all around us.

The concept of networks and extracting information has untapped potential, be it a social setting, consumer behavior, health management, education, politics. Though intellectuals have started seeing the benefits of identifying social groups for various applications, this concept has not become mainstream in the business world. This blog delves into SNA (Social Network Analysis) and how it can be used to analyze and solve business-related problems.

What is SNA?

Social Network Analysis (SNA), also known as network science, is a general study of the social network utilizing network and graph theory concepts. It explores the behavior of individuals at the micro-level, their relationships (social structure) at the macro level, and the connection between the two.

SNA uses several methods and tools to study the relationships, interactions, and communications in a network. This study is key to procedures and initiatives involving problem-solving, administration, and operations of that network.

The basic entities required for building a network are nodes and the edges connecting the nodes. Let us try and understand this with the help of a most common application of SNA, the Internet. Webpages are often linked to other web pages on their own page or other pages. In SNA language, these pages are nodes, and the links between the pages are the edges. In this way, we can interpret the entire internet as one large graph.

SNA is a commonly used approach for analyzing interpersonal connections on the internet due to the boom of social media networking. But this concept is not limited to online social networks; it can be used for any application that can be modeled as a network.

A Guide to the Most Used SNA Terminologies

As established earlier, nodes and edges are the building blocks for SNA. Few characteristics of the edges that define the features of a network are shown below.

The Edges connect the Nodes. The direction of connections determines the Edge type.

1.a Directed Edge: The nodes connected by this edge are ordered, that is, the connection between the nodes is one way. For example, Twitter, Instagram are predominantly directed edge networks. You can follow someone without them following you back.

1.b Undirected Edge: The relationship between the nodes connected by this edge is mutual, i.e., the connection is applicable both ways. E.g., Befriending a person on Facebook, LinkedIn automatically creates a two-way connection.

2. Weight: In a weighted network, an edge carries a label (weight) between the nodes. Different applications can have their own definition of weight. In social media analysis, a weight can define the number of mutual connections between the nodes connected by that edge.

In Figure 2 , John and Frank have two mutual friends, Rose and Amy. Thus, the edge connecting John and Frank carries a weight of 2.

3. Density : The relation between the number of existing connections in a network and all possible connections in the network is calculated as follows:

In Figure 3 , we have a five-point/node network. The total possible connections in this network are 10. Figure 3.a has nine edges; its density is 90%. Hence it is a high-density network. Whereas Figure 3.b has only four edges, it has a low density of 40%.

Centrality Measures:

a) Degree Centrality: Measures the number of direct ties to a node; this will indicate the most connected node in the group.

Let’s consider the network in Figure 4 . The degree centrality score of a network is the sum of edges connected to that node. For Node 1, the degree centrality is 1, and for Nodes 3 and 5, the score is 3.

The standardized score is calculated by dividing the score by (n-1), where n is the number of nodes in the network.

We can see that nodes 3 and 5 have a high degree centrality of 0.5, i.e., they are the most well-connected nodes in the network.

b) Closeness Centrality: Closeness measures how close a node is to the rest of the network. It is the ability of the node to reach the other nodes in the network. It is calculated as the inverse of the sum of the distance between a node and other nodes in the network. 

Let us take node 1 from Figure 4 ; the sum of distances from node 1 to all other nodes is 16.

Hence the Closeness score for node 1 will be 1/16. The standardized score is calculated by multiplying the score by (n-1).

We can conclude that node 4 is the closest/central node in the network with the highest closeness score of 0.6.

c) Betweenness Centrality: It is a measure of how often a node appears in the shortest path connecting two other nodes. Let us take node 5 in Figure 4 . Node 5 occurs in 9 shortest paths between a pair of nodes (as shown in Table 4 ).

If node 5 is the only node in the path, then the path value is 1. If it is one of the ‘n’ nodes in the shortest path, then the path value is 1/n. The sum of path values for node 5 for all nine pairs of nodes is its betweenness score. These values are then standardized by dividing the score by (n-1)*(n-2)/2

Nodes with high betweenness centrality are critical in controlling and maintaining flow in the network; hence these are critical nodes in the network

. d) Eigenvector Centrality: A relative measure of the importance of the node in the network. Each node is assigned a value or score depending upon the number of other prominent/ high scoring nodes it is connected to.

Why do we need such a relative measure? Consider the network in Figure 5 . Here ‘d’ represents the degree centrality score. Nodes A and B are connected to 4 nodes each, and hence both have a degree centrality score of 4. But when we look at their neighbors, we can see that node B is connected to nodes with a high degree. Hence, node B can be preferred over node A when we have to choose based on connectivity.

Real-world use cases of Social Network Analysis:

1. Supply Chain Management: A supply chain can be modeled into a network of supplier/consumer relations. Network analysis on the supply chain helps us improve the operation efficiency by identifying and eliminating less important nodes (suppliers/warehouses). It can help identify crucial nodes in the network and create a standby in crises or emergencies.

Nodes include Retailers, Suppliers, Warehouses, Transporters, Regulatory agencies.

SNA applications can help manufacturers identify more operationally critical nodes and identify potential sources to increase the number of connections to suppliers. This can also help identify any bottlenecks in the supply process and inventory management.

2. Human Resources:  HRM often strives to identify critical resources and understand their contribution to the organization flow, collaboration, participation, and information flow. By following the Organizational Network Analysis (ONA), an organization will optimize the talent connections, productivity, and utilization. 

It will also help identify the reach of an individual, identify accelerators of growth and poorly connected resources, and decide whom to give more opportunity.

3. Transmission of Infectious Diseases: SNA could help identify and isolate individuals and groups with high betweenness and out-degree centrality (transmitters of disease) and implement sound contact tracing activities to mellow the impact.

Apart from Contact tracing, SNA can also identify dominant themes and relations between keywords and identify the sentiment. Here is the connection between the top 10 words for COVID-19 themes:

4. Finance, Fraud detection : Financial organizations can use SNA for fraud detection. Fraud is often organized by groups of people loosely connected to each other. Such a network mapping will enable financial institutions to identify customers who may have relations to individuals or organizations on their criminal watchlist (network) and take precautionary measures.

SNA can also be used to deny access to potential hacking networks, identify a fraud ring, and series of money transactions that could be linked to Money Laundering activities.

As a Business Leader, you will have to make many critical decisions regarding effective employee performance, supply chain management , and eliminating bottlenecks in an operation process, contact tracking, credit risks, and several other use cases. SNA has immense potential to elevate existing analysis, given there is information flow and connections.

Get in touch with us or mail us at [email protected] to know how SNA can be applied to add value to your business.

  References:

• https://towardsdatascience.com/how-to-get-started-with-social-network-analysis-6d527685d374
• https://www.sciencedirect.com/science/article/pii/S2212017315001528
• https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-020-01119-3
• https://www.cgi.com/sites/default/files/white-papers/Implementing-social-network-analysis-for-fraud-prevention.pdf
• https://www.mphasis.com/content/dam/mphasis-com/global/en/nextlabs/resources/home/whitepapers/Social-Network-Analytics-for-Fraud-Detection.pdf

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Home > Books > Social Media and Journalism - Trends, Connections, Implications

Evolving Networks and Social Network Analysis Methods and Techniques

Reviewed: 22 May 2018 Published: 31 October 2018

DOI: 10.5772/intechopen.79041

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Evolving networks by definition are networks that change as a function of time. They are a natural extension of network science since almost all real-world networks evolve over time, either by adding or by removing nodes or links over time: elementary actor-level network measures like network centrality change as a function of time, popularity and influence of individuals grow or fade depending on processes, and events occur in networks during time intervals. Other problems such as network-level statistics computation, link prediction, community detection, and visualization gain additional research importance when applied to dynamic online social networks (OSNs). Due to their temporal dimension, rapid growth of users, velocity of changes in networks, and amount of data that these OSNs generate, effective and efficient methods and techniques for small static networks are now required to scale and deal with the temporal dimension in case of streaming settings. This chapter reviews the state of the art in selected aspects of evolving social networks presenting open research challenges related to OSNs. The challenges suggest that significant further research is required in evolving social networks, i.e., existent methods, techniques, and algorithms must be rethought and designed toward incremental and dynamic versions that allow the efficient analysis of evolving networks.

• evolving networks
• social network analysis

Author Information

Mário cordeiro *.

• Faculty of Engineering, University of Porto, Portugal

Rui P. Sarmento

Pavel brazdil.

• INESC TEC–LIAAD, Portugal

*Address all correspondence to: [email protected]

1. Introduction

One of the consequences of today’s information society is the rise of the digital network society [ 1 ]. Organizations and individuals are increasingly connected through a wide range of online and offline networks at different relational levels: social, professional, interaction, information flow, etc. The analysis and modeling of networks and also networked dynamical systems have been the subject of considerable interdisciplinary interest covering a wide range of areas from physics, mathematics, computer science, biology, economics and sociology, in the so-called “new” science of networks [ 2 ]. According to [ 3 ], media organizations, media content and audiences are no exception: news articles have hyperlinks to link other content; news organizations disseminate news via online social network (OSN) platforms like Twitter and Facebook; and users comment, share and react directly below online news. At the level of news events, recent observation proves that some events and news emerge and spread first using those media channels rather than other traditional media like the online news sites, blogs or even television and radio breaking news [ 4 , 5 ]. Natural disasters, celebrity news, products announcements or mainstream event coverage show that people increasingly make use of those tools to be informed, discuss and exchange information [ 6 ]. Concerning the novelty and timely dissemination of news events, empirical studies show that the online social networking services like Twitter are often the first mediums to break critical natural events such as earthquakes often in a matter of seconds after they occur [ 4 , 5 ]. Herewith, social networks’ temporal dimension of information is of crucial importance and follows a time decay pattern, that is, posted messages in social media are exchanged, forwarded or commented in early stages and decrease in importance as time passes. The importance of information contained in those messages has their importance peak right after being posted or in the following hours or days [ 7 ]. Besides, the timing of many human activities, ranging from communication to entertainment and work patterns is characterized by bursts of rapidly occurring events separated by long periods of inactivity, following non-Poisson statistics [ 8 ]. The nature of the time decay pattern communication, bursts or peaks, and inactivity periods, enforces the importance of dynamic network analysis methods and techniques in a network analysis context as the best approaches to model these problems.

1.1. Solving problems with evolving networks

Typical tasks of social network analysis involve the identification of the most influential, prestigious or central actors, using statistical measures; the identification of hubs and authorities, using link analysis algorithms; the discovery of communities, using community detection techniques; the visualization the interactions between actors; or spreading of information. These tasks are instrumental in the process of extracting knowledge from networks and consequently in the process of problem-solving with network data. Specifically, in the areas of journalism and investigation the following topics have been discussed actively in the last years: Criminological research. In 2001, according to [ 9 ], social network analysis has the genuine potential to uncover the complexities of criminal networks. Ref. [ 10 ] introduced the intersection of terrorism studies and what was called the “networked criminology”. In 2011, [ 9 ] concluded that the applications of social network analysis in criminology were still insufficient when compared to other research areas like sociology and public health [ 11 ]. Nevertheless, since then, social network analysis has become one of the major tools for criminal analysis with [ 12 ] identifying the three main areas of analysis and applications of social networks in criminological research. Other topics include the influence of personal networks on crime and, more generally, on delinquent behavior [ 13 , 11 ]; the analysis of neighborhood networks and their influence on crime [ 12 ]; and exploration and modeling of the organization of crime, that is, street gangs, terrorist groups and organized crime groups [ 12 ]. Concrete examples of criminological research using social network analysis are the Enron company dataset [ 14 ]; the Panama Papers analysis in connection with the economic network analysis of Portuguese companies; individuals with connections to offshore companies [ 15 ]; and the analysis of terrorist networks [ 16 , 17 ]. Gill and Malamud [ 18 ] presented a broad overview, characterization and visualization of the interaction relationships between natural hazards using social network analysis. In addition to the previous contributions, essential and recent work regarding social network analysis and terrorism were published by Malm et al. [ 19 ], while Berlusconi [ 20 ] devoted an entire book to social network analysis and crime prevention. Research on journalism: Fu [ 21 ] presented an essay with the purpose of promoting social network analysis in the study of journalism. Starting with a communication network taxonomy [ 22 , 23 ], their focus was on network relations in the study of journalism. The proposed framework presents the four types of communication relations that characterize different networked journalism phenomena [ 23 ]: Affinity relations describes the socially constructed relationships between two actors, such as alliances and friendships, with the valence of the relation being either positive or negative; flow relations refers to the exchange and transmission of data, resources and information; representational relations focuses on the symbolic affiliation between two entities; and semantic networks describes the associations, or semantic relations, among concepts, words or people’s cognitive interpretations toward some shared objects in the network, aiming to build a knowledge base. Another relevant journalism research example is Ref. [ 24 ] that examines the temporal dynamics of reciprocity in the setting of legislative co-sponsorship in the 113th US Congress (2013–2015).

1.2. Related work

In the past years, several overviews of social network analysis can be found in the literature. Ref. [ 25 ] provide a general and succinct overview of the essentials of social network analysis, for static networks, with emphasis on simple statistical measures, link analysis, properties of real-world networks and community detection. Tabassum et al. [ 26 ] in an updated overview of social network analysis, based on Oliveira’s and Gama’s [ 25 ] work, included a full section devoted to evolving networks. Devoted explicitly to evolutionary network analysis, the Aggarwal and Subbian [ 27 ] survey provides an overview of the vast literature on graph evolution analysis. Although the scope of Aggarwal and Subbian [ 27 ] work was graph analysis in general, that is, it did not address specifically the social network analysis problem, many of the mentioned applications and particular contexts of applicability of the methods are social networks. The literature analyzed by Aggarwal and Subbian [ 27 ] covered both snapshot-based and streaming methods and algorithms, and critical applications of evolutionary network analysis on different domains such as the world wide web, telecommunication and communication networks, recommendation networks and social network events, among others, were given. Spiliopoulou [ 28 ] said that the advances on evolution is social networks into a common framework to model a network across the time axis and identified the four dimensions associated with knowledge discovery in social networks: dealing with time, objective of study, definition of community, and evolution as an objective versus assumption. Spiliopoulou [ 28 ] enumerated the several challenges of the social network streams although this problem is generally conceived as a stream problem. An exciting application of temporal network theory and temporal networks to functional brain connectivity was presented by Thompson et al. [ 29 ]; in his work, the theory and methods that introduce the reader on how to add the temporal dimension to network analysis and precisely how many of well-known methods can be transposed from static networks to temporal networks were presented. Thompson et al. [ 29 ] included a complete list of network measures adapted or proposed for temporal networks.

2. Representation of social networks

A social network is a social structure consisting of a finite set of social actors, such as individuals or organizations, connected by interpersonal relationships. These relationships, also known as ties, can be of personal or professional nature and can range from casual friends, acquaintances or co-workers to the close family bonds. Besides the relations, social networks often represent flow of information, interactions and similarities, among the set of social actors. Social network analysis is the investigation of the relationship between actors. In network terminology, vertices—also known as nodes—refer to actors or subjects. Edges, also known as links or ties, describe the relationship between actors. Usually, this social structure, or network structure, is represented by graphs which are mathematical structures used to model pair-wise relations between objects. A graph in this context is made up of vertices, nodes or points which are connected by edges, arcs or lines. Therefore, a social network is a graph G composed of two fundamental components: a nonempty set of vertices V and a set of edges E . Formally it can be defined as G = V E . Vertices represent objects, states, positions, placeholders and are represented by a set of unique vertices. No two vertices represent the same object or state where V can be represented by v 1 v 2 v 3 … v n . For each graph edge e ∈ E , there is associated a pair of graph vertices u , v . Mathematically this can be formulated as ∀ e ∈ E e → u v where u , v ∈ V . Edges can be directed or undirected and can be weighted (or labeled) or unweighted. An undirected edge e = v i v j , with v i , v j ∈ V , indicates that the relationship or connection is bi-directional, that is, can go from v i to v j and vice versa. A directed edge e = v i v j specifies a one-directional relationship or connection, that is, can only go from v i to v j ; this means that v i v j ≠ v j v i . The total number of vertices n of graph G , mathematically ∣ V ∣ = n , is called the graph order . The total number of edges ∣ E ∣ = m is known as the size of the graph G . The maximum number of edges in a undirected graph is m max = n n − 1 2 , while for the directed ones, it is m max = n n − 1 . The representation of graphs is done via two distinct types of graph-theoretic data structures: list structures and matrix structures . List structures, such as incidence lists and adjacency lists, reduce the required storage space for sparse graphs. Matrix structures such as incidence matrices, adjacency matrices, sociomatrices, Laplacian matrices and distance matrices are appropriated to represent the full matrices with dimension n × n , where n is the total number of vertices of the graph. Figure 1 shows several types of graphs that can be used to model different kinds of social networks. The classification of graphs is done according to the direction of their links and according to the values assigned to each link. Graphs whose edges, or arcs, connect unordered pairs of vertices or, in other words, each edge of the graph that connects simultaneously two vertices in both directions are called undirected graphs or undirected networks. On the other hand, graphs whose all edges, or arcs, have an orientation assigned are called directed graphs or directed networks. Formally, a directed graph D is an ordered pair V A consisting of a nonempty set, V , of vertices, and a set A of arcs. These arcs are disjoint from V . If e 12 is an arc and v 1 and v 2 are vertices such that e 12 = v 1 v 2 then e 12 is said to join v 1 and v 2 , v 1 being called the initial vertex and v 2 called the terminal vertex . Depending on the presence of values assigned to the edges or arcs, the distinction between unweighted or weighted graphs or networks is made. Unweighted graphs or networks are binary by definition. This means that it is only represented by the presence or non-presence of an edge or arc between two vertices. Unless it is explicitly said, we always assume that graphs are unweighted. In weighted graphs, each edge has associated a weight w ∈ R 0 + providing more information about the relation between the two vertices (i.e., the strength of the relation). If e 12 is an arc between the two vertices v 1 and v 2 , w 12 defines the strength of the connection. For undirected and unweighted graphs, adjacency matrices are binary as a consequence of being unweighted and symmetric as a consequence of being undirected. The edge between vertices v 1 and v 2 is the same, e ij = e ji , with w ij = w ji = 1 . The absence of edges between vertices v k and v l is represented by w kl = w lk = 0 . For directed and weighted graphs, the matrices are nonsymmetric and values from the interval are thus: 0 max w .

(a) Types of edge graphs and their representation according to an adjacency matrix (b) or an adjacency list (c).

3. From static to evolving networks

Previously, the network types and their representations in a static context were described. In real life, however, many networks are dynamic. As time passes by, new nodes are added to the network, existing ones are removed and edges come and go too. Static networks lack one of the most critical dimensions, that is, the temporal dimension of a network. So by definition static networks are assumed not to change or evolve over time, ignoring the temporal dimension. In this section, we cope with the representation of evolving networks . Evolving networks arise in a wide variety of application domains such as the web, social networks and communication networks. In recent years the interest in the area of dynamic social networks leads to new research and the need of analysis of evolving networks. The evolution analysis in graphs has applications in a number of scenarios like trend analysis in social networks and dynamic link prediction—to mention two typical examples. Figure 2 shows the example of a contact evolving network with instantaneous interactions between vertices. When the interaction between network peers has a time duration, we are in the presence of interval evolving networks as shown in Figure 3(b) . Assuming that the time T during which a network is observed is finite we can consider the start point as t start = 0 and the end time as t end = T . A dynamic network graph G 0 , T D V E 0 , T on a time interval [ 0 , T [ consists of a set of vertices or nodes V and a set of temporal edges E 0 , T . The evolving network is a set of graphs across the time axis within discrete time points t 1 , t 2 , … , t n − 1 , t n . At time point t n a graph instance G V n E n is observed also denoted as G n where E n is the set of temporal edges; u v t n ∈ E 0 , T at time point t n with edges between vertices u and v on time interval as t n = t n begin t n end such that t n begin ≤ T and t n end ≥ t n begin ≥ 0 . Examples of network changes that may occur between two time points t n − 1 and t n are the addition of new edges, that is, E n ⊃ E n − 1 , and the appearance of additional nodes, that is, V n ⊃ V n − 1 .

Example of contact evolving network: (a) shows a labeled aggregate network where the labels denote the times of contact, and (b) shows a time-line plot, where each of the lines corresponds to one vertex and time runs from left to right.

Example of interval evolving network: (a) shows the labeled aggregate network where the labels denote the time interval of the relation, and (b) shows a time-line plot, where each of the lines corresponds to one vertex and gray zones the time duration between two edges.

3.1. Models of temporal representation

Several models for representing evolving networks are available in the literature. Kim and Anderson [ 30 ] introduced the concept of a time-ordered graph , and Thompson et al. [ 29 ] with a similar conceptual representation chose the time graphlet to represent time-varying graphs. Casteigts et al. [ 31 ] presented the time-varying graph formalism (TVG) with the concept of a journey to catch the temporal information on graphs. Santoro et al. [ 32 ] used this formalism to describe several network measures. Although there are differences in the representation and nomenclature, these models are conceptually equal. Figure 4 presents the concept of a time-ordered graph for an example network for the time interval 0 3 . Figure 4(a) shows all the time intervals aggregated into a single graph G 1 , 3 . The discretization of the network by converting the temporal information into a sequence of n snapshots is presented in Figure 4(b) . In this example the evolving network is represented as a series of static networks G 1 , G 2 , … , G n . The time-ordered graph G = V E of Figure 4(c) assumes that at each time step, a message can be delivered along a single edge. It is an asymmetric directed graph with a vertex v t for each v ∈ V and for each t ∈ 0 1 … n for each edge u v ∈ G t ; it has a directed edge from u t − 1 to v and vice versa. Although it was not represented in the figure, the time-ordered graph also has edges from v t − 1 to v t for all v ∈ V for all t ∈ 1 … n . The time-ordered graph G = V E constructed from n static networks of a dynamic network G i , j D = V E i , j is a powerful tool to define network metrics and capture their temporal characteristics. In the example of Figure 4(c) , the temporal shortest path from node u = A to node v = B is shown. The temporal shortest path from A to B in the interval 0 3 is A 0 → A 1 → D 2 → B 3 . The time-ordered graph of Kim and Anderson [ 30 ] will be the model used during the course of the rest of the document.

Comparison of aggregated representation (a) and time series representation (b). The corresponding time ordered (c) graph G is presented for the interval 0 3 .

3.2. Timescale of evolving networks

Regarding the evolution of the networks, not all networks evolve equally. Some networks evolve faster than others or have edges that are being added at different rates. Two distinct timescale examples of networks are email networks, where edges are added at the timescale of seconds, and bibliographic networks, where edges are added at the scale of weeks or months. Different time-evolving scenarios require different types of analysis [ 27 ]. Slowly evolving networks : When networks evolve slowly over time, snapshot analysis can be used very effectively. In this case, dynamic networks are discretized in time by converting temporal information into a sequence of n static snapshots. All the analysis can be done in each snapshot of the network at different times t 1 , t 2 , … , t n using static analysis methods. Usually, in slowly evolving networks, a discretization of the time axis into intervals of equal length occurs. For a time discretization in years, days or seconds, a time window size w for each snapshot are set to T / n with n being the number of snapshots. Another solution consists of record buckets of equal size for numerical discretization—a window size w , in this case, is set to a given number of network updates. In both cases the dynamic network can be represented as a series of static graphs G 1 , G 2 , … , G n with 0 ≤ n ≤ t n . A time point t n is the moment where the network suffers a set of changes in the network represented by the addition or removal of sets of edges ( + e 1 + e 2 − e 3 − e 4 … + / − e n ) and/or appearance or disappearance of vertices ( + v 1 + v 2 − v 3 − v 4 … + / − v n ). Signs + and − represent the additions or removals, respectively. Streaming networks : When networks are built by a never-ending flow of transient interactions, such as email or telecommunications networks, they should be modeled and represented as graph streams. Graph streams typically require real-time analytical methods. The scenario of graph streams is more challenging because of the computational requirements and the inability to hold complete graphs on memory or disc. Velocity is also an issue because common methods require dealing with graph updates at very high edge rates. Time point t i is the moment in which a single change in the network occurs. Guha et al. [ 33 ] defined this to be the stream model of computation with a stream being a sequence of records x 1 , x 2 , … , x n arriving in increasing order of the index i , where x i may be a new vertex v i or a new edge e i .

3.3. Landmark versus sliding windows

When the temporal dimension is added to the analysis of networks, different methodologies regarding the strategy to cope with data that is being analyzed vary. Figure 5  shows three types of graph data windowing strategies. Landmark windows by Gehrke et al. [ 34 ] encompass all the data from a specific point in time up to the current moment. In the landmark window, the model is initialized in a fixed time point, the so-called landmark that marks the beginning of the window. In successive snapshots, the data window grows to consider all the data seen so far after the landmark. Sliding windows are better suitable when we are not interested in computing statistics over all events of the past but only over the recent past [ 35 ]. Datar et al. [ 36 ] incorporate a forgetting mechanism by keeping only the latest information inside the window and disregarding all the data falling outside the window. Usually, the sliding windows are of fixed size. The time-based length sets the window length as a fixed time span. Sliding windows can be overlapping and non-overlapping depending on whether two consecutive windows share some data between them or not. From the several window models presented in the literature [ 37 , 38 ], two basic types of sliding windows are commonly defined: sequence-based models, where the size of the window is determined regarding the number of observations, and timestamp-based models where the size of the window is defined concerning duration. A timestamp window of size t consists of all elements whose timestamp is within a time interval t of the current period.

Types of data windows: Landmark window (a) non-overlapping sliding window (b) and overlapping sliding window (c).

3.4. Types of evolving network analysis

Depending on the timescale of the network and the chosen strategy to cope with network data, distinct evolving network analysis methods are available. These methods are divided into one of the following categories [ 27 ]. Maintenance methods : In these methods it is desirable to maintain the results of the data mining process continuously over time. Examples of maintenance methods are classification and clustering. Analytical evolution methods : In this case it is desirable to directly quantify and understand the changes that have occurred in the underlying network. Such models are focused on modeling change. Bridge methods : From a methodological point of view, and in the context of a few key problems, an overlapping of maintenance and analytical evolution methods occurs. These bridge methods, such as community detection, fall into both categories.

4. Elementary network measures

In this section, elementary network measures and popular metric used in the analysis of social networks are presented.

4.1. Actor-level statistical measures

Actor-level or node-level statistical measures determine the importance of an actor or node within the network. These measures reveal the individuals in which the most important relationships are concentrated and give an idea about their social power within their peers.

4.1.1. Degree or valency

D v = ∑ u = 1 n a u , v , 0 < D v < n E1 D v = ∣ N v ∣ , 0 < D v < n E2

The degree of valency of a node v is usually denoted as D v and measures the involvement of the node in the network. It is computed as the number of edges incident on a given node or as the number of neighbors of node v . The neighborhood N v is defined as the set of nodes directly connected to v . The degree is an effective measure to access the importance and influence of an actor in a network despite some of its drawbacks like not taking into consideration the global structure of the network. In static networks, the degree can be computed via the adjacency matrix by (1) or using the neighborhood of a node (2) . Depending on the type of the networks different degree calculation methods should be made for directed and undirected networks and weighted and unweighted networks.

For dynamic networks, and generalizing to a directed and unweighted network, the temporal degree D i , j v is the total number of inbound edges and outbound edges from a node v ∈ V on a time interval i j where 0 ≤ i < j ≤ n . If we disregard the self-edges from v t − 1 to v t for all t ∈ i + 1 … j , D i , j v is equal to ∑ t = i j 2 . D t v where D t v is the degree of v in G t (i.e., the dynamic graph at time t ). For directed networks, there are two variants of degree centrality: considering in degree , denoted by D i , j + v , (3) is the number of incoming edges to node v or edges that end at v and considering out degree , denoted by D i , j − v , (4) is the number of outgoing edges from node v or edges that start at v . For weighted networks, strength is the equivalent to degree but is computed as the sum of the weights of the edges adjacent to a given node (5) .

4.1.2. Betweenness

Node betweenness B v measures the extent to which a node lies between the other nodes in the network. For static networks, (6) is used, where σ sd denotes the number of shortest paths between vertices s and d (usually σ sd = 1 ) and σ sd ν expresses the number of shortest paths passing through node ν . Nodes with high betweenness occupy critical roles in the network structure once their position allows them to work as an interface between different regions of the network. The temporal betweenness B i , j v (7) for a node v ∈ V on a time interval i j where 0 ≤ i < j ≤ n is the sum of the proportion between all the temporal shortest paths passing by the vertex v and the total number of temporal shortest paths passing over all pairs of nodes in each time interval t j : i < t ≤ j . The temporal betweenness for node v is given by (7) . Examples of betweenness algorithms are the Brandes algorithm [ 39 ], the incremental algorithm proposed by Nasre et al. [ 40 ] and the algorithm proposed by Kas et al. [ 41 ] for evolving graphs.

4.1.3. Closeness

Closeness measures the overall position of an actor in the network giving an idea of how long it will take, on average, to reach other nodes from a given starting node. It is represented by the average length of the shortest path between the node and all other nodes in the graph. Thus more central a node is, the closer it is to all other nodes. In general, it is only computed for nodes within the largest component of the network as shown in (8) . The temporal closeness is defined by considering m intervals t j : i < t ≤ j where m = j − i by varying the start time t of each time interval from i to j − 1 instead of one time interval i j with the starting time as i . Formally the temporal closeness for a node v is given by (9) where Δ t , j u v is the temporal shortest path distance from u to v on a time interval t j . If there is no temporal path from v to u on a time interval t j , Δ t , j u v is defined as ∞ . Since the time-ordered graph G is a directed graph, Δ t , j u v is different from Δ t , j v u . Regarding the update of closeness centrality in evolving graphs, it was worked on by Kas et al. [ 42 ] and Sariyuce et al. [ 43 ]. Kas et al. [ 42 ] developed incremental closeness centrality algorithms for dynamic networks. An extension of the Ramalingam and Reps [ 44 ] algorithm computes the closeness values incrementally, using all-pairs shortest paths for streaming, dynamically changing social networks.

4.1.4. Eigenvector centrality

For a given graph G = V E with ∣ V ∣ vertices, let A = a v , t be the adjacency matrix of an unweighted network, that is, a v , t = 1 if vertex v is linked to vertex t , and a v , t = 0 otherwise. The relative centrality score of vertex v can be defined by (10) , where M v is a set of the neighbors of v and λ is a constant. This definition can be rewritten in vector notation as the eigenvector equation using small arrangements is shown in (11) . The classical eigenvector centrality had improvements or variants developed to approach the evolving graphs’ problem. Examples are Google’s PageRank [ 45 ] and Katz centrality [ 46 ] as the possible variants of this measure as proposed by Society [ 47 ]. The concrete implementation of PageRank variants to evolving networks was developed by several researchers, for example, by Bahmani et al. [ 48 ], Desikan et al. [ 49 ] and Kim and Choi [ 50 ]. These improvements over the original PageRank measure show significantly faster results when compared with the original PageRank that, for being an iterative process, did not scale well to large-scale graphs. This algorithm will be discussed in detail in Section 5.1.

4.1.5. Laplacian centrality

The Laplacian centrality permits to consider intermediate environmental information around a vertex or node to compute its centrality measure. The centrality of some vertex v is then characterized as a function of the number of 2-walks that vertex v takes part in the network. To estimate the centrality of a vertex, we need to reflect not only the first-order connections but also the importance of their neighbors. These results and related calculations describe the so-called Laplacian energy of the network. Therefore this strategy is known as the Laplacian centrality. The Laplacian energy E L G for a weighted network G = V E W with n vertices and λ 1 , λ 2 , … , λ n eigenvalues of its Laplacian matrix is defined by (12) . Considering that x 1 , x 2 , … , x n are the vertex sum weights calculated by x i = ∑ j = 1 n w i , j where w i , j is the weight of the edge from vertex i to j , the Laplacian energy E L G can be computed by (13) . The motivation for the incremental Laplacian centrality is supported by the fact that it is known to be a local measure [ 17 , 51 ].

4.1.5.1. Locality of the Laplacian centrality

The Laplacian centrality metric is not a global measure, that is, it is a function of the local degree plus the degrees of the neighbors (with different weights for each). Qi et al. [ 17 , 51 ] show that local degree and the 1-order neighbors’ degree are all that are needed to calculate the metric for unweighted networks ( Figure 6 ).

Calculated node centralities with edge {(4, 6)} added. Dark gray nodes affected by addition of edges. Light gray nodes centralities need to be calculated due to their neighborhood with affected nodes.

4.1.5.2. Dynamic Laplace centrality

Regarding the original Laplace centrality algorithm proposed by Qi et al. [ 51 ], despite being a static algorithm, it can be used to calculate centralities in changing networks. This is true by considering full calculations of the centralities for each network snapshot. In Sarmento et al. [ 52 ] proposal, Qi et al. [ 51 ] principles were adapted and resulted in two incremental algorithms. The incremental Laplace algorithm by Sarmento et al. [ 52 ] presents better computational efficiency, by performing careful Laplace centrality calculations only for the nodes affected by the addition and removal of edges in each one of the snapshots. Thus, it reuses information of the previous snapshot to perform the Laplace centrality calculations on the current snapshot, for unweighted networks only.

4.2. Network-level statistical measures

Before describing network-level statistical measures, it is important to describe three fundamental concepts that are common to static and dynamic networks. Path represents a sequence of nodes in which consecutive pairs of non-repeating nodes are linked by an edge. When adding the temporal dimension of dynamic networks, the concept of path slightly changes, because non-repeating nodes are now considered only within the same snapshot or time step in what is called a temporal path. Temporal paths can have repeating nodes in different time steps, for example, A 0 → B 0 → C 1 → B 1 → A 2 . Geodesic distance , or the shortest path, between nodes u and v is denoted as δ u v and defines the length of the shortest path, or minimal path, between nodes u and v in a static graph. For a given time-ordered graph G , a temporal path from node u to node v on time interval i j where i ≤ i < j ≤ n is defined as any path, p = < u i , … , v i > where i < k ≤ j , having the path length ∣ p ∣ = min i < l ≤ j δ u i v l . δ u v is the shortest path distance, in a static graph, from u to v . The temporal shortest path from node u to node v is defined as the temporal path connecting u to v which has minimum temporal length. In Figure 4 , an example of a temporal shortest path in a time-ordered graph was shown. Eccentricity is the greatest geodesic distance between a given vertex v and any other in the graph, that is, ε v = min i ∈ V G \ v d v i .

4.2.1. Edge bursts

A hallmark of a bursty edge is the presence of multiple edges with short interconnect times, followed by longer and varying interconnect times [ 29 ]. One of the methods available to quantify bursts is the burstiness coefficient B . Presented by Goh and Barabasi [ 53 ], it can be formulated for discrete graphs [ 54 ] where bursts are computed by edges using (14) , with τ ij being a vector of the intercontact times between nodes i and j though time, σ τ is the standard deviation and σ μ is the mean. For temporal connectivity being considered as bursty, that is, B > 0 , it occurs when the standard deviation σ τ is greater than the mean σ μ .

4.2.2. Fluctuability

As discussed before, centrality measures provide information about the degree of temporal connectivity while bursts describe the distribution of the temporal patterns of connectivity at the node level. Also, fluctuability can be used to retrieve information about the global state of a temporal network, in this case, the quantification of the temporal variability of connectivity [ 29 ]. The fluctuability F , as shown in (15) , is the ratio of the number of edges present in A over the sum of A t , with U being a function of the binary output: U A i , j is set to 1 if at least one of the edges occurs between nodes i and j across time t = 1 , 2 , … , T and 0 if not. T is the number of time points. The maximum value of F is 1 and occurs only when every edge is unique and occurs only once. The definition of fluctuability F i N at the node level, when U A i , j > 0 , is defined using (16) ; when U A i , j = 0 , F i N is equal to 0 ( Figure 7 ).

Variation of Fluctuability and volatility measures over three different evolving contact networks.

4.2.3. Volatility

The volatility V is a global measure of temporal order that represents how much, on an average, the connectivity between consecutive temporal time-ordered graphs changes [ 29 ]. This measure indicates how volatile the temporal network is over time and is computed by (17) , where D is a distance function and T is the total number of time points. The distance function quantifies the difference between the temporal time-ordered graph G t and the temporal time-ordered graph G t + 1 . One example of a distance function for volatility can be the Hamming distance. Volatility can be defined at the local level, for example, a per-edge volatility can be computed using (18) . An estimate of the volatility centrality of node i can be computed by taking the mean V i , j L over j ( Figure 7 ).

4.2.4. Reachability latency

Reachability measures, like reachability ratio and reachability time , focus on estimating the time taken to reach the nodes in a temporal network [ 55 ]. While the reachability ratio is the percentage of edges that have a temporal path connecting them, the reachability time is defined as the average length of all temporal paths. When applying these reachability measures to most real-world networks, if we consider a sufficient time interval, any vertex or node of the networks can reach all the others within that time span. With this assumption in mind, Thompson et al. [ 29 ] defined the reachability latency , which quantifies the average time it takes for a temporal network to reach an a-priori-defined reachability ratio as defined in (19) , where d i t is an ordered vector of length N of the shortest temporal paths for node i at time point t . Value k represents the rN th element in the vector. In case r = 1 , that is, all nodes are reachable, the former formula can be simplified to (20) , which is also known as the temporal diameter of the network [ 56 ].

4.2.5. Temporal efficiency

For static networks, efficiency is computed as the inverse of the average shortest path for all nodes [ 29 ]. Temporal efficiency , at first, is calculated at each time point as the inverse of the average shortest path length of all nodes; subsequently, these values are averaged across time points to obtain an estimate of global temporal efficiency as shown in (21) .

4.2.6. Diameter and radius

The diameter D is given by the maximum eccentricity of a set of vertices D = max ε v : v ∈ V and, analogously, the radius R is defined as the minimum eccentricity of the set of vertices R = min ε v : v ∈ V .

4.2.7. Average geodesic distance

The average geodesic distance L gives an idea on how far apart nodes will be, on average. For static networks, all combinations of vertex pairs in a network are computed as in (22) , where δ u v is the geodesic distance between nodes u and v and 1 2 n n − 1 is the number of possible edges in a network of n nodes. Tang et al. [ 57 , 58 ] defined the characteristic temporal path length as the natural extension of the average geodesic distance to time-varying graphs. It is defined as the average temporal distance over all pairs of nodes in the graph as shown in (23) , with the temporal distance d u , v between u and v as the temporal length of the temporal shortest path from u to v .

4.2.8. Average degree

The average degree is the mean of the edges of all vertices in a network for all time steps t , with a t being the adjacency matrix at time t , as shown in (24) .

4.2.9. Reciprocity

For static networks, reciprocity r is a specific quantity of directed networks that measures the tendency of pairs of nodes to form mutual connections between each other. The value of reciprocity represents the probability that two nodes in a directed network point to each other. For each of the n n − 1 / 2 dyads in the network are assigned to one of the three types: mutual, that is, node i has a tie to node j and node j has a tie to i ; asymmetric, that is, either i has a tie to j or j has a tie to i but not both; or null, that is, neither the i to j tie nor the j to i tie is present [ 59 ]. Given this, reciprocity can be computed using (25) , where # mutual denotes the number of mutual dyads and # asymmetric the number of asymmetric dyads. In an undirected network, reciprocity is always maximum ( r = 1 ) because all pairs of nodes are symmetric, that is, dyads are of the type mutual. Brandenberger [ 24 ] analyzed the temporal dynamics of reciprocity in congressional collaborations using relational event models.

4.2.10. Density

Density ρ explain the general level of connectedness of a network. It is computed by measuring the proportion of edges in the network relative to the maximum possible number of edges as seen in (26) , where m G is the total number of edges of network G and m max G the number of possible edges of network G , which is n n − 1 2 for undirected networks and n n − 1 for directed ones.

4.2.11. Global clustering coefficient

Cui et al. [ 60 ] propose two definitions of the temporal clustering coefficient of a temporal network. The definitions are temporal-delayed clustering coefficient and the temporal-weighted clustering coefficient.

5. Link analysis

In network theory, link analysis is a data analysis technique used to evaluate relationships (connections) between nodes. Link analysis has been used for the investigation of fraud detection, terrorist networks, computer security analysis, search engine optimization (SEO), market research and medical research, among others. To find the most valuable, authoritative or influential node or the list of nodes in networks, link analysis algorithm were devised to solve this problem in the past. By exploring the relationship between links and the content of web pages, the PageRank algorithm [ 45 ] is one of the seminal methods employed to the build of modern and efficient search engines and the information retrieval system in the web.

5.1. Incremental PageRank algorithm

There have been several attempts to improve the original PageRank algorithm [ 45 ]. The purpose of several of these improvements was to adapt this algorithm for streaming data. In the original algorithm, each page rank is dependent of the ranks of the pages pointing to it. The PageRank value of a page p is mathematically written as:

where n is the number of vertices/pages in the graph and OutDegree q is the number of hyperlinks on the node/page q . Eq. (27) illustrates an example of computing PageRank of a page P from the pages ( Figure 8(a) ) P 1 , P 2 and P 3 pointing to it using (28) :

PageRank and graph partitioning used in Desikan et al. [ 49 ] incremental page rank.

Desikan et al. [ 49 ] provided a solution for the update of nodes’ PageRank values in evolving graphs in an incremental fashion. The algorithm explores the fact that the web evolves incrementally and with small changes between updates. Figure 8(b) shows the two partitions created; one of them, partition P, is unchanged since the last computation, and it has only outgoing edges to the other partition. The other partition, partition Q, is the rest of the graph, which has changed since the last time the metric was computed. The principal idea is to find a partition P in a way that there are no incoming links in the graph from the other partition Q (includes all changed nodes). Then the computation of the PageRank of partition Q can be done separately, scaled and merged with the rest of the graph to get the updated PageRank values of the vertices in this partition. The PageRank of partition Q is computed, taking the border vertices that belong to partition P and have edges pointing to the vertices in partition Q. The PageRank values of partition P are obtained by simple scaling, due to the addition of new nodes. Let the graph of Figure 8(b) at the new time be G V E : V b is the vertex on the border of the left partition (only outgoing edges to the right partition); V ul , vertex on the left partition remains unchanged; V ur , vertex on the right partition remains unchanged but whose PageRank is affected by vertices in the changed component; V cr is the vertex on the right partition which has changed, or there has been a new addition. Desikan et al. [ 61 ] proposed a divide and conquer approach for efficient PageRank computation based on these assumptions. Other page rank analysis algorithms, in which it is desirable to estimate the page rank on a dynamic evolving graph stream, are available in [ 62 , 63 ]. Sarma et al. [ 62 ] developed a method that can estimate the page rank distribution, the mixing time and the conductance of the graph. Bahmani et al. [ 63 ] developed a method for real-time estimation of the personalized page rank in graph streams. Zhang et al. [ 64 ] proposed a method for an approximate personalized PageRank on dynamic graphs. The update of PageRank node values in dynamic graph streams has been extensively used to leverage the efficiency of large-scale link analysis, inclusively with applications that have known issues with scalability like, for example, text streams [ 65 ].

5.2. Link prediction

To understand the association between two specific nodes, researchers commonly study the dynamics of evolving graphs. In link prediction, the problem we wish to solve is the prediction of the likelihood of a future association between two nodes, knowing that there is no association yet between the nodes, that is, no edge between the nodes. Link prediction is used in bioinformatics, where potential protein connections are inferred from known connections, and during the research of terrorist/criminal networks, where potential criminal connections are inferred from current knowledge of the relationships between criminals. Link prediction is a complex problem. For a social network G V E , there are n 2 − m possible edges to infer from our current graph. This is true if we randomly select a non-existing edge. If G is sparse, then m ≋ n . Thus, in limit situations, with a high amount of nodes, we have a n 2 edges to choose from, and the probability of inferring correctly at random is 1 / n 2 . Commonly, social networks derived from real-world phenomena are sparse, so inferring random edges is expected to have low accuracy. As networks evolve, it is expected that nodes are added to the network, and the number of possible links grows quadratically while it is expected that new edges grow in a linear fashion with added new nodes. Thus, it is a problem that gets worse in evolving networks as time goes forward.

5.2.1. Common neighbors

Newman has verified a significant correlation between the number of common neighbors of u and v at time t , and there is the probability that u and v will connect or collaborate at sometime after t [ 66 ]. The common-neighbors predictor concept is based on the assumption that two—not yet connected—nodes with common neighbors will get connected sometime in the future. This introduction between unconnected nodes means the effect of “closing the triangle”.

5.2.2. Jaccard coefficient

The Jaccard coefficient is a common metric in measuring the similarity between different samples. It is used throughout validation tasks in information retrieval research. It measures the probability that both u and v have a feature f , for a randomly selected feature f that either u or v has.

where N u is the list of neighbors of u , and N v is the list of neighbors of v . Thus, in (29) , the numerator is the number of common neighbors, and the divisor is the number of unique u and v neighbors.

5.2.3. Adamic/Adar

This measure—also called frequency-weighted common neighbors—refines the simple counting of common features in JC by weighting rarer features more heavily [ 67 ]. The Adamic/Adar predictor is based on the intuitiveness of considering unusual features more critical in predicting future outcomes. In this example u and v would have to be introduced by a common friend z , person z will have to choose to introduce the pair ( u , v ) from N z pairs of his connections.

5.2.4. Preferential attachment

Another concept, this time with lower complexity, is the preferential attachment [ 68 ]. This metric is only in need of node degree information. The intuitiveness is that those nodes with a higher degree have more probability to connect to each other than with a neighbor with a lower degree.

5.2.5. Katz

The Katz concept [ 46 ] is based on the assumption that the closer connected nodes are with a higher number of paths in the network, and these nodes will have more probability of connecting in the future. The concept is also called “exponentially damped path counts”.

where β L is exponentially damped by length ∣ Path u , v L ∣ of the Path , with L being the number of hops between u and v .

5.2.6. Recent developments

Ibrahim and Chen [ 69 ] present a method for link prediction in dynamic networks by integrating temporal information, community structure and node centrality in the network providing greater weights for frequently occurring links. Wahid-Ul-Ashraf et al. [ 70 ] described the parallelism between Newton’s law of universal gravitation and the link prediction tasks. To apply this law, the authors attributed nodes with the notion of mass and distance. Node centrality could be considered as mass, and the authors inclusively tested this concept with degree centrality. The distance between nodes was considered obtainable through several possible methods, that is, by retrieving the shortest path, path count or inverse similarity, by using previously stated measures like Adamic/Adar, Katz score or others. Choudhury and Uddin [ 71 ] considered the evolutionary aspects of community network structure. They build dynamic similarity metrics or dynamic features to measure similarity/proximity between actor pairs.

6. Community detection

As a consequence of both global and local heterogeneity of edge distribution in a graph, specific regions of a graph evidence the high concentration of edges within particular regions, called communities , whereas interregions have low concentrations of edges. In the context of networks, these occurrences of groups of nodes in a network that are more densely connected internally than with the rest of the network are called community structures . Also known as modules or clusters , communities can, therefore, be straightforwardly defined as similar groups of nodes. A complete definition using the concept of density can be the following: communities can be understood as densely connected groups of vertices in the network, with sparser connections between them.

6.1. Finding communities in static networks

Fortunato [ 72 ] has a comprehensive survey about methods and techniques regarding finding communities. Hierarchical clustering methods can be of two types: agglomerative algorithms, in which clusters are iteratively merged if their similarity is sufficiently high, and divisive algorithms, in which clusters are iteratively split by removing edges connecting vertices with low similarity. Divisive algorithms : One of the most known divisive algorithms is the one proposed by Girvan and Newman [ 73 ]. The philosophy of divisive algorithms is the idea that a simple way to identify communities in a graph is to detect the edges that connect vertices of different communities and remove them so that the clusters get disconnected from each other. Agglomerative algorithms : Examples of agglomerative algorithms are the ones that assume that high values of modularity indicate good partitions. So the partition corresponds to maximum value of modularity on a graph. Therefore a modularity measure Q is used to evaluate the quality of the community structure of a graph. Modularity serves as the objective function during the process of calculating the communities [ 74 ]. Modularity Q with higher values means better community structures. Therefore, to obtain a global higher modularity, the objective is to find community assignments for each one of the nodes of the network such that Q is also maximized. A greedy algorithm based on modularity optimization has been introduced by Blondel et al. [ 75 ] where initially all vertices of the graph are put in different communities ( Figure 9(b) ). The first step consists of a sequential sweep over all vertices, for each of the neighbors picks the community that yields the largest increase of modularity ( Figure 9(c) ). At the end of the sweep, one obtains first-level partition. In the second step, communities are replaced by super vertices, and the weight of the edge between the super vertices is the sum of the weights of the edges between the represented communities at the lower level ( Figure 9(d) ). The two steps of the algorithm are then repeated, yielding new hierarchical levels and supergraphs ( Figure 9(f) ).

Example of an agglomerative community detection algorithm. In this case the original Louvain [ 75 ] with all algorithm steps.

6.2. Finding communities in dynamic networks

When discussing methods for finding communities in dynamic networks, the division of methods for slowly evolving networks and streaming networks is consensual [ 27 ]. In the following section, an algorithm for both scenarios will be presented and analyzed.

6.2.1. Slowly evolving networks

When moving from static community detection to dynamic community detection, often, static techniques are used to detect communities in evolving network. The Louvain algorithm by Blondel et al. [ 75 ] is no exception, and it is still one of the fastest ways to perform community detection on evolving networks by considering individual static snapshots. Frequently employed in dynamic network community detection scenarios by performing individual runs of the algorithm in snapshots of the network, this approach is computationally inefficient and does not allow the tracking of communities in a fine-grained way between static snapshots. The community detection work referenced in the Fortunato [ 72 ] survey was later complemented by an incremental community detection algorithm based on modularity and was proposed by Shang et al. [ 76 ]. The algorithm applies the principles of events in the life of communities (growth, contraction, merging, splitting, birth and death) as defined by Palla et al. [ 77 ] and, in each one of the iterations, calculates the modularity gain of affected communities. This allows to detect and track communities over time in incremental networks. This algorithm only considers the addition of new edges and relies on the original two-step approach used in community detection for static communities. The QCA [ 78 ], presented as a fast and adaptive algorithm, provides efficient identification of the community structure of dynamic social networks by allowing the addition and removal of nodes and edges dynamically. The algorithm starts with the initial communities calculated via the Louvain method, and then it applies the adaptive node community changes by considering each node as an autonomous agent demonstrating flocking behavior toward their preferable neighboring groups [ 79 ]. The AFOCS [ 80 ] community detection algorithm for dynamic networks shares the same principles of QCA being only modified in order to allow the possibility of detection of overlapping communities. A detailed comparison between QCA and AFOCS was presented by Nguyen et al. [ 80 ]. Label propagation techniques and specifically speaker-listener label propagation (SLPA) were used in community detection over large networks. LabelRank [ 81 ] and GANXiSw [ 81 , 82 ] used the SLPA technique to perform static network community detection while LabelRankT [ 83 ] was designed to handle dynamic networks. Being designed for overlapping community detection, all of the previous algorithms also work in a non-overlapping mode, with satisfactory performance for low overlapping density networks [ 84 ].

Cordeiro et al. [ 85 ] presented a modularity-based dynamic community detection algorithm. The algorithm is a modification of the original Louvain method where dynamically added and removed nodes and edges only affect their related communities. In each iteration, the algorithm remains unchanged in all the communities that were not affected by modifications to the network. By reusing community structure obtained by previous iterations, the local modularity optimization step operates in smaller networks where only affected communities are disbanded to their origin. The stability of communities is also an improvement over the original algorithm ( Figure 10 ). Given that only parts of the network change during iterations, the non-determinism of the algorithm will have a reduced effect on the community assignment. Most node-community assignments remain unchanged between snapshots, providing better community stability than its counterparts.

Example of Cordeiro et al. [ 85 ] dynamic Louvain for the addition of a cross-community edge (1–4). Top figures show the lower-level network. At the bottom, are shown, the corresponding upper-level network with aggregated communities.

6.2.2. Streaming networks

For the cases when a large number of edges, representing interactions, arrive continuously, in some cases at high or very high rates, and are superposed over much larger networks, streaming graph algorithms should be preferred to perform community detection. In streaming scenarios, the ability to perform the deletion of edges in community detection algorithms is important. In short, as discussed in Section 3.3, this will dictate if the method of analysis is to be performed over the sliding window of edges, and therefore edges are deleted from the tail end of the sliding window, or over a landmark window, in case there is no possibility to delete or forget old edges. Several methods were proposed for dynamic community discovery in graph streams. Wang et al. [ 86 ] motivated by the variability of the underlying social behavior of individuals over different graph regions modeled the problem according to the so-termed local heterogeneity , where a local weighted-edge-based pattern (LWEP) summary is efficiently maintained and used afterward to cluster the graph stream and perform dynamic community detection in weighted graph streams. Taking an almost linear time, Raghavan et al. [ 87 ] investigated a simple label propagation algorithm that uses the network structure alone as its guide and requires neither optimization of a predefined objective function nor prior information about the communities. By analyzing the problem of real-time community detection in large networks and having by baseline the algorithm proposed by Raghavan et al. [ 87 ] with linear time O m on a network with m edge-label propagation, or “epidemic” community detection, Leung et al. [ 88 ] proposed a method with near-linear time community detection in graphs. Leung et al. identified the characteristics and drawbacks of the base [ 87 ] algorithm and extended it by incorporating different heuristics to facilitate reliable and multifunctional real-time community detection. Yun et al. [ 89 ] proposed two efficient streaming memory-limited clustering algorithms for community detection based on spectral methods. Yun and Proutière [ 90 ] proposed community detection via random and adaptive sampling. Sariyuce et al. [ 91 ] proposed SONIC, a find-and-merge type of overlapping community detection algorithm that can efficiently handle streaming updates. Recently, Hollocou et al. [ 92 ] proposed SCoDA, a linear streaming algorithm, for community detection in very large networks.

7. Visualization of evolving networks

The visualization of networks is known to be challenging, and this task gains additional complexity when moving from static to evolving networks. In this section an overview of the methods and techniques is presented, currently used for the visualization of evolving networks.

7.1. Challenges of evolving networks’ visualization

The dynamics of social networks remain a challenge regarding visualization [ 93 ]. Many researchers argue that traditional graph visualization methods have issues when applied to evolving networks. Additionally, the application of conventional node-link methods to large-scale networks provides low-quality cluttered insights. The overlap of nodes in these conditions is not appropriated when trying to extract information from the network. Zaidi et al. [ 94 ] and Aggarwal and Subbian [ 27 ] presented an overview of the different techniques and methods that exist for the analysis and visualization of dynamic networks. It included the discussion of the basic definitions, formal notations and a set of the most important and recent work regarding analysis and the visualization of dynamic networks. While static graph visualizations are often divided into node-link and matrix representations, Beck et al. [ 95 , 96 ] presented a hierarchical taxonomy of dynamic graph visualization techniques. This survey about the state of the art in visualizing dynamic graphs identified the representation of time as the major distinguishing feature for dynamic graph visualizations. Two major visualization categories were found: in one category, graphs are represented as animated diagrams or in a second one, visualizations are a set of static charts based on a timeline. Similar conceptual dynamic network visualization categories were devised by Moody et al. [ 97 ], and the authors divide dynamic network visualizations also called as network movies into static flip books, where the node position remains constant but edges cumulate over time and dynamic movies, where nodes move as a function of changes in relations. The graph animation is often used to lower the cognitive effort required to follow the transition from one visualization to the next, according to Brandes and Corman [ 98 ]. To facilitate the simultaneous analysis of state and change, a layered three-dimensional network visualization was proposed by Brandes and Corman [ 98 ] in which the evolution of the network is unrolled, and each step is represented as a layer. A complex network with a larger number of links may prevent users from recognizing salient structural patterns. To overcome this common problem with visualization, two widely known link reduction algorithms, namely minimum spanning trees (MSTs) and pathfinder networks (PFNETs), were analyzed and compared by Chen and Morris [ 99 ]. Bender-deMoll and McFarland [ 100 ] propose a framework for visualizing social networks and their dynamics and presented a tool that enables debate and reflection on the quality of visualizations used in empirical research. With the focus on the evolution of communities over time, Falkowski et al. [ 101 ] proposed two approaches to analyze the evolution of two different types of online communities on the level of subgroups. This analysis was conducted by observing changes in the interaction behavior of the members of the communities. Chen [ 102 ] devised a generic approach for detecting and visualizing emerging trends and transient patterns in scientific literature. Other recent work of interest is presented by Beck et al. [ 103 , 104 ] and the visualization of evolving graphs with multiple visual metaphors of Burch [ 105 ]. The combination of dynamic network visualization with graph sampling techniques is often used [ 106 ].

8. Conclusion and future trends

This chapter provided an overview of the methods and techniques for modeling, analyzing, measuring and visualizing evolving social network analysis. In the past, static techniques were adapted to dynamic networks with relative success, but nowadays, with the advent of social media, scale and velocity of most of those static techniques reveal weaknesses that only can be addressed by methods and techniques designed for dealing with evolving data. After presenting two areas of direct applicability of evolving network analysis such as criminological research and research on journalism, the ways on how dynamic networks can be represented and modeled according to their timescale, windowing strategies and methods of analysis were discussed. These theoretical aspects were then used to present elementary network measures, link analysis methods, community detection methods and visualization techniques. It is clear that in recent years this area of research will continue to have significant development in the future, several problems are still unsolved and many of them can be significantly improved. The areas of applicability of evolving networks and social network analysis are also broader, with many of the abovementioned techniques moving from well-succeeded areas like world wide web, communication, telecommunication and mobile networks, to newer areas like social network recommendations, news and blog analysis and social network event detection. Specifically in the area of social network event detection, the detection of unusual patterns, anomalies or changes in trends in the social streams can lead to valuable information, which can be used timely in many real-word scenarios [ 107 ]. Cordeiro [ 108 ] addressed the monitoring and tracking of the dynamics of social network communities with the objective to unveil real-world events, whereas Cordeiro [ 109 ] was devoted to the problem of mining the twitter stream to unravel events, interactions and communities in real time. Future trends of social network analysis will continue to be driven by future trends and characteristics of the network data, such as the size of data, which is incredibly getting large, and changes in space and time. On one side, there is the urge for scalable and efficient social network analysis methods, and on the other side, there is the need for methods to study the dynamics and evolution of social networks, able to deal with future velocity and timescale dimensions of the network data. Stray [ 110 ] focused network analysis as a tool to bridge the “research to reporting” gap in journalism, starting with two use cases (Seattle Art World [ 111 ] and Hot Wheels [ 112 ]) and the recent state-of-the-art network analysis and visualizations applied to the Panama Papers case [ 113 ] where graph databases and entity recognition were used to build interactive network maps from structured data and raw documents. Therefore, it is expected that the study of evolving networks will continue to be a significant strand of research in the context of social network analysis in the near future.

Acknowledgments

This work was fully financed by the Faculty of Engineering of the Porto University. Rui Portocarrero Sarmento also gratefully acknowledges funding from FCT (Portuguese Foundation for Science and Technology) through a PhD grant (SFRH/BD/119108/2016). The authors also want to thank the reviewers for the constructive reviews provided in the development of this publication.

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BRIEF RESEARCH REPORT article

A network analysis of social problem-solving and anxiety/depression in adolescents.

• 1 Wenzhou Seventh People's Hospital, Wenzhou, China
• 2 Department of Psychology, School of Education, Wenzhou University, Wenzhou, China

Social problem-solving (SPS) involves the cognitive-behavioral processes through which an individual identifies and copes with everyday problems; it is considered to contribute to anxiety and depression. The Social Problem-Solving Inventory Revised is a popular tool measuring SPS problem orientations and problem-solving styles. Only a negative problem orientation (NPO) is considered strongly related to anxiety and depression. In the present study, we investigated the detailed connections among the five components of SPS and 14 anxiety-depression symptoms and specified the role of NPO and other components in the anxiety-depression network. We employed network analysis, constructed circular and multi-dimensional scaling (MDS) networks, and calculated the network centrality, bridge centrality, and stability of centrality indices. The results were as follows: (1) the MDS network showed a clustering of anxiety and depression symptoms, with NPO and avoidance style components from SPS being close to the anxiety-depression network (demonstrated by large bridge betweenness and bridge closeness); (2) the NPO and positive problem orientation from SPS were most influential on the whole network, though with an opposite effect; (3) strength was the most stable index [correlation stability (CS) coefficient = 0.516] among the centrality indices with case-dropping bootstraps. We also discussed this network from various perspectives and commented on the clinical implications and limitations of this study.

Introduction

Social problem-solving (SPS) is believed to be strongly related to anxiety and depression, which is very popular among Chinese people. For adults, 4% ( 1 ) before and 20.4% ( 2 ) during the COVID-19 epidemic suffer from anxiety and depression; for adolescent, the prevalent of anxiety and depression is 11.2%/14.6% ( 3 ) before and 19%/36.6% ( 4 ) during the epidemic. SPS plays a significant role in psychological adjustment and constitutes an important coping strategy that has the potential to reduce or minimize psychological distress ( 5 , 6 ). Previous research has found that strong SPS abilities reduce the morbidity associated with anxiety and depression by aiding young people in controlling and modifying their health behavior ( 7 ); they are of key importance in managing emotions and wellbeing ( 8 ). Conversely, poor problem orientation has consistently linked depression and anxiety ( 9 ). Furthermore, depressed patients frequently exhibit deficiencies in social problem-solving, producing fewer effective solutions than do normal control subjects ( 10 ).

Essentially, SPS involves the cognitive-behavioral processes through which an individual identifies and copes with everyday problems ( 11 ). It comprises problem orientation (a general motivational and appraisal component) and problem-solving style (the cognitive and behavioral activities a person uses to cope with problems). The Social Problem-Solving Inventory Revised (SPSI-R) provides a corresponding scale and comprehensive assessment of all theoretical components linked to contemporary models of social problem-solving [i.e., both problem orientation and problem-solving style ( 12 , 13 )]. The SPSI-R consists of a scale of 25 (in the short form) or 52 (in the long form) items, and is one of the most prominent instruments used to study SPS ( 14 ). The SPSI-R is a theory-based measure of SPS processes. It consists of five dimensions, as follows: (1) positive problem orientation (PPO), (2) negative problem orientation (NPO), (3) rational PPO problem-solving (RPS), (4) impulsivity/carelessness style (ICS), and (5) avoidance style (AS). The SPSI-R assesses a person's perception of his or her general approach to and styles of solving problems in everyday living that have repeatedly been found to be reliable and valid ( 15 , 16 ).

SPSI-R research has shown that SPS is an important measure of psychological distress, wellbeing, and social competence [i.e., depression, distress, anxiety, health-related behaviors, life satisfaction, optimism, situational coping, aggression, and externalizing behaviors ( 17 – 19 )]. Previous research has found that certain specific components of SPS can contribute significantly to anxiety and depression. For example, anxious and depressed patients may have difficulties at different stages of the problem-solving process ( 20 , 21 ); Kant et al. (author?) ( 22 ) found that all five problem-solving dimensions measured by the SPSI-R were significantly related to both anxiety and depression in at least one of two samples (i.e., the middle aged and elderly); additional follow-up analyses indicated that NPO contributed most to the significant mediating effect between problems and depression.

Specifically, NPO is strongly related to depression and emotional distress. Abu-Ghazal and Falwah ( 23 ) found that employing PPO to solve problems leads to positive psychological wellbeing, while NPO is associated with depression. In Australia, researchers examined the relationship between NPO and depression-anxiety in 285 young adults using the NPO dimensions of the SPSI-R, finding strong connections between the two ( 24 ). Additionally, many researchers have found that social anxiety is related to NPO ( 25 , 26 ). In Hungary, Kasik and Gál ( 27 ) studied the relationships among SPS, anxiety, and empathy in 445 Hungarian adolescents, finding that regardless of age, adolescents with an increased level of anxiety also have high levels of NPO and AS. Furthermore, studies have found a link between NPO and stress ( 28 – 32 ). Therefore, anxiety and depression have the strongest association with NPO, above all other SPS components ( 8 , 33 – 35 ), and success in reducing symptoms of anxiety and depression appears to be more strongly predicated on the absence of NPO than presence of PPO ( 34 ).

These studies suggest that NPO plays an important role in anxiety and depression. We also explored the detailed connections between problem-solving orientations (including NPO) and problem-solving styles with anxiety-depression symptoms. In other words, we integrated the components of SPS into the anxiety-depression network and investigated the link between these components and anxiety-depression symptoms. We identified the components of social problem-solving most strongly associated with certain symptoms in the anxiety-depression network and determined which components were most centrally located.

Thus, network analysis was employed to analyze the relationships among components of SPS and anxiety-depression symptoms, working from the bottom up, without applying any top-down construct consistent with the standard biomedical and reductionist model ( 36 ). A key premise of network theory is that psychopathological symptoms are interacting and reinforcing parts of a network, rather than clusters of underlying disorders ( 37 ). To test this argument, network analysis has been used to describe the relationships within and between disorders ( 37 ). The dynamics and interrelationships between comorbidities can be identified in network analysis and gaps not considered by factor analysis methods can be addressed ( 38 ). A network is defined as a set of nodes (symptoms) and edges (connections between nodes). In a network model, the symptoms themselves constitute the disorder. The onset and maintenance of symptoms are determined by tracing the pathways of the network ( 38 ).

In an estimated network structure, a centrality measure denotes the overall connectivity of a particular symptom (or component). Central nodes contribute the most to the interrelatedness of symptoms (or components) within the estimated network structure ( 39 , 40 ). A tightly connected network with many strong connections among the symptoms is considered risky because activation of one symptom can quickly spread to other symptoms, leading to more chronic symptoms over time ( 41 ). In other words, when a highly central component is activated (i.e., a person reports the presence of a symptom), it influences other components, causing them to become activated as well, and thus maintaining the network. Considering the importance of problem orientation and problem-solving styles to emotional wellbeing, the nodes should be strongly linked to symptoms of anxiety and depression. In addition, we calculated the bridge-centrality. Previous research has found that deactivating bridge nodes prevents the spread of comorbidity (i.e., one disorder activating another) ( 42 ). Through this network analysis, we gained insight regarding the relationship between SPS and anxiety-depression, which may have clinical implications such as helping to modify patients' problem-solving styles to alleviate related symptoms.

In summary, social problem solving is highly correlated with anxiety and depression and can lead to a number of mental illnesses. There are few study about how the aspects of social problem solving that contribute to depression and anxiety and how they both interact with each other. The present study is to explore the detailed connections between problem-solving orientations and problem-solving styles with anxiety-depression symptoms. NPO, specifically, is hypothesized to be related to depression and emotional distress. We characterized the network structure of SPS components and anxiety-depression symptoms using psychiatric and regular samples. We first investigated the node and bridge centrality, and then determined the stability of the centrality indices for the network.

Participants

The samples, consisting of adolescents aged 12–17 years, was obtained from a psychiatric hospital and two secondary schools, collected from October 2021 and completed in March 2022. The 100 adolescents from the hospital were outpatients who had mental health assessments done by psychiatrists. When patients enter the psychological assessment room, they are briefly introduced to the purpose of our study and then asked to fill out the relevant scales based on the most recent week. They could ask the psychiatrists for help if they have any questions. When the task was finished, the psychiatrists have a check to make sure that all responses are completed, and then the subject leaves the assessment room. The other 100 participants were randomly selected middle school students; they conducted the self-rating assessments while monitored by their teachers in the classrooms. All participants signed an informed consent form and were explained about the rules regarding anonymity, confidentiality, and their right to quit.

Ten samples (from the middle schools) were excluded from data collection because they failed the manipulation check ( 43 ). Therefore, 190 participants were included in the data analysis.

Hospital anxiety and depression scale

The HADS assesses both anxiety and depression, which commonly coexist ( 44 ). The measure is employed frequently, due to its simplicity, speed, and ease of use. Very few literate people have difficulty completing it. The HADS contains a total of 14 items, including seven for depressive symptoms (i.e., the HADS-D) and seven for anxiety symptoms (i.e., the HADS-A), focusing on symptoms that are non-physical. The correlations between the two subscales vary from 0.40 to 0.74 (with a mean of 0.56). The Cronbach's alpha for the HADS-A varies from 0.68 to 0.93 (with a mean of 0.83) and for the HADS-D from 0.67 to 0.90 (with a mean of 0.82). In most studies, an optimal balance between sensitivity and specificity was achieved when a cut point was set at a score of 8 or above on both the HADS-A and HADS-D. The sensitivity and specificity for both is 0.80. Many studies conducted around the world have confirmed that the measure is valid when used in a community setting or primary care medical practice ( 45 ).

SPSI-R (Chinese version)

There have been several revised versions of the SPSI-R for use in the Chinese language, such as the measure published by Siu and Shek ( 46 ) and Wang ( 47 ). The present study used the latter, which shows both good reliability and validity. The overall Cronbach's alpha is 0.85, and the RPS, AS, NPO, PPO, and ICS subscales are 0.85, 0.82, 0.70, 0.66, and 0.69, respectively. The SPSI-R uses a five-point Likert-type scale ranging from 0 to 4, as follows: (0) Not at all true for me, (1) slightly true for me, (2) moderately true for me, (3) very true for me, and (4) extremely true for me.

Network analysis

We used a Gaussian graphical model (GGM) to build the network via the R package (R Core Team version 4.1.3) qgraph (version 1.9.2) ( 48 , 49 ). GGMs estimate many parameters (i.e., 19 nodes required the estimation of 171 parameters: 19 threshold parameters and 19 * 18/2 = 171 pairwise association parameters) that would likely result in false positive edges. Therefore, it is common to regularize GGMs via a graphical lasso ( 49 – 51 ), leading to a sparse (i.e., parsimonious) network that explains the correlation or covariance among nodes with as few edges as necessary. Node placement was determined by the Fruchterman-Reingold (FR) algorithm, which places nodes with stronger average associations closer to the center of the graph ( 52 ). The R package qgraph was used to calculate and visualize the networks. We also measured the centrality and stability of the established network. The R package qgraph and estimatenetwork automatically implement the glasso regularization, in combination with an extended Bayesian information criterion (EBIC) model, as described by Foygel and Drton ( 53 ).

In network parlance, anxiety-depression symptoms and SPS components are “nodes” and the relationships between the nodes are “edges”. The edge between two nodes represents the regularized partial correlation coefficients, and the thickness of the edge indicates the magnitude of the association. The graphical lasso algorithm makes all edges with small partial correlations shrink to zero, and thus facilitates interpretation and establishment of a stable network, solving traditional lost-power issues that emerge from examining all partial correlations for statistical significance [for greater detail, see ( 54 )]. For the present network, we divided the components into three groups or communities: anxiety (seven symptoms), depression (seven symptoms), and SPS (five components).

Most network studies in psychopathology have used the FR algorithm to plot graphs ( 52 ). The FR algorithm is a force-directed graph method [see also ( 55 )] that is similar to creating a physical system of balls connected by elastic strings. Importantly, the purpose of plotting with a force-directed algorithm is not to place the nodes in meaningful positions in space, but rather to position them in a manner that allows for easy viewing of the network edges and clustering structures ( 56 ). We used the “circle” layout for easier viewing, which places all nodes in a single circle, with each group (or community) put in separate circles (see Figure 1A ). In addition, we employed a multi-dimensional scaling (MDS) approach to display the network (see Figure 1B ). MDS represents proximities among variables as distances between points in a low-dimensional space [e.g., two or three dimensions; ( 57 )]. MDS is particularly useful for understanding networks because the distances between plotted nodes are interpretable as Euclidean distances ( 56 ).

Figure 1 . Estimated network structure based on a sample of 190 adolescents. The network structure is a GGM, which is a network of partial correlation coefficients. Green edges represent positive correlations and red edges indicate negative correlations. The thickness of the edge reflects the magnitude of the correlation. (A) Network structure with the “circle” layout for easy viewing, but it is important to note that the node positions don't indicate Euclidean distances. (B) Network structure with MDS, showing proximities among variables as distances between points in a low-dimensional space.

We calculated several indices of node centrality to identify the symptoms or components most central to the network ( 58 ). For each node, we calculated the strength (i.e., the absolute sum of edge weights connected to a node), closeness (i.e., the average distance from the node to all other nodes in the network), betweenness (i.e., the number of times a node lies on the shortest path between two other nodes), and expected influence (i.e., the sum of edge weights connected to a node). For SPS and anxiety-depression networks considering the relationship in both direction (i.e., both positive and negative), strength rather than expected influence (which only calculates neutralized influence) is suitable. The node bridge strength is defined as the sum of the value of all edges connecting a given node in one community with nodes in other communities, and was computed by the R-package networktools ( 42 ). Higher node bridge strength values indicated a greater increase in the risk of contagion to other groups or communities ( 42 ).

Stability of centrality indices

We investigated the stability of centrality indices by estimating network models based on subsets of the data and case-dropping bootstraps ( n = 1,000). If correlation values declined substantially as participants were removed, we considered this centrality metric to be unstable. The robustness of the network was evaluated by the R-package bootnet using the bootstrap approach ( 54 ). This stability was quantified using the CS coefficient, which quantified the maximum proportion of cases with a 95% certainty that could be dropped to retain a correlation with an original centrality higher than 0.7 (by default) ( 54 ).

The students' average age was 15.54 years ( SD = 1.302); the group included 102 males and 88 females. We conducted descriptive statistics for the scores of each scale on different demographic variables. The results are shown in Table 1 , which demonstrate the number of participants in each group and the mean score and standard deviation (in the parenthesis) for each scale. Due to some missing data for some participants, the total the number of people with different conditions does not equal 190.

Table 1 . The descriptive statistics of the six SPS components, anxiety, and depression.

As for the network, ~41.5% of all 171 network edges were set to zero by the EBICglasso algorithms. Figure 1 presents the network of SPS components and anxiety-depression symptoms. Figure 1A displays an easily viewable circular network with weights on each edge. For example, the strongest edge (weight = 0.32) among the anxiety symptoms was between Btt 1 (“I get sort of a frightened feeling, like 'butterflies' in the stomach”) and Pnc (“I get sudden feelings of panic”). Among depression symptoms, the strongest edge (weight = 0.25) was between Chr (“I feel cheerful”) and Fnn (“I can laugh and see the funny side of things”). For SPS components, the strongest edge (weight = 0.46) was between PPO (positive problem orientation) and RPS (rational problem-solving). Figure 1B display the MDS network. Highly-related nodes appear close together, whereas weakly-related nodes appear further apart. The anxiety-depression symptoms and SPS components cluster within their own communities, and anxiety-depression nodes are closer to each other. The NPO (negative problem orientation) and AS (avoidance style) nodes are nearest to the anxiety-depression network, while other components are distant from that network.

Centrality indices

For the centrality indices, the values were scaled (i.e., normalized) relative to the largest value for each measure. Figure 2 shows the centrality indices, which are ordered by strength . For strength , Rlx (“I can sit at ease and be relaxed”) from the anxiety symptoms is the most central symptom, 2 followed by Frw (“I look forward with enjoyment to things”) from the depression symptoms and PPO (positive problem orientation) from the SPS components, indicating that these nodes had the strongest relationships to the other nodes. For closeness and betweenness , Frw again ranked the highest, indicating that it was closest to all other nodes in the network and on the shortest path between two other nodes. As for expected influence , considering the direction of the relationship (both positive and negative), Rlx and Pnc from the anxiety community was most positively and PPO most negatively influential on the whole network, indicating that Rlx may be an important risk factor and PPO an important protective factor. NPO most positively influenced the network from the SPS community, and Slw (“I feel as if I am slowed down”) did the same for the depression community.

Figure 2 . Centrality indices for the nodes of the present network including those for strength betweenness closeness expected influence. The values are normalized to be within the range of 0–1. The full names of the abbreviations can be found in Figure 1 .

We also calculated the bridge centrality indices (see Figure 3 ). Rlx, Frw , and NPO for anxiety-depression and SPS were found to have the strongest connections (i.e., bridge strength) with other communities ( 42 ). For bridge closeness, Frw, AS , and NPO ranked the highest. For bridge betweenness, Frw, AS , and ICS comprised the top three. For bridge expected influence, Rlx, Slw , and NPO were the most influential.

Figure 3 . Estimated bridge centrality indices for the present network, including bridge strength, bridge betweenness, bridge closeness, and bridge expected influence. The full names of the abbreviations for the nodes can be found in Figure 1 .

Stability of the centrality indices

Figure 4 shows that the average correlations dropped between the centrality indices of networks sampled with persons and the original sample. The stability levels of closeness and betweenness dropped steeply, while the stability levels of the node strength and expected influence less so. The Correlation-Stability (CS) coefficient value should preferably be above 0.5 and not be below 0.25 ( 59 ). In this research, the CS coefficient indicated that the betweenness [CS (cor = 0.7) = 0.205] was not stable, while the closeness [CS (cor = 0.7) = 0.437] was relatively stable in the subset cases. Node strength and expected influence performed best [CS (cor = 0.7) = 0.516], reaching the cutoff of 0.5 and indicating that the metric was stable. Therefore, we found that the order of node strength and expected influence were most interpretable (with some care), while the order of betweenness was not.

Figure 4 . Average correlations between the centrality indices of networks sampled with persons and the original sample. Lines indicate the means and areas ranging from the 2.5th quantile to the 97.5th quantile.

Anchored in the network perspective ( 39 ), this study illustrated the node pathways, central indices, and central bridging indices for the SPS and anxiety-depression networks. From a “network-network” perspective, the node connections were closer within (vs. between) the anxiety-depression and SPS networks, demonstrating their relative independence from one other. This result is in keeping with previous comorbidity studies of anxiety and depression that employed network analysis ( 60 , 61 ), underscoring that the SPS network is distant from the anxiety-depression network (though the NPO and AS nodes are close to the anxiety-depression network, which can be measured by bridge closeness, as seen in Figure 3 ). Further, the SPS seems more strongly related to anxiety than depression networks, given the longer mean distance from SPS to depression. The reason could be that anxiety is more related to problems or events (the uncertainty of the future) ( 62 ) while depression is more related to self (usually accompanied by low self-esteem, low self-efficacy, and hopelessness) ( 63 ). This explanation is reasonable but required further verifications. The MDS structure is a useful tool for displaying the spatial relationships of nodes, and thus its use should be encouraged in the future.

From a “nodes-in-network” perspective, the node centrality indices revealed that the NPO node from SPS and Rlx and Frw from anxiety-depression were likely to be the most central in the entire SPS-anxiety-depression network. Considering that mood disorders affect how people look at and deal with problems, it is appropriate to put anxiety, depression, and SPS components into a single network. In terms of clinical implications, from our results, we can infer that therapy will yield the greatest rewards by modifying NPO , encouraging relaxation training, and enhancing the expectation of enjoyment for coming things. In addition, the NPO and AS nodes are nearest to the anxiety-depression network, especial to the anxiety symptoms. Therefore, we may even consider that NPO and AS (very close to each other) are innate components of anxiety, as anxious people are worried about the future but do not positively view the problem and do not actively cope with the problem ( 64 ). However, this hypothesis requires further confirmation.

From a “network-node-network” perspective, the results of bridge centrality found that the NPO in SPS community had the strongest association (for both bridge strength and bridge closeness) with the anxiety-depression network, echoing previous research that NPO most strongly contributes to anxiety and depression. However, PPO is located away from the anxiety-depression network and the most negatively correlated ( 65 ), as can be seen from the low levels of bridge expected influence and bridge closeness. Furthermore, the RPS node is strongly connected with PPO but valued low in the four indices of bridge centrality, indicating its unimportance because both of them should “stay away” from the network which is main consists of negative nodes ( 66 ). In short, PPO is the protective and NPO the risk factor for the anxiety-depression network. In clinical settings, encouraging PPO and discouraging NPO would be an effective approach to reducing symptoms of anxiety and depression.

Some limitations of this research will direct future research. First, a cross-sectional design was adopted to build the SPS and anxiety-depression networks. Therefore, this study could not be used to ascertain whether anxiety-depression symptoms impact SPS components or vice versa. Thus, future work will adopt a longitudinal approach with repeated measures of anxiety-depression and SPS components to clarify the causal relationship between anxiety-depression and SPS components. Second, it is probable that the detected potential pathways among the components are limited to the SPSI-R and HADS scales applied. Self-report tools for the SPSI-R and anxiety-depression usually vary in their constructs. This diversity limits the connections that can be found in terms of network structure. Nevertheless, the scales we used are broadly employed; they were carefully implemented based on their psychometric constructs and applicability for adolescents. Therefore, the present research adds to the literature of how among adolescents, anxiety-depression symptoms may be associated with SPS components. This study may also act as an incentive for future research applying other scales for SPS and anxiety-depression to ascertain the stability of these novel findings.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Ethics statement

The studies involving human participants were reviewed and approved by Ethics Committee of Wenzhou Seventh People's Hospital. Written informed consent to participate in this study was provided by the participants' legal guardian/next of kin.

Author contributions

Q-NR conceived and designed the experiments. W-JY and CC performed the experiments. ZL, Q-NR, and W-JY wrote and revised the manuscript. ZL gave financial support. All authors contributed to the article and approved the submitted version.

This research was supported by the Medicine and Health Science and Technology Project of Zhejiang, China (No. 2019KY669), and Wenzhou Science and Technology Project of Zhejiang, China (Y20210112).

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

1. ^ Following, the node labels with abbreviations will be in italics.

2. ^ Rlx (“I can sit at ease and be relaxed”) and Frw (“I look forward with enjoyment to things”) are not symptoms per se , but for measuring the symptoms “restless” and “pessimistic” using reverse questions.

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Keywords: network analysis, social problem-solving, anxiety, depression, adolescent

Citation: Ruan Q-N, Chen C, Jiang D-G, Yan W-J and Lin Z (2022) A network analysis of social problem-solving and anxiety/depression in adolescents. Front. Psychiatry 13:921781. doi: 10.3389/fpsyt.2022.921781

Received: 16 April 2022; Accepted: 21 July 2022; Published: 10 August 2022.

Reviewed by:

Copyright © 2022 Ruan, Chen, Jiang, Yan and Lin. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Wen-Jing Yan, eagan-ywj@foxmail.com ; Zhang Lin, 409814552@qq.com

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

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How social network analysis can be used to monitor online collaborative learning and guide an informed intervention

Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing – original draft

* E-mail: [email protected]

Affiliations Department of Computer and System Sciences (DSV), Stockholm University, Kista, Stockholm, Sweden, Qassim University, College of Medicine, Qassim, Melida, Kingdom of Saudi Arabia

Roles Conceptualization, Data curation, Methodology, Supervision, Writing – original draft, Writing – review & editing

Affiliation Department of Computer and System Sciences (DSV), Stockholm University, Kista, Stockholm, Sweden

Roles Formal analysis, Methodology, Supervision, Writing – original draft, Writing – review & editing

Affiliation School of Computing, University of Eastern Finland, Joensuu, Finland

Roles Methodology, Supervision, Writing – original draft, Writing – review & editing

• Mohammed Saqr, 
• Uno Fors, 
• Matti Tedre, 
• Jalal Nouri

• Published: March 22, 2018
• https://doi.org/10.1371/journal.pone.0194777
• Reader Comments

To ensure online collaborative learning meets the intended pedagogical goals (is actually collaborative and stimulates learning), mechanisms are needed for monitoring the efficiency of online collaboration. Various studies have indicated that social network analysis can be particularly effective in studying students’ interactions in online collaboration. However, research in education has only focused on the theoretical potential of using SNA, not on the actual benefits they achieved. This study investigated how social network analysis can be used to monitor online collaborative learning, find aspects in need of improvement, guide an informed intervention, and assess the efficacy of intervention using an experimental, observational repeated-measurement design in three courses over a full-term duration. Using a combination of SNA-based visual and quantitative analysis, we monitored three SNA constructs for each participant: the level of interactivity, the role, and position in information exchange, and the role played by each participant in the collaboration. On the group level, we monitored interactivity and group cohesion indicators. Our monitoring uncovered a non-collaborative teacher-centered pattern of interactions in the three studied courses as well as very few interactions among students, limited information exchange or negotiation, and very limited student networks dominated by the teacher. An intervention based on SNA-generated insights was designed. The intervention was structured into five actions: increasing awareness, promoting collaboration, improving the content, preparing teachers, and finally practicing with feedback. Evaluation of the intervention revealed that it has significantly enhanced student-student interactions and teacher-student interactions, as well as produced a collaborative pattern of interactions among most students and teachers. Since efficient and communicative activities are essential prerequisites for successful content discussion and for realizing the goals of collaboration, we suggest that our SNA-based approach will positively affect teaching and learning in many educational domains. Our study offers a proof-of-concept of what SNA can add to the current tools for monitoring and supporting teaching and learning in higher education.

Citation: Saqr M, Fors U, Tedre M, Nouri J (2018) How social network analysis can be used to monitor online collaborative learning and guide an informed intervention. PLoS ONE 13(3): e0194777. https://doi.org/10.1371/journal.pone.0194777

Editor: Petter Holme, Tokyo Institute of Technology, JAPAN

Received: November 11, 2017; Accepted: March 11, 2018; Published: March 22, 2018

Copyright: © 2018 Saqr et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: The data are not publicly available due to ethical and legal restrictions since it contains information that compromises students and teachers’ confidentiality and violates the regulations of National Committee of Bioethics (NCBE) and the data protection policy of Qassim College of Medicine. The data that support the findings of this study are available on request from the e-learning unit [email protected] pending approval of the Regional Ethical Committee.

Funding: The authors received no funding for this work.

Competing interests: The authors have declared that no competing interests exist.

Introduction

With the advent of the Internet, the use of information technology in education has become increasingly commonplace, and computer-supported collaborative learning (CSCL) has gained grounds in online learning environments [ 1 , 2 ]. One of the most common implementations of CSCL is the asynchronous discussion board (forum). Forums offer learners the opportunity to collaborate, cooperate, and interact online in themed discussions, as well as the convenience of transcending the physical barriers of time and place [ 1 – 4 ]. The written nature of the contributions in online forums enables explicit writing, reflection, and permanent access to submissions [ 2 ].

The benefits of online collaborative learning are supported by a growing body of evidence environments [ 1 , 2 ]. Online collaborative learning has been associated with higher academic achievement, deeper levels of learning, retention of learned information for longer times, better problem solving, and higher-order critical thinking skills [ 5 – 8 ]. However, working online together does not necessarily mean collaboration [ 4 , 6 , 9 – 12 ], and offering the learners the opportunity to interact in CSCL does not directly translate to effective collaboration [ 5 , 6 , 11 ]. Common barriers to effective collaboration include social loafing, dysfunctional group dynamics, lack of appreciation of values, absence of a stimulating task or script, lack of preparation, and lack of social skills [ 7 , 10 , 11 , 13 , 14 ]. For successful online collaboration to take place, there should be active coordination of group dynamics [ 11 ], mutual engagement of the learners, discussion moderators [ 6 , 10 , 15 ], scaffolding by instructors [ 11 , 13 , 15 ], and a stimulating environment that maximizes efficient interactions among participants [ 5 , 12 ].

To ensure that forums meet their intended pedagogical goals (are actually collaborative and stimulate learning), mechanisms are needed for monitoring the efficiency of online collaboration; such methods commonly fall under collaboration analysis [ 4 , 10 , 16 – 19 ]. Computer based interaction analysis (IA) is one such method that uses data drawn from participants’ activities in order to understand computer-mediated activities and interactions. After its inception, IA was often used to help regulate students’ actions, such as the mode and degree of participation, or to increase awareness of student activity. For teachers, it is used as a tool for supporting decision-making regarding moderation tactics, for anticipating potential problems, and for assessing students’ participation [ 19 , 20 ]. IA falls short of relational and social aspects. For instance, IA statistics do not offer information about the patterns of interactions, structure of the group, active or inactive participants, influential students, teacher’s role, the patters of flow of information, group dynamics or cohesion, or timeline of interactions [ 4 , 16 – 18 , 21 , 22 ]. Lately, a growing body of research has demonstrated the practicality of using Social Network Analysis (SNA) in offering valuable insights about the social structure, collaborative patterns and roles and position of collaborators [ 22 – 24 ].

Social network analysis

Social network analysis is a method for studying the structure of relationships and the effect this social structure has on the attitudes, behavior, and performance of the individual actors or groups [ 25 ]. A social network has two fundamental elements: nodes (network actors or participants) and edges (ties or relations) connecting them [ 25 ]. In CSCL, nodes represent students and teachers or other actors, and edges represent the interactions or other ties among them. Networks are visually represented by mapping edges (interactions) among nodes (actors) in a special graph commonly known as a “sociogram”. Each node in the network is represented by a circle, and each interaction is represented by an arrow or a line from the source to the target node [ 25 ].

The use of SNA visual analytics, along with quantitative network analysis (centrality measures), may broaden the understanding of the properties of online collaboration and the collaborators [ 23 , 24 ]. SNA complements the level of activity indicators commonly obtained by computer-based IA with insights into three main areas; 1) position in information exchange/collaborative knowledge construction [ 8 , 22 , 26 – 28 ]; 2) role identification and relational insights [ 16 , 23 , 29 – 31 ]; and 3) group properties, cohesion and dynamic evolution of relations [ 32 , 33 ].

A typical use of SNA in collaboration is the of analysis student’s position and role in collaborative knowledge sharing. A preferential student position might positively affect his or her learning and academic achievement—a concept that has garnered a considerable volume of SNA research and explanations [ 28 , 34 ]. According to the social capital theory, well-connected students have better access to resources and to emotional and educational support, which can boost their sense of belongingness and motivation [ 35 , 36 ]. Students who connect or mediate communications have another form of social capital; brokerage social capital. Besides having control over the flow of information, they also have privileged access to varying points of view. According to Kranton, Pfeffer [ 28 ], individuals who connect to otherwise unconnected groups of collaborators (structural holes) may provide novel ideas and have a better chance of success.

Wenguang, Xinhui [ 34 ] demonstrated that students with brokerage positions were important to knowledge construction networks in an online course. Similar results were reported by Gunawardena, Flor [ 37 ], who described how students’ positions facilitated information processing and the dissemination of critical knowledge among peers, which benefited the whole groups and assisted relatively peripheral students to make substantive contributions. Zhang and Zhang [ 27 ] found that the level of knowledge construction in the studied course was minimal because few students acted as conduits for information exchange in the learning network. They recommended taking measures to improve the quality of interaction and students’ positions in the learning networks. Similar recommendations were reported by Heo, Lim [ 8 ] after studying knowledge construction in project-based learning.

Another perspective that can be revealed by using SNA in collaboration analysis is the identification of roles through visual or mathematical analysis [centrality measures) [ 16 , 29 , 31 ]. Rabbany, Takaffoli [ 16 ] have demonstrated how SNA can be used to study the structure of online communities, identify active and inactive students, and detect students who are central to the flow of information in discussion forums. Their method can be used to guide the instructor and students about the flow of the course. Similarly, Bakharia and Dawson [ 30 ], and Lockyer, Heathcote [ 38 ] used SNA to identify interactive and isolated students. Additionally, their research extended to identifying the emergence and evolution of undesirable instructor roles during knowledge sharing where interactions are dominated by instructors albeit being expected to be distributed among participants. Recently, Marcos-García, Martínez-Monés [ 29 ] used SAMSA , a tool that combines SNA visualization along with interaction analysis to demonstrate the possibility of automatic identification of different collaborative roles and thereafter offer a method for supporting those roles tailored to participants’ needs.

Roles minimize the inert knowledge problem and help collaborators approach the task from different perspectives as well as appreciate different points of view [ 39 ]. Preset roles may minimize conflicts and counterproductive self-assignment of undesired roles [ 40 ]. On the group level, roles help facilitate intragroup coordination, enhance group cohesion and support participants’ responsibility. Therefore, roles can be used to promote accountability and positive interdependence among collaborators [ 33 ]. Using roles within the framework of collaboration scripts is a popular method to prompt engagement in cognitive and socially meaningful interactions [ 14 , 20 , 39 , 40 ]. Roles are usually predefined by assigning certain duties or responsibilities to collaborators; Nonetheless, they can also emerge during group interaction [ 29 , 36 ].

The third construct that SNA may reveal about collaborative groups is cohesiveness, which is measured by density of interactions and clustering coefficient. Density is a measure of group cohesion and diversity of contributions. In contrast to simple quantification of interactions, density is a relative measure that increases when more members participate. Dense groups are more socially cohesive, share different points of view, and show higher levels of satisfaction and stability [ 22 , 33 , 34 ]. Cohesion and interdependence are key concepts of collaborative learning and monitoring group density can uncover an important aspect of collaborative behavior on the group level [ 33 ].

The use of monitoring strategies can inform educators about the status of collaboration and allow them to take data driven interventions when needed [ 14 , 20 , 22 ]. SNA visual analytics, along with quantitative SNA indicators have the potential to offer insights on both quantity and quality of collaboration as well as the role of collaborators. The possibility of monitoring online interactions in real-time might open new frontiers for the study of collaboration and how events evolve online [ 17 , 23 ]. Although research in the field of SNA in education dates back to the late 1990s, studies in education have only focused on the potential of using SNA, but not on the actual benefits they achieved [ 8 , 16 , 22 , 23 , 26 , 27 , 30 , 31 , 38 , 41 – 44 ]. The recent SNA reviews by Cela, Sicilia [ 23 ] who reviewed 37 studies and Dado et al. who reviewed 89 studies [ 24 ] reported no studies about actual interventions in a learning setting. The study we report on here investigated how social network analysis can be used to monitor online collaborative learning, find aspects in need for improvement, guide an informed intervention, and assess the efficacy of intervention using an experimental, observational repeated measurement design in three courses over a full-term duration.

This study was guided by the overall research question: How can social network analysis be used to guide a data-driven intervention in online collaborative learning as well as assess the efficacy of the intervention?

The context

Qassim University, College of Medicine in Saudi Arabia uses CSCL as a means to enhance clinical reasoning and critical thinking skills in an online collaborative environment [ 13 , 45 , 46 ]. In the three studied courses, teachers use online clinical case scenarios, the cases are posted and moderated by the teacher through CSCL, and students are encouraged to engage in collaborative discussions regarding the case. The case scenarios describes certain medical conditions in terms of hypothetical patient cases with a description of the history, symptoms, clinical findings, and sometimes laboratory investigations or radiological findings. The idea is to stimulate the students through the case to discuss the patient symptoms, reasoning of clinical findings, diagnosis and management. For example, a case in the emergency course described a patient who presented to the emergency department with a cloudy consciousness following a severe headache episode. Students were asked to discuss the case diagnosis, investigations, and treatment. In the surgery course, a case described a child with a cleft palate, students were asked to discuss the possible risk factors, symptoms and management. Interaction analysis indicators reported by the learning management system (Moodle) have shown that a number of clinical courses were highly active in terms of the number of posts, topics, and participating students. However, a pilot study performed during the academic year 2013–2014 concluded that the pattern of online interactions in the studied courses was not as collaborative as hoped. The interactions were mostly instructor-centric, student-student interactions were scarce, most posts were repetitions of answers, and there were few discussions or reflections among participants [ 31 ]. Based on these findings, we designed a research plan divided into three stages:

• Stage 1: Establish a monitoring mechanism that monitors CSCL and identifies areas of need for intervention in three courses in the first mid-term.
• Stage 2: Build an intervention plan based on the analysis of data derived from Stage 1.
• Stage 3: Compare post-intervention to pre-intervention and evaluate the whole experiment.

Three courses were involved: Surgery A (course A), Surgery B (course B), and Emergency (course C). The three courses were almost a full term in duration. The teaching method in these courses was blended learning, where the online component included clinical case discussions moderated by the course organizer. Table 1 details the number of students, number of posts, and topics in each course.

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https://doi.org/10.1371/journal.pone.0194777.t001

Study design

The study design followed an experimental, observational repeated measurement design approach. In the first midterm, subjects were monitored using real-time social network analysis; the data were collected by the end of first mid-term and subsequently analyzed. An intervention plan was then formulated based on the analysis of the first mid-term data, and at the end of the second term, data from both terms were compared and analyzed.

Data collection

Interaction data were extracted using two methods: Graphfes web service and Structured Query Language (SQL) queries. Graphfes was used for the monitoring of CSCL in the learning management system. Graphfes is a web service that extracts interaction data from Moodle forums and generates SNA visualizations of course interactions [ 17 ]. It has the advantage of being feasible to implement, fast, and capable of instant rendering of interactions [ 17 , 18 ]. Although Graphfes was useful for getting an overall instant view of all course interactions, the final results required more in-depth analysis and extraction of metadata about the users, their attributes, and the properties of the messages, which necessitated the use of custom SQL queries.

SQL was used to extract detailed interaction data (subject, content, ID, parent forum, author, reply, author of the reply, creation time, modification time, group ID) and user profile data (user ID, name, course, email). The data were then cleaned by removing incomplete, missing, or garbled records (6 records were missing the source or target of interaction). Personal data that could identify users were deleted, and students and participants were coded. The students were coded as G1 to G17 in course A, S1 to S33 in course B, and L1to L32 in course C. The teachers were coded Q1, T1 and D1. Finally, the data were converted to a format compatible with Gephi.

Gephi 0.9.1 was chosen for both visualization and network quantitative analysis (centrality measures). Gephi is an open source application with clustering, filtering, and partitioning capabilities [ 47 ]. It has several built-in visualization engines and can create animated dynamic network visualizations, which enabled us to study the evolution of interaction patterns before and after the intervention. The visualization was done using Gephi’s default layout algorithm (Forced Atlas 2), which renders each node’s position according to its relations and connections, and has the capability to update the structure according to the time of the interaction [ 48 ].

Data analysis

For the purpose of analysis in this study, we considered two types of indicators, IA and SNA, on both the individual and the group level. Regarding interaction analysis on the group level, we included number of posts, number of topics, and average contribution of each member. On the individual level, the number of contributions, replies, and received interactions were included. These parameters give an overview about the status of interactivity in the group and the contribution of members.

Regarding SNA, on the individual level, the centrality measures relevant to collaborative knowledge sharing were included, these SNA parameters represent the constructs discussed in detail earlier: the level of activity, position in information exchange, and role in the group. On the group level we used group SNA indicators of interactivity and group cohesion.

Level of activity (Quantity of participation parameters) : The level of activity of a collaborator was measured by three centrality measures: The out-degree, the in-degree and the degree centrality. In principle, the SNA level of activity indicators may be considered IA indicators as they are measuring the same concept. Out-degree centrality was used to indicate the quantity of participants’ interactions, and was calculated by counting all interactions by a participant[ 49 , 50 ]. A more important measure regarding the size used was in-degree centrality or influence , which is the number of interactions a participant receives. A participant usually receives an interaction when he contributes knowledge that is beyond what has been contributed by others, or a point of view that merits discussion, or receives an argument or a reply. In-degree centrality is an indication of influence and quality of contributions as voted by peers [ 51 , 52 ]. In knowledge exchange contexts, higher in-degree centrality can be considered a sign of expertise, popularity, or leadership. The third measure of size was degree centrality , which is the total number of contributed ( out-degree) and received ( in-degree) interactions [ 51 , 53 ]. Degree centrality is another interactivity indicator that takes into account the both directions of interactions.

Position in information exchange : The role in information transfer was measured by three measures. The first was betweenness centrality ; the number of times a participant played a role in coordinating interactions among otherwise unconnected collaborators [ 49 , 50 ]. Betweenness centrality is an indication of involvement in relaying arguments or argumentations in a forum. It is considered by some as an indicator of influence on the information exchange [ 28 , 54 ]. Higher betweenness centrality translates to a higher brokerage capital, and possessing a brokerage capital is a sign of creativity and prominence in spreading information and ideas in a network [ 22 , 28 , 35 ]. Lower values of betweenness centrality are a sign of difficulty in or indifference to reaching out to other members of the group without an intermediary or a mediator. The second indicator was closeness centrality , which is an indication of how close the user is to other participants—in other words, easy to reach and interact with. Higher values of closeness centrality reflect a reachable position in information exchange, and lower values can be viewed as a sign of social isolation and poor communications [ 27 , 34 , 49 , 53 ]. The third indicator was information centrality , which is an indicator of the amount of information flowing through a participant in a social network; having a position through which information flows is a privileged asset during information exchange [ 30 , 50 , 55 ].

Role in the group : For role identification, our analysis used a combination of visual analysis and centrality scores to label different roles of the participants [ 16 , 29 , 50 ]. The method is based on Marcos-García et al.’s detailed description of each role [ 29 ]. They specified three roles for the teacher: guide, facilitator, and observer. The case scenarios used in the three courses in our study required a facilitator role; a facilitator teacher monitors discussions, answers queries when required, supports collaborators with access to resources, and moderates conflicts. According to Marcos-García, Martínez-Monés [ 29 ], the SNA criteria for identifying a facilitator teacher based on these aforementioned duties are moderate participation levels (out-degree), reachability (closeness centrality), moderate or low influence (in-degree), medium to high mediation (betweenness centrality). Combining the SNA criteria with visualization helps clarify the relations and dynamics of the role. Regarding student role, Marcos-García, Martínez-Monés [ 29 ] identify a range of student roles ranked according to activity level (leader, coordinator, animator, active, peripheral, quiet and missing). Since our case scenarios are flexible, we expect students to be active (participatory), and we expect the emergence of other roles by some students such as coordinators (mediate discussions and partake in argumentations) and leaders (highly active, encourage others and mediate discussions). The SNA criteria for identifying these roles are as follows:

• Leader : A high level of activity (moderate to high out-degree, in-degree and degree centralities), an active role and good position in information transfer (moderate to high levels of betweenness centrality and closeness centrality.
• Coordinator : A moderate level of activity (moderate out-degree, in-degree and degree centralities), beside a good coordination position (moderate to high levels of betweenness centrality and closeness centrality).
• Active : The active role can be participatory (AP) , with moderate level of activity and interaction with other students, beside a moderate to low position in information exchange. An active non-participatory (ANP) role has minimal interactivity with other members (moderate to high levels of out-degree and very low in-degree levels).
• Peripheral : Low activity, low in-degree as well as a limited role in information exchange.

As for SNA parameters on the group level, we included group interactivity parameters (average in-degree, average out-degree and average degree). The average degree was calculated by dividing the total degree of all participants by the group size (the arithmetic mean), the average in-degree and average out-degree were calculated in the same way. Group cohesion was measured by density of interactions and clustering coefficient. Density is a measure of group cohesion and collaborative behavior that was discussed in details earlier while the average clustering coefficient is a measure of each group member tendency to interact with others. Since group SNA interactivity parameters overlap with IA indicators, for simplicity, we will report the SNA indicator in case of a duplicate construct.

Research ethics

This research was approved by the Medical Research Ethics Committee of Qassim University, College of Medicine. An online privacy policy that details possible use of data for research and user protection guarantees was signed by all participants. Learners’ data were anonymized, identifying and personal information was masked, and all personal or private information were excluded from analysis. The College privacy guidelines and policies of dealing with students’ data were strictly followed. It is worth noting that using the LMS is neither graded nor mandatory and the authors of this study did not participate in teaching or examination in any of the courses involved in the study.

The first mid-term (pre-intervention stage)

Visual analysis..

By the end of the first mid-term, data were collected and analyzed by means of social network analysis. Fig 1 presents a sociogram of all interactions in the three courses. The sociograms were configured so that size of the node corresponds to the total number of interactions (degree centrality). The sociograms showed the following:

• Most interactions were targeting the teacher (an instructor-centric pattern), seen as arrows pointing towards teacher nodes, and as thick arrows (frequent interactions). This was most obvious in course A, followed by course B, and then C. In a collaborative environment, we expect a facilitator teacher or a moderator in a non-dominating role.
• Student-to-student interactions were scarce, as demonstrated by very few inter-connections between student nodes in course A, very few interconnections in course B, and few thin lines in course C. The paucity of student interactions is another sign of poor collaboration.
• The degree centrality (sum of incoming and outgoing interactions) of teachers was far larger than for any student, seen as larger teacher nodes compared to those of the students. Teacher-to-student interactions were scarce, except for course C, which showed moderate interactions, seen as bidirectional arrows; an example can be seen in Q1-G8, Q1-G12, Q1-G14, Q1-G24 and Q1-G32. A combination of high degree centrality and few students’ connections means teacher received many interactions, yet they replied infrequently. That implies that students might not have received enough feedback from teachers.
• Teachers had high betweenness centrality (dark green colored nodes), compared to low betweenness centrality of students (light nodes), which indicates that students played little role in relaying information or connecting others in conversations.

Each circle (node) corresponds to a participant. Node size is proportional to the degree centrality (sum of incoming and outgoing interactions). Arrows between nodes represent interactions, and the thickness of the arrows represents frequency of interactions. The arrow heads point to the target of interaction. The color range corresponds to betweenness centrality.

https://doi.org/10.1371/journal.pone.0194777.g001

To demonstrate the information giving network , the size of nodes was configured by out-degree centrality (outgoing interactions), where students with more posts have larger nodes. The sociogram in Fig 2 shows that nodes corresponding to students were larger than those in Fig 1 . In course A and B many student nodes were larger than the instructor node, indicating that the students wrote more posts than the instructor did. However, the color of the nodes, which was configured to reflect in-degree centrality, shows many very light colored nodes, which indicates that students only gave information or answered queries and had not received interactions from neither peers nor the instructors, so they neither negotiated their arguments, debated others nor got feedback from the instructor.

Each circle (node) corresponds to a participant. Node size is proportional to the out-degree centrality (sum of outgoing interactions). Arrows between nodes represent interactions, and the thickness of the arrows represents frequency of interactions. The arrow heads represent the target of interaction. The color range corresponds to in-degree centrality.

https://doi.org/10.1371/journal.pone.0194777.g002

To better visualize information transfer across the network, we plotted information centrality graph in Fig 3 . Information centrality is a measure of each participant’s role in information transfer (how much information traffic passes through a node). The nodes close to the center have a leading role in information transfer, and more distant nodes have more minor roles. The three plots show a common pattern, where the instructors D1, T1, and Q1 occupy a central spot and students lie few steps from the center, indicating that the instructors were dominating rather than facilitating the discussions.

The closer the node is to the center, the more important role it has in information transfer, so D1, T1 and Q1 (the teachers) are the center of information transfer in the networks.

https://doi.org/10.1371/journal.pone.0194777.g003

Quantitative analysis.

Looking at the interaction analysis parameters (number of posts and topics in Table 1 , and the average degree and out-degree centralities in Table 2 ) shows that the three courses were active on both group and learner level. However, looking at the SNA centrality measures in Table 2 and the roles students played in discussions in Table 3 , a different picture unfolds. While the level of activity was high as measured by out-degree or number of posts, in Course A each student received a reply for each 35 posts, but in Course B the ratio was one to seven. This significant imbalance is a sign of absence of interactions among students and poor collaboration. Furthermore, most students had a very limited role in information exchange, as manifested by low betweenness and information centrality scores, although being reachable (having moderate closeness centrality).

The table lists mean centrality scores in SNA constructs, level of activity and position in information exchange in the three courses before intervention. The reported values of betweenness, closeness, and information were normalized by Gephi.

https://doi.org/10.1371/journal.pone.0194777.t002

AP = Active participatory, Active Non-participatory = ANP, P = Peripheral.

https://doi.org/10.1371/journal.pone.0194777.t003

Using the role definitions described earlier in section 2.5 to interpret the different roles played by students; the results tabulated in Table 3 show that only 15 (18.3%) of students were active and participatory, and the majority of roles were not participatory (did not participate in discourse, exchange information or negotiate with others), around third of students were peripheral (rarely participated).

Based on the visualization and quantitative analysis, we can conclude that the three courses had a non-collaborative pattern of interactions, very few interactions among students, and limited information exchange or negotiation. Students’ network of information exchange was very limited and dominated by the teacher.

The intervention

The intervention aimed at improving the shortcomings in the online collaborative learning regarding the three constructs identified in the monitoring stage (scarce student-student interactions, instructor-centric pattern and poor participation of students in information exchange /negotiation). The intervention was driven by previous recommendations of research in the field of SNA, which called for monitoring and guiding communicational activities as a means to a more efficient collaboration, namely interactivity [ 19 , 20 ], position in information exchange [ 8 , 22 , 26 , 27 ], role in the collaborative group [ 16 , 23 , 29 ], and group cohesion [ 27 , 30 ]. It was also inspired by evidence that encouraging certain procedures and practices that enhance online collaborative practices would positively enhance learning and improve learning outcomes [ 2 , 3 , 11 , 12 , 45 , 46 , 56 ]. The intervention was structured into five actions: increasing awareness, promoting online collaboration, improving the content and content negotiation through scripting, preparing teachers, and finally practicing with feedback. The main part of the intervention was a full day workshop to implement the awareness, training, and practice. The design followed principles suggested by Johnson et al. [ 57 ] and Abrami et al [ 12 ] through the following steps.

• Awareness : Participants were shown anonymized SNA visualizations and transcripts of the first mid-term online discussions. They commented and reflected upon them and suggested improvements. We stressed the importance of participation of all members in future discussions to their learning and highlighted the social and cognitive benefits of contribution [ 3 ].
• Attitude: Emphasizing the importance of positive attitude and behavior in the training, namely: 1) Positive interdependence (each participant’s success positively enhances the success of his or her peers); 2) Individual accountability (each participant is responsible for his or her own learning as well as for helping other participants learn.)
• Promoting interactions: Encouraging participants to help each other analyze and understand the concepts in discussions, share relevant knowledge and resources, promote effective feedback, and work constructively towards a common goal.
• Group processing and social skills: Training participants to evaluate their own and group contribution to ideas, listening to arguments, and encouraging each other’s participation.
• Teacher training : Teachers were trained on how to facilitate online discourse, engage students in discussions, and stimulate debates [ 21 , 58 ]. The teachers were encouraged to use clinical cases that are integral to the curriculum objectives, match them to students’ individual learning needs, and motivate the use of prior knowledge, clinical reasoning skills, and argumentation [ 12 ].
• Content : Content was improved by using a flexible collaborative script approach; clarifying the objectives, types of activities, sequencing, and explaining roles in order to prevent students from rushing to final conclusions or solving the clinical problem, and to engage the students in a meaningful discourse [ 14 , 20 , 39 , 40 ]. Such scripting can rectify the instructor centric role problems by stimulating students to negotiate together and use teachers as facilitators. Scripting might also have a positive effect on students’ position in information exchange [ 14 , 20 , 40 ]. The online case scenarios were re-structured so that they provided explicit learning objectives; the general objectives were to discuss the clinical reasoning of each case clinical presentation, and how to approach the patient regarding investigations and management plan. Students were advised to start by discussing the clinical findings of the case, the significance of patients’ symptoms and signs, then suggest investigations and proceed later to diagnosis and management. They were advised to debate each other’s approach, provide alternative explanations or plans. Each case scenario was followed by initiating questions about the case, such as “How can you link the case presentation to a certain laboratory finding”, “Should we monitor the patient during treatment and why”, or “what alternative diagnosis you should consider and how to rule it out”. The instructions were flexible regarding specific student roles, the aim was to simulate real life case discussions where in most occasions doctors have comparable roles. Emphasis was laid on participating, following the sequence suggested, offering different perspectives, proposing alternate approaches, and debate/agree with each other’s point of view. Moreover, students were assured that activities are not graded and that reaching a diagnosis is not appreciated better than any other type of interaction. We expect some roles to emerge during collaborative interactions, as students might take the coordinator role and connect different points of views, few others might take the leadership role and the majority to take an active participatory role. Regarding the teachers’ role, they were asked to facilitate, support when asked, and interfere when required in cases of conflict.
• Practice and feedback : Students were allowed to practice in a training online environment, for which they were given feedback and guidance. In addition, a simulation video was published on the front page of the LMS explaining how to participate effectively in a collaborative discussion.

The second mid-term (post-intervention stage)

The analysis of the second mid-term by means of social network analysis revealed a picture different from the first mid-term, with improvement across the three constructs of SNA that we used as basis of the monitoring strategy, especially level of interactions among students, role in information sharing, and role in groups. As shown in Fig 4 , which gives an overview of all interactions in the three courses, there was a marked increase in student-student interactions, reflected in dense and thick interconnections between students’ nodes. Teacher-student interactions also increased significantly; this was most marked in courses C and B, and to a lesser extent in course A. An important development is the appearance of “coordinator students,” who had high betweenness centrality seen as dark green nodes, and who were involved in relaying and connecting other peers.

Each circle (node) corresponds to a participant. Node size is proportional to the degree centrality (sum of incoming and outgoing interactions). Arrows between nodes represent interactions, and the thickness of the arrows represents frequency of interactions. The arrow heads represent the target of interaction. The color range corresponds to betweenness centrality.

https://doi.org/10.1371/journal.pone.0194777.g004

Similarly, the information giving network ( Fig 5 ) has improved in a number of ways; compared to the instructor, students’ participation has increased (seen as bigger students’ node sizes indicating higher out-degree centrality). Several students have received more interactions (seen as dark green colored nodes indicating higher in-degree centrality) compared to very few before, indicating more student-student interactions and a distribution of interactions among most members of the groups. In contrast to the first mid-term, Figs 4 and 5 show participatory networks where students interact together, more students play an active role the discussions and mediating information. Regarding information negotiation, the information centrality plot in Fig 6 shows more students closer to the center of the plot in each course, which indicates that more students played a role in information transfer, significantly improving from the first mid-term.

https://doi.org/10.1371/journal.pone.0194777.g005

The closer the node is to the center, the more important role it has in information transfer, more students are close to the center compared to the pre-intervention.

https://doi.org/10.1371/journal.pone.0194777.g006

Following the visual analyses, a statistical analysis of IA parameters and SNA indicators were performed on both individual and group levels. A comparison was made between the two measurement periods using data from all courses combined as well as on the individual course level.

Fig 7 compares the centrality measures corresponding to three constructs of SNA, level of activity, role in information exchange. The Shapiro-Wilk test of normality showed that most centrality measures did not follow a normal distribution, so a non-parametric test, Wilcoxon Signed Ranks test, was conducted to compare pre-intervention to post-intervention results. The test ranks students according to their activity level and compares their ranks across two points of measures. The Wilcoxon test was performed on the general level, including data from all students in the three courses combined in Fig 7 , as well as on individual course basis. Results of all students showed a statistically significant positive improvement in all measures of centrality across the three constructs. The improvement was more marked in the information exchange indicator; information centrality increased in 98.8% of the students, followed by reachability (closeness centrality). The significant change in information centrality as well as the other centrality measures is an indication of a shift towards efficient information exchange in the network. Full details of all significant centrality measures are shown in Fig 7 .

The figure shows the number of students who had their positions improved, students who did not change and students who declined in the three centrality constructs (Level of activity and position in information exchange). The test compares students’ ranks across the two points of measures (Pre-and post-intervention). A positive rank is an improvement in centrality score, a negative rank is a decline.

https://doi.org/10.1371/journal.pone.0194777.g007

Regarding individual courses, there was a consistent and significant improvement in most of the SNA centrality measures corresponding to role in information exchange. Full details are available in Table 4 .

The table shows the number of students in each course who had their positions improved, students who did not change and students who declined in the three centrality constructs (Level of activity and position in information exchange). The test compares students’ ranks across two points of measures (Pre-and post-intervention). A positive rank is an improvement in centrality score, a negative rank is a decline.

https://doi.org/10.1371/journal.pone.0194777.t004

The third construct of SNA we investigated was the roles. The analysis revealed that, in contrast to the first midterm, in each course, more students played an active collaborative role. Moreover, new roles emerged: six leaders and four coordinators compared to none before. There was also a significant increase in active participatory roles from 15 to 40, and consequently decrease in non-participatory roles from 67 to 32 students. Table 5 presents full details on role changes, including per-course roles.

L = leader, C = Coordinator, AP = Active, participatory, Active Non-participatory = ANP, P = Peripheral.

https://doi.org/10.1371/journal.pone.0194777.t005

On the group level.

There was an improvement in all group properties that reflect the quality of collaboration. The average in-degree centrality, which reflects student-student interactions, increased by 1827.7% in course A, 244.3% in course B and 166.3% in course C. Similarly, the network density, which is a measure of group cohesion, increased by 293.2% in course A, 142.7% in course B and 132.1% in course C. Clustering coefficient, a measure of how much members tend to interact together, also increased significantly in all courses, most markedly in course A by 580%, full details are presented in Table 6 . The reason for the change is that students directed all their efforts to their course instructors rather than engage in a constructive discussion. Their replies were often a reiteration of the same contribution of their peers, thinking that teachers evaluate them by how much they participate. This approach was discouraged and students were advised to start by analysis of the clinical case, summarize the important points, elaborate and build on each other’s perspectives, discuss, debate or offer a different approach, relate information to what they learnt and interdependently reach a solution to the problem.

The table compares the average values of interaction parameters (Degree, In-Degree, Out-degree) and group cohesion indicators of each course across the two points of measurement. There is a significant increase in cohesion indicators in each course. AV = Average, Co = Coefficient.

https://doi.org/10.1371/journal.pone.0194777.t006

The marked increase in in-degree, density and clustering coefficient are signs that interactions in the second midterm included wider range of participants and were more collaborative, groups became more cohesive and cooperative, and many students were a part of the positive change. Degree centrality and out-degree (can also be considered as interaction parameters) were also better in the second mid-term except for course B. However, these are measures of volume of participation and were not considered a target for our intervention.

Dynamic networks

For a demonstration of the timeline of events that formed the full picture described above in terms of visualization and quantitative analysis, we compiled all interactions in the largest course (course B) along with their respective timestamps in an animated video showing each interaction as it happened in a time-lapse video. In S1 Video , the first midterm (left side) shows a network as it forms, dominated by the teacher with very few student-student interactions. Later, during the course, a similar pattern of interactions continues, but with some exchange between students. The second midterm (left side) shows a participatory network forming from the first day. The teacher participates but does not dominate, interactions are distributed among a wide range of members, the participatory pattern continues throughout the whole course, and the teacher continues to be a moderator, but is no longer the center of all interactions.

To further illustrate the dynamics of interaction at the individual discussion level, the largest discussions of course B were chosen; one from the first midterm and another from the second midterm, since the largest discussions contained many enough interactions to illustrate the patterns. S2 Video shows both discussions side-by-side. The left side shows a clear teacher-centered pattern of interaction. Interestingly the replies are immediate, and all are responses to the teacher. The right side shows a more relaxed rate of interactions, and students take considerable time between each interaction. Many members are participating, S4 and S5 being the most prominent members of the group along with the teacher.

The process of learning analytics is a closed loop that starts by data collection, followed by data analysis to generate insights, which are later used to design interventions or make informed decisions [ 44 , 59 , 60 ]. Closing the loop by creating an appropriate intervention is a key step towards successful learning analytics, and assessing the efficacy of the intervention is another essential step towards improving and refining the whole process [ 59 ]. This research study was conducted to assess the value of the full cycle of learning analytics using SNA in monitoring online collaborative learning to diagnose possible gaps or pitfalls, design an appropriate intervention, and test the efficacy of that intervention. The collaboration analysis we used relied mainly on SNA visual and quantitative analysis. Our monitoring included three SNA constructs for each participant, these constructs were first, the level of interactivity of each participant; second the role and position in information exchange and third, the role played by each participant in the collaboration. On the group level, we included interactivity and group cohesion indicators.

Regarding the level of activity, the statistics reported by our interaction analysis showed high level of posts and high activity, seemingly demonstrating sound collaborative activity. However, using SNA proved otherwise. The interactions were not participatory or collaborative. In fact, there were very few interactions among students, limited information exchange or negotiation, and students’ networks were very limited and dominated by the teacher. Using SNA derived insights helped expose the non-participatory interaction patterns, as well as flag some dissatisfactory aspects in collaborative learning that were amenable to intervention. The intervention stimulated student-student interactions, teacher-student interactions, as well as facilitated a collaborative pattern of interactions among students facilitated by the teachers. Ensuring that CSCL are truly interactive and collaborative is a worthwhile effort and deserves the due attention of teachers and learning designers as well. Bernard, Abrami [ 56 ] synthesized the evidence from a review of 74 studies and concluded that increasing interactivity between peers, instructors, or content positively affects learning. They reported a significant adjusted average effect of 0.38. They speculated that interaction leads to fostering of internal mental processes, namely meaningfulness and cognitive engagement [ 56 ]. Further evidence has been recently reported in a meta-analysis by Borokhovski, Bernard [ 5 ], whose primary finding was that courses designed to support collaborative learning by planning activities that promote student-student interaction significantly add to learning [ 56 ].

Using SNA to monitor students’ position in information exchange and negotiation has proved useful in uncovering their limited role, which if left unmanaged might affect the collaborative knowledge construction [ 27 , 34 , 37 ]. Our intervention, based on the conducted SNA monitoring, encouraged students to play a more active role, motivated some to moderate discussions and help bond their unconnected peers. Peer moderation of CSCL has affective, cognitive and performance benefits as well as positive effect on engagement and participation [ 8 , 27 , 34 , 37 ].

In contrast to IA, which describes roles played by students in terms of quantity. SNA methods helped reveal several dimensions of the collaborative role such as cooperative behavior, brokerage of information, reach and sphere of influence, besides outlining the relation to other collaborators through visualization. Mapping the roles in this study helped identify the ostensibly active however non-participatory roles that were addressed in the intervention. The proper identification and support of roles played by students can greatly enhance the success of the collaboration process, whether the roles were explicitly defined or emerged during interaction [ 29 , 39 ]. Furthermore, SNA revealed a non-collaborative instructor-centric role; the teacher assumption of a controlling role, where information flows in a teacher-to-student hierarchical mode is expected to affect collaborative learning negatively [ 11 , 58 , 61 ]. A collaborative role can be a moderator, a facilitator, a helper, or a “guide on the side” [ 7 , 11 , 21 ]. Since interaction with teachers can positively influence student academic achievement [ 56 ] and predicts good performance [ 44 , 62 , 63 ], it was important to identify and manage the roles played by teachers [ 12 , 21 , 58 ]. The last monitoring target of our study was group interactivity and cohesion. Using SNA indicators of cohesion such as density and clustering coefficient reflects the diversity of contributions and the tendency of group members to work together and externalize their understanding [ 32 ]. Since participatory and cohesive groups are stable, efficient and cooperative [ 22 , 32 – 34 ], it is an important target for monitoring so that an informed action can be taken when needed [ 33 , 34 ].

In this study, we used two types of SNA analysis: visual (instant and cumulative at the end of each term) and quantitative analysis. Visualization of interactions offered a convenient general overview of the status of online collaborative learning. The main strengths of visual analysis lied in the extent of information it offered and the ability to quickly render thousands of posts. The analysis was quick to produce, effortless, and updated instantly. It helped to identify a non-collaborative teacher-centered pattern of interactions (hierarchical pattern), map the relations between collaborators and the information exchange networks. The quantitative analysis complemented the visuals by adding a more accurate quantification of level of activity by participants, how they participated in information exchange, their personal networks and offered a platform for identifying the role they played.

These results have implications on different levels. Administrators and instructors need to realize the importance of quality over quantity: high number of discussion posts is not a good sign of collaboration unless those interactions are participatory [ 6 , 9 , 11 , 22 ]. SNA enables evaluation of the participatory nature of those discussions so they can meet the intended objectives of the course. For students, automated or semi-automated feedback on their contributions can help improve their performance, enhance their team working skills, foster interdependence, and improve the way they contribute to knowledge construction [ 3 ]. For teachers, automatic evaluation of participation quality in a course can be used to inform teachers about problem spots, or to trigger automatic adjustments and interventions, enabling teachers to focus their efforts elsewhere.

Using SNA for evaluating collaborative online learning has its limitations; for example, a reliable automated content analysis could have helped enhance the way we evaluate collaborative learning. However, educational data mining (EDM) tools are difficult to use or interpret by teachers, subject to misinterpretation with no uniform vocabulary or a framework for reporting results [ 64 ]. The manual methods require effortful coding and analysis, which may render this time-consuming process challenging to implement, especially for courses with thousands of posts [ 22 ]. The methods used to extract SNA data could be considered another limitation; they were not easy to implement and required technical proficiency not available for educators without technical training.

Conclusions

This study investigated the potential of using social network analysis in monitoring online collaborative learning, finding gaps and pitfalls in application, and the possibility of guiding an informed intervention. SNA-based visualization helped to analyze thousands of discussion posts. The automated SNA visual analysis was quick to produce, updated in instantly, and was easy to interpret. The combination of visual analysis and quantitative analysis enabled us to identify a non-collaborative teacher-centered pattern of interactions in the three courses studied, very few interactions among students, and limited information exchange or negotiation. Students’ network of information exchange was very limited and dominated by the teacher. The information derived from the monitoring enabled us to design a relevant data-driven intervention, and assess its efficacy using experimental, observational, repeated-measurement design. The intervention was able to significantly enhance student-student interactions and teacher-student interactions, improve information exchange, group cohesion as well as achieve a collaborative pattern of interactions among students and teachers. Since efficient, communicative activities are an essential prerequisite for successful content discussion and the realization of the goals of collaboration, we assume that our SNA-based approach can positively affect teaching and learning in many educational domains. Our study offers a proof of concept of what SNA can add to the tools we have to monitor and support teaching and learning in higher medical education.

Supporting information

S1 video. an animated compilation of interactions in course b..

For a demonstration of the timeline of events that formed the full picture, we compiled all interactions in the largest course, showing each interaction as it happened in a time-lapse video. In S1 video, the first midterm (left side) shows a network as it forms, dominated by the teacher with very few student-student interactions. The second midterm (left side) shows a participatory network forming from the first day.

https://doi.org/10.1371/journal.pone.0194777.s001

S2 Video. An animated compilation of interactions in two sample discussions.

To further illustrate the dynamics of interaction at the individual discussion level, the largest discussions of course B were chosen; one from the first midterm and another from the second midterm, S2 video shows both discussions side-by-side. The left side shows a clear teacher-centered pattern of interaction. The right side shows a more relaxed rate of interactions, and students take considerable time between each interaction. Many members are participating, S4 and S5 being the most prominent members of the group along with the teacher.

https://doi.org/10.1371/journal.pone.0194777.s002

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Social Network Analysis: How to Get Started

Social network analysis is a great way to analyze relationships. Here’s how to build your own network graph.

Networks are all around us  —  road networks, internet networks and online social networks like Facebook. While this article focuses on social network analysis (SNA), these techniques will give you valuable tools to gain insight on a variety of data sources.

In order to build SNA graphs, we need two key components: actors and relationships. We commonly use SNA techniques with the internet. Web pages often link to other sites  —  either on their own website or an external page. These links can be considered relationships between actors (web pages) and this is a key component of search engine architecture.

What Is Social Network Analysis?

What does a social network graph look like.

A social network graph contains both points and lines connecting those points  —  similar to a connect-the-dot puzzle. The points represent the actors and the lines represent the relationships. An example of a social network graph would be this one, which demonstrates  community detection of ISIS Twitter accounts .

More From Mitch Ditch Your Passwords — They’re Only Hurting You

What Tools Do I Need to Get Started?

Like many things in data science, there are a variety of tools you can use to conduct SNA. This guide focuses on a specific set of tools in order to get you started making network graphs and conducting analysis on them. In no way are these the only or best tools available.

We’ll use Gephi , a free software for Mac, PC, and Linux, in order to build network graphs and run some analytics on them. Gephi provides a GUI interface (seen below) and will not require any coding. 

Python/Excel

In order to build network graphs in Gephi, we’ll need to use a specific data format and we’ll need to fit our data in the correct format (CSV files). With simple data, Excel should suffice. However, when using large amounts of data or data that must have its relationships extracted, I recommend Python. Don’t fret if you don’t have any Python skills — you should still be able to build basic networks.

Data Source

You’ll also need a data source for your network. Network data have two requirements: actors and relationships. Some data will require these relationships to be extracted, and others will be more explicit. I recommend using data sets from Kaggle to get started, such as:

Marvel Universe Social Network

Wikipedia Article Network

Deezer Social Network

Defining Our Terms

Nodes and edges.

Up until now, I’ve referred to both actors and relationships. In network science, actors are referred to as nodes (the dots on the graph) and relationships as edges (the lines on the graph).

Nodes can represent a variety of actors. For example, in internet networks nodes can represent web pages while in social networks nodes can represent people. While nodes can represent a variety of things, each node always has a relationship with another thing.

Edges can represent a variety of relationships. In internet networks, edges can represent hyperlinks and in social networks edges can represent connections. Nodes and edges are a key concept in networks, so make sure you have a good understanding of them before tackling the other concepts.

Edge Direction

There are two types of edges: directed and undirected. It will be necessary to decipher what type of edge your data contains when building a network graph. 

Directed edges are applied from one node to another with a starting node and an ending node. For example, when a Twitter user tags another Twitter user in a tweet, that relationship is directed. The user who wrote the tweet (starting node) applied that relationship to the user who they tagged (ending node). The tagged user has not necessarily reciprocated that relationship. Another example of a directed edge are payments. If a customer (starting node) pays a coffee shop (ending node) for a coffee, that relationship is not necessarily reciprocated because the coffee shop has not also paid the customer.

Undirected edges are the opposite of directed edges. These relationships are reciprocated by both parties without a clear starting node or ending node. For example, if two people are friends on Facebook, that relationship is undirected. This is because person A is friends with person B, but we can also say person B is friends with person A.

Edge Weight

An edge’s weight is the number of times that edge appears between two specific nodes. For example, if person A buys a coffee from a coffee shop three times, the edge connecting person A and the coffee shop will have a weight of three. However, if person B only buys coffee from the coffee shop once, the edge connecting person B and the coffee shop will have a weight of one.

Centrality Measures

Centrality is a collection of metrics used to quantify how important and influential a specific node is to the network as a whole. It’s important to remember that centrality measures are used on specific nodes within the network, and don’t provide information on a network level. There are several centrality measures, but this guide will cover degree, closeness and betweenness.

A node’s degree is the number of edges the node has. In an undirected network, there’s only one measure for degree. For example, if node A has edges connecting it to node B and node D, then node A’s degree is two.

However, in a directed network, there are actually three different degree measures. Because these edges have a starting and end node, the in-degree (number of edges the node is an end node of), out-degree (number of edges a node is a starting node of), and degree (number of edges a node is either a starting node or end node of) can be calculated.

Closeness measures how well connected a node is to every other node in the network. A node’s closeness is the average number of hops required to reach every other node in the network. A hop is the path of an edge from one node to another. For example, node A is connected to node B, and node B is connected to node C. For node A to reach node C it would take two hops.

Betweenness

Betweenness measures the importance of a node’s connections in allowing nodes to reach other nodes (in a hop). A node’s betweenness is the number of shortest paths the node is included in divided by the total number of shortest paths. This will provide the percentage of shortest paths in the node’s network.

Network-Level Measures

We can also calculate metrics on the network level to evaluate the entire network instead of merely a single node. Like centrality measures, there are a variety of network-level measures. We’ll look at size and density.

Network Size

Network size is the number of nodes in the network. The size of a network does not take into consideration the number of edges. For example, a network with nodes A, B, and C has a size of three.

Network Density

Network density is the number of edges divided by the total possible edges. For example, a network with node A connected to node B, and node B connected to node C, the network density is 2/3 because there are two edges out of a possible three.

Path-Level Measures

Path-level measures provide information for a path between one node and another node. Paths follow edges between nodes, known as hops. There are also many different path-level measures, but we’ll look at length and distance.

Length is the number of edges between the starting and ending nodes, known as hops. We must predetermine a path in order to calculate the length between two nodes. 

Distance is the number of edges or hops between the starting and ending nodes following the shortest path. Unlike length, the distance between two nodes uses only the shortest path  —  the path that requires the least hops.

Read More From Our Experts What Is Multiple Regression?

Connected Components and Bridges

Not all nodes in a network will necessarily be connected to each other. A connected component is a group of nodes that are connected to each other, but not connected to another group of nodes. Another way of thinking of this is a group of connected nodes that have no path to a node from another group. Depending on the network, there can be many connected components, or even only one. The diagram below shows a network with two connected components.

A bridge is a node that when removed, creates a connected component. Another way of thinking about it is that a bridge is a node that is the sole connection of a group of connected nodes to another group of connected nodes.

Hubs and Authorities

Hubs and Authorities are node classifications used in directed networks. A hub is a node that has many edges pointing out of it. You can also think of a hub as a node that’s the starting node of many edges. An authority, on the other hand, is a node that has many edges pointing to it. You can also think of authority as a node that is the ending node of many edges. There’s not a pre-determined number of edges that makes a node a hub or an authority; it will depend on the network. In addition, remember that not all nodes in a directed network will be a hub or an authority.

Dyads and Cliques

Dyads and cliques are pairings of nodes connected by edges. A dyad is a pairing of two nodes, while a clique is a pairing of three or more nodes. While a dyad or clique may be a connected component, they can also be part of a larger connected component.

Implementation

Now that you have an understanding of social network analysis terms and concepts, this guide will walk you through applying these techniques to a data set using Gephi

Download and Install Gephi

First, download and install the Gephi software for the operating system your machine is running. Gephi is available for Mac, PC, and Linux .

More Built In Tutorials Create a Linux Virtual Machine on Your Computer

For this guide, we’ll be using the Marvel Universe Social Network data set from Kaggle . While this data set is already laid out with a node and edge list, when working with data sets not structured as a network this will require some data transformation skills. I recommend using Python and Pandas in these situations.

After downloading the data set, there will be three csv files: nodes, edges, and network. Open the file nodes.csv in Excel.

The nodes file contains a list of all the nodes in the network. This file has two columns: node and type. This network contains two different types of nodes that represent different actor types: heroes and comics.

There is no data preparation needed to import this node list into Gephi, so we’ll close the file.

Next, open the file edges.csv in Excel.

The edges file also contains two columns: hero and comic. Each row in this table represents a single edge. The hero node and comic node are the two nodes connected by the edge.

In Gephi, an edges table requires the column headers of “source” and “target.” In an undirected network it doesn’t matter which node is in which column. However, in a directed network the source column contains the starting node and the target column contains the ending node. Rename column A to “source” and column B to “target.” Then save the file.

Loading Network Data into Gephi

Now that the node and edge lists are properly formatted for Gephi, it is time to load the data.

Open the Gephi software. It should look like this:

Click on new project. If you don’t see the welcome screen, go to file>new project.

Then, click the data laboratory tab.  

The data laboratory tab is where we’ll load in our edge and node list files. To import a list click the import spreadsheet button.

Then navigate to the folder containing the data sets and open the nodes file.

An import wizard will then walk you through correctly importing the node list. Set separator to comma, import as to nodes table, and charset as UTF-8. Then click next.

After clicking next, the wizard will provide additional setting configurations. Set time representation to intervals. For imported columns, check the node and type boxes and set their data types to string. Then, click finish.

There is one more step in importing the nodes list. Set graph type to undirected and edges merge strategy to sum. Ensure that it’s set up to append to the existing workspace. Then, click OK.

You should now see some data in the data laboratory window! Next we need to import the edges list.

Now that you’ve imported the  data it’s s time to view the graph. Click on the overview tab.

Using Layout Functions

You might be disappointed in the graph that was visualized. It will likely look like the black mess below.

In order to make the graph more readable, we’ll need to use a layout function to change the position of nodes in the graph.

There are a variety of layout functions in Gephi but let’s focus on the ForceAtlas 2 function for now. Select this function and then click run. You’ll see the nodes move in real-time, and you can stop the function when you like the nodes’ position.

After running the layout function your graph should look something like the one below. You can continue to play with other layout functions if you wish to get a better node position. While we’re using the stock ForceAtlas 2 parameters, changing them can give you better control over the node positions. In addition, you can change the parameters of layout functions.

Calculating Network-Level Measures

Now let’s calculate  the network size and density of this Marvel network.

The network size is easy to find. In the upper right-hand corner is a pane called context. This window provides the number of nodes and edges in the graph. Because a network’s size is the number of nodes in it, the network size of our Marvel network is 19,090.

To find the network density, we’ll take our first dive into the statistics window. Click on the statistics tab.

This is what you should see:

The statistics window contains many measures that can be calculated on the network. To find the network density, click run for graph density.

Select undirected, and then click OK.

A new window will pop up showing the results. This Marvel network has a density of 0.001.

You can save this report by clicking the save button in the bottom left-hand corner, or close it by clicking the close button in the bottom right-hand corner.

Calculating Centrality Measures

Recall that centrality measures are on a node-level, and not a network-level. However, we can also average centrality measures to get a network-level metric. In Gephi, you calculate centrality measures as a network-level average, which then also inputs the centrality measure on a node-level into the data laboratory tab.

Node Degree

To calculate node degree, click run on the average degree algorithm in the statistics window.

The report will provide you with the average degree for the network, as well as a distribution graph. While these can be useful in some applications, we are more interested in the degree on a node-level. Close the report.

To see the degree for each node in the network, go back to the data laboratory window and click on the node table. You will see a new column in the data titled degree.

Node Closeness and Betweenness

Calculating node closeness and betweenness is a similar process as calculating node degree. In the statistics window, click run on the network diameter algorithm.

Select undirected and click OK. Depending on the specs of your machine this may take a little while to calculate.

Like with the node measure, Gephi will provide a network-level report. Click close on this report and go to the data laboratory.

In the data laboratory, you’ll find additional columns in the node table including the node betweenness and closeness.

Calculating Edge Weights

Edge weights are auto-calculated in Gephi. You can find them in the edge list within the data laboratory.

Using Color in Network Graphs

Currently, our graph nodes and edges are black, providing no additional information. You can color-code both nodes and edges in Gephi. The coloring options are in the appearance window.

To color-code the nodes of the graph based on the node degree, click on the nodes button and the color palette button in the appearance window.

There are three options to encode information in the color of nodes: unique, partition and ranking. If you want to change all the graph’s nodes to the same color, use the unique window. Partition will break the nodes into color-coded groups. Ranking will color-code the nodes on a scale.

Let's color the nodes by their degree. To do this, click on the ranking section and select degree.

A color scale will be used to color the nodes. To select a new scale, click on the color selector button to the right of the color scale.

You can select any color scale to use. Then click apply.

As you can see in the above image, coloring our nodes also colored our edges. You can change the color of edges to a specific color using the unique color tab for edges, or apply a ranking or partitioning color scale to them.

Using Size in Network Graphs

You may also notice that the majority of the graph is colored red. This is because most nodes in the graph have a low degree. Zooming in will show that some nodes are yellow or blue.

To make these nodes easier to see in the graph let’s scale the size of the nodes to the node degree as well. To do this click on the nodes and size buttons in the appearance window.

Then, click on ranking and select degree. Change the minimum size to 1 and the maximum size to 100.

Then click apply. We can now better see what nodes have a high degree.

Changing Background Color

Let's also change the background from white to black. Depending on the colors in a graph, either color may look better and it’s often up to personal preference. To change the color to black, press the lightbulb button.

More from Expert Data Scientists How to Write Good Pseudocode

Putting It All Together

This should get you started as you make your first network graph using the Marvel data set and I encourage you to continue playing around with this graph in Gephi. There are many more measures you can calculate and other appearances you can use.

Your next step should be to take another data set and try to reproduce these steps. Eventually, you can try to collect your own data and transform it into a new social network data for analysis.

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• Original Article
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Social network analysis in innovation research: using a mixed methods approach to analyze social innovations

• Nina Kolleck 1  

European Journal of Futures Research volume  1 , Article number:  25 ( 2013 ) Cite this article

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The importance of social networks for innovation diffusion and processes of social change is widely recognized in many areas of practice and scientific disciplines. Social networks have the potential to influence learning processes, provide opportunities for problem-solving, and establish new ideas. Thus, they can foster synergy effects, bring together key resources such as know-how of participating actors, and promote innovation diffusion. There is wide agreement regarding the usefulness of empirical methods of Social Network Analysis (SNA) for innovation and futures research. Even so, studies that show the chances of implementing SNA in these fields are still missing. This contribution addresses the research gap by exploring the opportunities of a mixed methods SNA approach for innovation research. It introduces empirical results of the author’s own quantitative and qualitative investigations that concentrate on five different innovation networks in the field of Education for Sustainable Development.

Introduction

Scholars interested in innovation processes and futures research have often stressed the importance of social networks. Social networks are seen as an important factor in how ideas, norms, and innovations are realized. Social network research understands individuals within their social context, acknowledging the influence of relationships with others on one’s behavior. Hence, social networks can promote innovation processes and expand opportunities for learning. Despite the consensus regarding the value of social network approaches, there is a lack of empirical investigations in innovation and futures studies that use Social Network Analysis (SNA). In most cases, the scientific literature uses the concept of social networks metaphorically, ignoring the chances presented by SNA methods. At the same time, conventional empirical research in innovation and futures studies often disregards relational information. Hence, analyses of statistical data on structural and individual levels are treated as separately. Activities that are expected to have impacts on future developments are usually modeled as isolated individual or group behavior, on the one hand, or as the characteristics of structural issues, on the other hand. SNA provides us with empirical tools that capture the social context and help to better understand how innovations are implemented and diffused and why social change takes place. Network approaches explicitly challenge the difference between deduction and induction and highlight the relevance of relationships. Individuals both shape and are shaped by the social context in which they interact. By applying techniques of SNA, actor-centered and structuralist reductions are avoided. Instead, SNA emphasizes the mutual influence of structure and social connections. In order to better understand and model developments in innovation and futures research, relational data inherent to the social network perspective is needed.

This contribution addresses the opportunities of SNA for innovation research. It is divided into six sections. After this introduction , the second section briefly defines crucial concepts of SNA and provides theoretical background. The third section discusses the value of a social network perspective for innovation research. The methodological approach, along with the empirical case studies used, is outlined in the fourth section. The fifth section shows how a combination of both insights from structure based on quantitative SNA and subjective perceptions revealed with qualitative SNA is helpful for understanding innovation processes. Here, the integration of qualitative SNA such as egocentric network maps in quantitative techniques of SNA is illustrated. The contribution concludes with a summary of main arguments.

Theoretical and methodological background

While in the scientific literature there are diverse understandings on what a social network is, this contribution draws on the definition used by Stanley Wassermann and Katherine Faust:

“A social network consists of a finite set or sets of actors and the relation or relations defined on them. The presence of relational information is a critical and defining feature of a social network” [ 1 ].

This conception of social network permits both a governance approach and empirical techniques of SNA. Scholars of governance research understand social networks as a certain type of governance that can be differentiated from other ideal types of governance: markets and hierarchies. Social networks combine market-based and hierarchic dimensions and serve as a form of hybrid governance [ 2 ]. Both weak and strong modes of coordination are integrated into the network concept of governance research, where strong coordination is defined as “the spectrum of activity in which one party alters its own … strategies to accommodate the activity of others in pursuit of a similar goal” [ 3 ]. Weak coordination, on the other hand, takes place when actors observe each other’s behavior, “and then alter their actions to make their … strategies complementary with respect to a common goal” [ 3 ].

Because they promote constant exchange and deliberation, social networks have strong potential to promote ideological or structural changes and to generate new knowledge. Hence, network governance is not reduced to governmental action, but refers to the search for collective and participative problem-solving strategies and the promotion of innovations. Footnote 1 This article uses the concept of network governance to highlight the relevance of relationships for innovation research. Hence, it confronts the assumption that individual behavior is independent of any others, but instead conceives “problem-solving as a collaborative effort in which a network of actors, including both state and non-state organizations, play a part” [ 4 ]. Footnote 2

In order to better understand the opportunities of SNA for innovation research, this contribution introduces innovation networks in five different regions as case studies. Innovation networks are understood as social networks that aim at establishing a social innovation. Here, the social innovation of Education for Sustainable Development (ESD) is used. At the same time, the term social innovation refers to processes of implementing and diffusing new social concepts across different sectors of society. While “innovation” implies a kind of renewal, “social” connotes interaction of actors. Social innovations have a direct connection with the search for solutions to social problems and challenges [ 6 , 7 ]. Likewise, Education for Sustainable Development can be defined as education that empowers people to foresee, try to understand, and solve the problems that threaten life on our planet. With the goal of promoting behavioral changes that will shape a more sustainable future, ESD integrates principles of sustainable development into all aspects of education and learning.

Change and innovation through social relations

How can social networks evoke changes and what are the opportunities for SNA to promote innovation processes? SNA has the potential to overcome uncertainties related to innovation processes. The chance of an innovation gaining acceptance increase significantly if it is supported by interconnected actors rather than singular individuals. Social networks foster change processes and promote innovation diffusion. SNA techniques thus help to understand existing networks and to identify innovation potentials in order to generate new information and reveal options for structural developments. SNA has the capacity to promote innovation processes by dealing with the following issues:

Identification of innovation networks (existing, missing, possible, and realistic cooperation) and investigation of actors, structures, and network boundaries:

By using SNA methods, network structures were determined in previously defined fields. Thus, techniques of egocentric SNA provide us with necessary information with respect to network membership and structural interconnections between actors. Structural properties detected in the context of this project are, for example, centrality, prestige, or weak and strong ties.

Innovation potentials through network development strategies:

Looking at network structures not only fosters the development and diffusion of new ideas. It can also reveal where and how structural conditions enable innovations and development processes. Furthermore, Social Network Analyses disclose where and how cooperation can be optimized and where and how alterations are possible and reasonable. Presenting stakeholders the results of SNA can foster structural changes.

Identification and promotion of coordination, information, and motivation:

Analysis of social networks provides us with useful insights into knowledge transfer processes, showing where they exist and how “well” they function. Also, problems of coordination, information, and motivation become evident, providing us with knowledge related to development potentials.

Development of strategies to reduce uncertainties related to innovation processes:

The costs of information exchange are not only material (money, time), but also social. Uncertainties, lack of confidence, and the fear of a loss of reputation can prevent actors from sharing information and knowledge. Results of SNA help us to identify weaknesses in the knowledge transfer process.

Social network analysis in innovation research

In order to illustrate the key opportunities of SNA in innovation research, this section draws on the author’s own empirical investigations that used a mixed methods approach based on quantitative and qualitative SNA. Data on network members was drawn from five different German municipalities and included initiatives, institutions, thematic groups, and individuals engaged in the field of ESD. The municipalities studied are Alheim, Erfurt, Frankfurt am Main, Gelsenkirchen, and Minden. These municipalities have been awarded by the United Nations Decade of Education for Sustainable Development (UNDESD), 2005–2014, and are characterized by active networks in the field of the social innovation of ESD. Organizations, initiatives, and actors from different sectors of non-formal, informal, and formal education seek to further establish and diffuse the concept of ESD worldwide. Thus, networks within these municipalities can be regarded as best practices concerning their performance in the area of ESD. It should be taken into account, however, that the social networks analyzed here are neither institutionalized nor formally established organizations. Instead, every person engaged in the field of the social innovation is regarded as part of the network to be analyzed. Hence, defining the network boundaries was an important part of the empirical investigation.

The research design included three main steps. First, qualitative data was collected in order to gain a better understanding of the object of research and generate research hypotheses. Second, quantitative SNA was conducted, using both egocentric SNA and complete SNA techniques. Network membership and network boundaries were defined by mixed-mode egocentric SNA. In a first step, a 12-page questionnaire was sent to all persons in each of the five municipalities listed in the data base of the UNDESD. In a second step, all persons from different sectors named more than once were also approached with the questionnaire [ 8 – 10 ]. Referring to Fischer [ 11 ] and Burt [ 12 , 13 ], a name generator was used which allowed to name all relevant persons in the field of ESD. In this way, nodes were only included if they were mentioned more than once by an interviewee in the field of ESD.

The questionnaire first asked respondents to mark people in their ESD network, defined by efforts to contact, cooperation, collaboration, problem-solving, and idea exchange. Respondents were also asked to assess the quality and contact frequency for each relation mentioned and to name those persons with whom the interviewee cooperated especially closely or had established high levels of trust. They were then requested to score their named connections’ impact and the relevance with respect to the diffusion of information and the implementation of ESD. Finally, the questionnaire included questions on future prospects, desires, and developmental possibilities.

Egocentric network data was aggregated in order to enable applications of complete SNA. The (strictly adjusted) dataset of the whole network of all five municipalities consists of 1,306 persons and 2,195 edges. Subsequent to the quantitative studies, qualitative network maps were created in order to gain deeper insights into the qualitative characteristics of the networks’ structural properties. Footnote 3 This article focuses mainly on results from the second and the third part of the data analysis.

Insights from structures and individuals: engaging top-down and bottom-up approaches

Empirical results were visualized drawing back on UCINET, Netdraw, and Pajek in order to provide a comprehensive foundation for stakeholders [ 14 , 15 ]. Top-down visualizations of network data were used to generate courses of action, guidance, and network management strategies with the persons involved in the process. Thus, network visualizations and empirical insights enabled stakeholders to detect weaknesses related to structural issues, information flows, and communication problems.

In order to visualize the networks, directional relations between network members were entered into UCINET and mapped with Netdraw. The iterative method of “spring embedding” was chosen for the graph-theoretic layout, because it supports neat illustrations of data sets. Thus, the lengths of the ties do not have information content. The nodes in network visualizations represent persons engaged in implementing ESD in their municipalities. Against the backdrop of the definition of network boundaries, persons that are represented by nodes with only one ingoing link and no outgoing link were not interviewed.

To give an example, one surprising result was the low level of cooperation beyond municipal borders, as measured by network connections, as seen in Fig.  1 .

Trans-regional ESD network, generated with the graph theoretical layout spring embedding, source: Author’s data

In contrast to Manuel Castells [ 16 ], who observed a diminishing relevance of space due to the information age, the present study finds that space remains a constraint for diffusion of ESD. It seems much easier to establish the social innovation ESD in the local context with dense network structures and to subsequently foster its diffusion through weak ties [ 17 , 18 ].

Furthermore, municipal stakeholders were confronted with the unexpected existence of many structural holes and brokerage positions. The concepts “brokerage” and “structural hole” refer to actors’ structural embeddedness. A person who maintains connections with people, who do themselves not become interconnected, has the ability to mediate between these contacts and to obtain benefits from his brokerage position [ 19 – 21 ]. At the same time, structural holes impede innovation processes and information flows.

Figures  2 and 3 take Erfurt and Gelsenkirchen as examples and show relations regarding to the question of who is contacted to develop new ideas related to ESD. Only those relationships with a contact frequency of at least once a month are represented in this figure. The ESD network of Erfurt is chosen as an extreme example, because the structure of its social network exhibits the highest number of structural holes.

Cooperation in the development of new ideas in Erfurt, source: Author’s data

Cooperation in the development of new ideas in Gelsenkirchen, source: Author’s data

There are only a few network members engaged in developing new ideas with respect to ESD in Erfurt; many structural holes shape the ESD network.

In contrast, cooperation in the development of new ideas related to ESD works very well in Gelsenkirchen, as seen in Fig.  3 .

Figure  3 presents productive relationships in Gelsenkirchen. Gelsenkirchen was chosen as an example here because it demonstrates a nearly perfect cooperation basis, which is very supportive for successful innovation processes. Such results can be used by involved actors in order to disclose strengths and weaknesses and reveal where and how structural conditions enable innovations and development processes.

The network visualizations shown so far are mainly reduced to structural information. Network visualizations can also integrate further actor-related information. Not least, structural characteristics of social networks, processes of innovation, idea exchange, and trust also depend on the areas of activity to which network members belong. Thus, Fig.  4 integrates some actor-specific information. Nodes represent those people who are actively engaged in the field of ESD in Alheim. The color of the nodes indicates the sector in which the relevant person deals with ESD. The size of the nodes correlates with the individual centrality index. Centrality is measured by the frequency of the responses—the indegree [ 1 , 22 ]. The more often a person was identified by others, the more central she appears in the picture. The thickness of the connections varies depending on its individual clustering value. While there are two different measures (global and local) for clustering, the local version was used to give an indication of the embeddedness of single nodes [ 23 ]. Thus, clustering is defined as the number of common acquaintances; the thickness of the arrow connecting two nodes points to the number of triangular connections.

ESD network in Alheim; color of the nodes according to the area of activity ( blue black : non-formal education, red : administration/policy, yellow : NGOs, green : economy, light blue : formal education, orange : church, grey : other areas), numbers indicate the IDs of individuals, illustration in cooperation with fas.research, source: Author’s data

Figure  4 indicates the central role that people in the field of non-formal education play in Alheim, as measured by how often they were named by other people. Another central position is held by someone in government. The big red node has many incoming and outgoing links, but few triangle relations and thus a low clustering value. Further comparative quantitative studies reveal that despite its high density value, there is little clustering in Alheim. Certainly, the clustering value always depends on the data collection process, but as the study for this article has used the same methodological approach for all five municipal networks, it is possible to compare the municipal clustering values. However, the low clustering value in Alheim is because cooperation beyond institutional borders works very well in this municipality and persons are not always connected to the same partners. The fear expressed by other municipalities, that ESD in Alheim would be dominated by powerful politicians, cannot be confirmed from these results.

In general, quantitative SNA is able to highlight network boundaries and structural characteristics of social networks that are important to understand innovation potential and impediments. It is difficult or even impossible, however, to reveal the causes, motivations, ideas, or perceptions that lie behind such network structures by solely drawing back on quantitative SNA. How, for example, can we explain the central role of one politician in Alheim, while there are many other central persons from non-formal education? What role does this central politician play for the clustering value in Alheim? In order to answer these questions, the study had to draw on further qualitative social network research methods. The researchers thus used a combination of egocentric network maps and semi-structured interviews.

Egocentric network maps are more individual-oriented than quantitative SNA methods. One benefit of network map visualizations lies in their potential for mental or cognitive support. Such visualizations are able to promote subjective validations of interview narratives as well as to highlight subjective perceptions, reasons, motivations, and network dynamics. The technique of structured and standardized network maps, which has often been described as the “method of concentric circles” [ 24 ], was chosen for this study [ 25 ]. Here, network maps are not only aids, but a main purpose of the survey. A sheet with four concentric circles is given to the interviewee. The inner circle represents the ego, that is to say the interviewee. Interviewees are then asked to draw the initials of people important to them personally, differentiated by the degree of emotional proximity or contact frequency. The three circles around the ego represent the emotional closeness or formal distance with respect to her or his alters (or connections). The closer to the ego, the tighter a contact person is perceived by the interviewee. In addition, the circles are divided in parts through lines; each part represents a different area of activity. In this way, interviewees can dedicate their contacts to specific areas of activity, such as civil society, formal education, non-formal education, business or government. The space around ego is structured by both concentric circles that illustrate the closeness of the alters to ego and the area of activity in which alters are engaged for ESD. An essential advantage of the structured and standardized instruments in relation to unstructured techniques lies in the comparability between different network cards (both intrapersonal and interpersonal).

At the same time, the high degree of structuring and standardization constrains the significance of the data obtained. Indications beyond the pre-fixed circles are only possible if interviewers get the opportunity to pose further questions or if interviewees are encouraged to further discuss issues that are not explicitly part of the visualization process. In order to combine both standardization and openness, this study enabled the interviewers to pose further important questions and explore relevant information related to the research aims. The application of egocentric network maps also served as a medium through which interviewees talked about their relationships. In this sense, network maps were integrated into semi-structured interviews in order to generate narratives and disclose relevant relationships and action orientation. In addition, interviewees had the opportunity to choose the categories representing different areas of activity as well as the colors for the visualizations. Thus, the technique implemented in the study supported the comparability of the cases, but it was also open for new variables and dimensions related to the specific context.

Altogether 25 network maps and interviews, five in every municipality, were generated. Interviewees were chosen according to their area of activity (to obtain a variance of the cases), their position within the social network, and their centrality indexes. To give an example, Fig.  5 presents the network map of a central politician in Alheim. This network map of Alheim is also chosen to further illustrate the case of Alheim, which was also depicted in Fig.  4 . Furthermore, this ESD actor in Alheim possesses a high centrality value according to quantitative SNA.

Network Map of a central politician in Alheim, anonymized, source: Author’s data

As Fig.  5 shows, the interviewee mainly distinguishes five areas of activity: civil society, educational institutions, government/administration, business, and persons from trans-regional contexts. In some cases, the politician just wrote down an organization. During the interview, he referred to concrete persons from these organizations. Surprisingly, the sector of government/administration, to which the interviewee himself belongs, is empty: no persons or organizations are indicated. This is also reflected in the visualization based on quantitative network data (Fig.  4 ), where only one individual from government plays a central role. In a sense, qualitative studies validate quantitative results by showing that the social innovation ESD in Alheim is mainly implemented by actors from non-formal education. At the same time, qualitative results stress that the topic is supported and disseminated by one central politician who bridges structural holes between different sectors. Furthermore, school actors are not represented in the network map, whereas the closest contact persons are from civil society, educational institutions, and business. The great variety of close contact persons from different sectors can be regarded as one reason for the success of the social innovation in Alheim. The central politician in Alheim himself mentions this as playing a significant role. Further actors within the community stress that the ideological foundation and the adoption of ESD would not be possible without this politician. Hence, the establishment of ESD in Alheim can also be traced back to its structural and discursive power and the general trust of ESD actors in this well-connected politician.

The central role of the interviewee in Alheim can be ascribed to the fact that he bridges institutional clusters, supports cooperation beyond government/administration, and combines close cooperation with weak ties in the field of ESD. Furthermore, centrality is not reduced to one person or one sector. Instead, actors from different sectors play a central role in the field of ESD and cooperation between state and non-state actors is very high. In this way, it was possible to develop and realize aims in the area of political accountability in a short space of time. The dense network structure, supported by strong relations between one central politician and actors from other sectors, resulted in the elaboration of an innovative educational plan, composed according to the principles of ESD. At the same time, future strategies should focus on integrating actors from other important areas such as schools. In addition, strategies that foster trans-regional cooperation would be helpful with the diffusion of ESD.

With respect to some of the municipalities, a future strategy that fosters greater participation of stakeholders from other areas of activity, as required by the UN’s International Implementation Scheme (IIS) and the National Action Plan of the UN Decade may be helpful in promoting the implementation and diffusion of the social innovation ESD. Business actors and teachers, in particular, complain about not being sufficiently integrated into ESD networks and that the same people always take control and create turf wars. Furthermore, a lack of transparency and information exchange on existing ESD projects was seen. Business actors in these municipalities faced biases from other actors concerned that they ignored ecological and social dimensions of sustainable development. In some municipalities, ESD is mainly concentrated on environmental topics and many ESD actors express reservations about business aims. However, if different sectors are not integrated, it’s difficult to achieve a balance between ecological, economic, and social dimensions, as it has been proclaimed by the concept of sustainable development as such.

This article has explored the role of Social Network Analysis in analyzing and supporting innovation processes. In order to better understand the opportunities of SNA in innovation research, the author presented empirical results of her own quantitative and qualitative research on innovation networks in five German municipalities actively engaged in the field of ESD. The article showed the value of using a combination of both quantitative and qualitative SNA in order to better understand how and why social innovations are implemented and the opportunities to further develop the network.

Quantitative SNA was implemented to analyze the impact of structural characteristics of social networks on the implementation and the diffusion of the social innovation of ESD. It was discovered, for example, that cooperation in the field of ESD mainly takes place within municipalities and that cooperation beyond municipal borders is low and marked by structural holes. Furthermore, it was shown that social networks in the area of ESD are mostly composed of small and dense groups each representing different sets of actors (e.g., local administration, educational institutions, and business) and pursuing different interests and ideas under the umbrella of ESD. Weak ties, on the contrary, are very important in the field of ESD as they are responsible for the diffusion of innovations.

However, structural holes also exist within the municipalities with respect to the quality of the relations. The extreme example of Erfurt illustrated how the development of new ideas can be hampered by structural weaknesses. In contrast, cooperation and innovation development in the field of ESD are regarded to work well in Gelsenkirchen. In Alheim, actors from different sectors are integrated. Most central roles are played by non-formal education actors, whereas one central role is wielded by a politician. In terms of innovation diffusion, Alheim can be regarded as a best practice. Not least, cooperation beyond institutional borders works well and individual clustering values are low: persons are not always connected to the same clusters. Finally, the implementation of ESD in Alheim benefits from strong relations between one well-connected political and actors from other sectors. The central politician connects different areas of activity and promotes the integration of ecological, economic, and social dimensions in terms of sustainable development.

Quantitative techniques of SNA enabled to identify innovation networks, to determine network boundaries, to define actors within the innovation network, and to investigate the network position of actors. Problems of coordination, information, and qualitative relations were discussed. At the same time, quantitative SNA was shown unable to analyze reasons, motivations, and perceptions behind network structure. These issues were then analyzed by using qualitative SNA methods, such as network maps. A combination of qualitative and quantitative SNA techniques may thus prove the most fruitful for innovation research. In order to better understand the role of social networks in the diffusion of social innovations and to generate knowledge related to innovation potential and courses of action, qualitative techniques were used to supplement the quantitative analysis. It was assumed that the costs of information exchange are not only material (money, time), but also social. Conflicts and lack of confidence between actors, for example, may prevent successful innovation diffusion. Qualitative egocentric network maps could validate quantitative results as well as disclose subjective perceptions and orientations. The central position of one politician in Alheim could thus be traced back to its discursive and structural power. Actors in Alheim have great trust in the ideological competences of the well-connected person who supports the establishment of ESD in many sectors. Visualizations with qualitative network maps support the completion of the interview situation with visual representations. Visualized networks can also serve as mental or cognitive assistance. In combination with quantitative results, however, qualitative network maps enable us to detect where and how innovations and development processes may be possible due to structural and subjective conditions. Finally, compared to conventional statistical analysis that treat structural and individual levels as separately, analyses and visualizations of network data give us more information about the influence of social relations. SNA enables us to capture the interaction between actors and social context, to better understand how innovations are implemented and diffused, to analyze how and why social or educational change takes place or does not take place, and to disclose opportunities for future strategies.

This contribution has shown that SNA can begin to answer questions related to innovation processes. I hope it will open new avenues for further uses of SNA in innovation and futures research.

At the same time, there is little research on the democratic implications of network governance [ 5 ] as well as on the strengths and limits of the concept related to issues of educational innovations such as Education for Sustainable Development (ESD).

When examined through the framework of Social Network Analysis (SNA), the deficits of the concept of ‘Educational Governance’ become evident. In the scientific literature and in educational and political praxis, the concept of Educational Governance is often exclusively related to institutions of formal learning such as schools or educational training. In this manner, it is not possible to capture the real boundaries of social networks and to conceptualize social networks as can be done with SNA techniques. Furthermore, many actors, initiatives, and activities that play an important role in learning processes are analytically excluded in current applications of Educational Governance. For that reason, this article does not use an Educational Governance approach. Instead, it uses a governance approach that draws on theoretical concepts developed in social science.

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I thank the editors and two anonymous reviewers for their constructive comments, which helped me to improve the article. The article is based on results of a study I conducted at the Freie Universität Berlin. I would also like to thank Gerhard de Haan for useful information and for supporting my research.

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Kolleck, N. Social network analysis in innovation research: using a mixed methods approach to analyze social innovations. Eur J Futures Res 1 , 25 (2013). https://doi.org/10.1007/s40309-013-0025-2

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A network analysis of social problem-solving and anxiety/depression in adolescents

Qian-nan ruan.

1 Wenzhou Seventh People's Hospital, Wenzhou, China

De-Guo Jiang

Wen-jing yan.

2 Department of Psychology, School of Education, Wenzhou University, Wenzhou, China

Associated Data

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Social problem-solving (SPS) involves the cognitive-behavioral processes through which an individual identifies and copes with everyday problems; it is considered to contribute to anxiety and depression. The Social Problem-Solving Inventory Revised is a popular tool measuring SPS problem orientations and problem-solving styles. Only a negative problem orientation (NPO) is considered strongly related to anxiety and depression. In the present study, we investigated the detailed connections among the five components of SPS and 14 anxiety-depression symptoms and specified the role of NPO and other components in the anxiety-depression network. We employed network analysis, constructed circular and multi-dimensional scaling (MDS) networks, and calculated the network centrality, bridge centrality, and stability of centrality indices. The results were as follows: (1) the MDS network showed a clustering of anxiety and depression symptoms, with NPO and avoidance style components from SPS being close to the anxiety-depression network (demonstrated by large bridge betweenness and bridge closeness); (2) the NPO and positive problem orientation from SPS were most influential on the whole network, though with an opposite effect; (3) strength was the most stable index [correlation stability (CS) coefficient = 0.516] among the centrality indices with case-dropping bootstraps. We also discussed this network from various perspectives and commented on the clinical implications and limitations of this study.

Introduction

Social problem-solving (SPS) is believed to be strongly related to anxiety and depression, which is very popular among Chinese people. For adults, 4% ( 1 ) before and 20.4% ( 2 ) during the COVID-19 epidemic suffer from anxiety and depression; for adolescent, the prevalent of anxiety and depression is 11.2%/14.6% ( 3 ) before and 19%/36.6% ( 4 ) during the epidemic. SPS plays a significant role in psychological adjustment and constitutes an important coping strategy that has the potential to reduce or minimize psychological distress ( 5 , 6 ). Previous research has found that strong SPS abilities reduce the morbidity associated with anxiety and depression by aiding young people in controlling and modifying their health behavior ( 7 ); they are of key importance in managing emotions and wellbeing ( 8 ). Conversely, poor problem orientation has consistently linked depression and anxiety ( 9 ). Furthermore, depressed patients frequently exhibit deficiencies in social problem-solving, producing fewer effective solutions than do normal control subjects ( 10 ).

Essentially, SPS involves the cognitive-behavioral processes through which an individual identifies and copes with everyday problems ( 11 ). It comprises problem orientation (a general motivational and appraisal component) and problem-solving style (the cognitive and behavioral activities a person uses to cope with problems). The Social Problem-Solving Inventory Revised (SPSI-R) provides a corresponding scale and comprehensive assessment of all theoretical components linked to contemporary models of social problem-solving [i.e., both problem orientation and problem-solving style ( 12 , 13 )]. The SPSI-R consists of a scale of 25 (in the short form) or 52 (in the long form) items, and is one of the most prominent instruments used to study SPS ( 14 ). The SPSI-R is a theory-based measure of SPS processes. It consists of five dimensions, as follows: (1) positive problem orientation (PPO), (2) negative problem orientation (NPO), (3) rational PPO problem-solving (RPS), (4) impulsivity/carelessness style (ICS), and (5) avoidance style (AS). The SPSI-R assesses a person's perception of his or her general approach to and styles of solving problems in everyday living that have repeatedly been found to be reliable and valid ( 15 , 16 ).

SPSI-R research has shown that SPS is an important measure of psychological distress, wellbeing, and social competence [i.e., depression, distress, anxiety, health-related behaviors, life satisfaction, optimism, situational coping, aggression, and externalizing behaviors ( 17 – 19 )]. Previous research has found that certain specific components of SPS can contribute significantly to anxiety and depression. For example, anxious and depressed patients may have difficulties at different stages of the problem-solving process ( 20 , 21 ); Kant et al. (author?) ( 22 ) found that all five problem-solving dimensions measured by the SPSI-R were significantly related to both anxiety and depression in at least one of two samples (i.e., the middle aged and elderly); additional follow-up analyses indicated that NPO contributed most to the significant mediating effect between problems and depression.

Specifically, NPO is strongly related to depression and emotional distress. Abu-Ghazal and Falwah ( 23 ) found that employing PPO to solve problems leads to positive psychological wellbeing, while NPO is associated with depression. In Australia, researchers examined the relationship between NPO and depression-anxiety in 285 young adults using the NPO dimensions of the SPSI-R, finding strong connections between the two ( 24 ). Additionally, many researchers have found that social anxiety is related to NPO ( 25 , 26 ). In Hungary, Kasik and Gál ( 27 ) studied the relationships among SPS, anxiety, and empathy in 445 Hungarian adolescents, finding that regardless of age, adolescents with an increased level of anxiety also have high levels of NPO and AS. Furthermore, studies have found a link between NPO and stress ( 28 – 32 ). Therefore, anxiety and depression have the strongest association with NPO, above all other SPS components ( 8 , 33 – 35 ), and success in reducing symptoms of anxiety and depression appears to be more strongly predicated on the absence of NPO than presence of PPO ( 34 ).

These studies suggest that NPO plays an important role in anxiety and depression. We also explored the detailed connections between problem-solving orientations (including NPO) and problem-solving styles with anxiety-depression symptoms. In other words, we integrated the components of SPS into the anxiety-depression network and investigated the link between these components and anxiety-depression symptoms. We identified the components of social problem-solving most strongly associated with certain symptoms in the anxiety-depression network and determined which components were most centrally located.

Thus, network analysis was employed to analyze the relationships among components of SPS and anxiety-depression symptoms, working from the bottom up, without applying any top-down construct consistent with the standard biomedical and reductionist model ( 36 ). A key premise of network theory is that psychopathological symptoms are interacting and reinforcing parts of a network, rather than clusters of underlying disorders ( 37 ). To test this argument, network analysis has been used to describe the relationships within and between disorders ( 37 ). The dynamics and interrelationships between comorbidities can be identified in network analysis and gaps not considered by factor analysis methods can be addressed ( 38 ). A network is defined as a set of nodes (symptoms) and edges (connections between nodes). In a network model, the symptoms themselves constitute the disorder. The onset and maintenance of symptoms are determined by tracing the pathways of the network ( 38 ).

In an estimated network structure, a centrality measure denotes the overall connectivity of a particular symptom (or component). Central nodes contribute the most to the interrelatedness of symptoms (or components) within the estimated network structure ( 39 , 40 ). A tightly connected network with many strong connections among the symptoms is considered risky because activation of one symptom can quickly spread to other symptoms, leading to more chronic symptoms over time ( 41 ). In other words, when a highly central component is activated (i.e., a person reports the presence of a symptom), it influences other components, causing them to become activated as well, and thus maintaining the network. Considering the importance of problem orientation and problem-solving styles to emotional wellbeing, the nodes should be strongly linked to symptoms of anxiety and depression. In addition, we calculated the bridge-centrality. Previous research has found that deactivating bridge nodes prevents the spread of comorbidity (i.e., one disorder activating another) ( 42 ). Through this network analysis, we gained insight regarding the relationship between SPS and anxiety-depression, which may have clinical implications such as helping to modify patients' problem-solving styles to alleviate related symptoms.

In summary, social problem solving is highly correlated with anxiety and depression and can lead to a number of mental illnesses. There are few study about how the aspects of social problem solving that contribute to depression and anxiety and how they both interact with each other. The present study is to explore the detailed connections between problem-solving orientations and problem-solving styles with anxiety-depression symptoms. NPO, specifically, is hypothesized to be related to depression and emotional distress. We characterized the network structure of SPS components and anxiety-depression symptoms using psychiatric and regular samples. We first investigated the node and bridge centrality, and then determined the stability of the centrality indices for the network.

Participants

The samples, consisting of adolescents aged 12–17 years, was obtained from a psychiatric hospital and two secondary schools, collected from October 2021 and completed in March 2022. The 100 adolescents from the hospital were outpatients who had mental health assessments done by psychiatrists. When patients enter the psychological assessment room, they are briefly introduced to the purpose of our study and then asked to fill out the relevant scales based on the most recent week. They could ask the psychiatrists for help if they have any questions. When the task was finished, the psychiatrists have a check to make sure that all responses are completed, and then the subject leaves the assessment room. The other 100 participants were randomly selected middle school students; they conducted the self-rating assessments while monitored by their teachers in the classrooms. All participants signed an informed consent form and were explained about the rules regarding anonymity, confidentiality, and their right to quit.

Ten samples (from the middle schools) were excluded from data collection because they failed the manipulation check ( 43 ). Therefore, 190 participants were included in the data analysis.

Hospital anxiety and depression scale

The HADS assesses both anxiety and depression, which commonly coexist ( 44 ). The measure is employed frequently, due to its simplicity, speed, and ease of use. Very few literate people have difficulty completing it. The HADS contains a total of 14 items, including seven for depressive symptoms (i.e., the HADS-D) and seven for anxiety symptoms (i.e., the HADS-A), focusing on symptoms that are non-physical. The correlations between the two subscales vary from 0.40 to 0.74 (with a mean of 0.56). The Cronbach's alpha for the HADS-A varies from 0.68 to 0.93 (with a mean of 0.83) and for the HADS-D from 0.67 to 0.90 (with a mean of 0.82). In most studies, an optimal balance between sensitivity and specificity was achieved when a cut point was set at a score of 8 or above on both the HADS-A and HADS-D. The sensitivity and specificity for both is 0.80. Many studies conducted around the world have confirmed that the measure is valid when used in a community setting or primary care medical practice ( 45 ).

SPSI-R (Chinese version)

There have been several revised versions of the SPSI-R for use in the Chinese language, such as the measure published by Siu and Shek ( 46 ) and Wang ( 47 ). The present study used the latter, which shows both good reliability and validity. The overall Cronbach's alpha is 0.85, and the RPS, AS, NPO, PPO, and ICS subscales are 0.85, 0.82, 0.70, 0.66, and 0.69, respectively. The SPSI-R uses a five-point Likert-type scale ranging from 0 to 4, as follows: (0) Not at all true for me, (1) slightly true for me, (2) moderately true for me, (3) very true for me, and (4) extremely true for me.

Network analysis

We used a Gaussian graphical model (GGM) to build the network via the R package (R Core Team version 4.1.3) qgraph (version 1.9.2) ( 48 , 49 ). GGMs estimate many parameters (i.e., 19 nodes required the estimation of 171 parameters: 19 threshold parameters and 19 * 18/2 = 171 pairwise association parameters) that would likely result in false positive edges. Therefore, it is common to regularize GGMs via a graphical lasso ( 49 – 51 ), leading to a sparse (i.e., parsimonious) network that explains the correlation or covariance among nodes with as few edges as necessary. Node placement was determined by the Fruchterman-Reingold (FR) algorithm, which places nodes with stronger average associations closer to the center of the graph ( 52 ). The R package qgraph was used to calculate and visualize the networks. We also measured the centrality and stability of the established network. The R package qgraph and estimatenetwork automatically implement the glasso regularization, in combination with an extended Bayesian information criterion (EBIC) model, as described by Foygel and Drton ( 53 ).

In network parlance, anxiety-depression symptoms and SPS components are “nodes” and the relationships between the nodes are “edges”. The edge between two nodes represents the regularized partial correlation coefficients, and the thickness of the edge indicates the magnitude of the association. The graphical lasso algorithm makes all edges with small partial correlations shrink to zero, and thus facilitates interpretation and establishment of a stable network, solving traditional lost-power issues that emerge from examining all partial correlations for statistical significance [for greater detail, see ( 54 )]. For the present network, we divided the components into three groups or communities: anxiety (seven symptoms), depression (seven symptoms), and SPS (five components).

Most network studies in psychopathology have used the FR algorithm to plot graphs ( 52 ). The FR algorithm is a force-directed graph method [see also ( 55 )] that is similar to creating a physical system of balls connected by elastic strings. Importantly, the purpose of plotting with a force-directed algorithm is not to place the nodes in meaningful positions in space, but rather to position them in a manner that allows for easy viewing of the network edges and clustering structures ( 56 ). We used the “circle” layout for easier viewing, which places all nodes in a single circle, with each group (or community) put in separate circles (see Figure 1A ). In addition, we employed a multi-dimensional scaling (MDS) approach to display the network (see Figure 1B ). MDS represents proximities among variables as distances between points in a low-dimensional space [e.g., two or three dimensions; ( 57 )]. MDS is particularly useful for understanding networks because the distances between plotted nodes are interpretable as Euclidean distances ( 56 ).

Estimated network structure based on a sample of 190 adolescents. The network structure is a GGM, which is a network of partial correlation coefficients. Green edges represent positive correlations and red edges indicate negative correlations. The thickness of the edge reflects the magnitude of the correlation. (A) Network structure with the “circle” layout for easy viewing, but it is important to note that the node positions don't indicate Euclidean distances. (B) Network structure with MDS, showing proximities among variables as distances between points in a low-dimensional space.

We calculated several indices of node centrality to identify the symptoms or components most central to the network ( 58 ). For each node, we calculated the strength (i.e., the absolute sum of edge weights connected to a node), closeness (i.e., the average distance from the node to all other nodes in the network), betweenness (i.e., the number of times a node lies on the shortest path between two other nodes), and expected influence (i.e., the sum of edge weights connected to a node). For SPS and anxiety-depression networks considering the relationship in both direction (i.e., both positive and negative), strength rather than expected influence (which only calculates neutralized influence) is suitable. The node bridge strength is defined as the sum of the value of all edges connecting a given node in one community with nodes in other communities, and was computed by the R-package networktools ( 42 ). Higher node bridge strength values indicated a greater increase in the risk of contagion to other groups or communities ( 42 ).

Stability of centrality indices

We investigated the stability of centrality indices by estimating network models based on subsets of the data and case-dropping bootstraps ( n = 1,000). If correlation values declined substantially as participants were removed, we considered this centrality metric to be unstable. The robustness of the network was evaluated by the R-package bootnet using the bootstrap approach ( 54 ). This stability was quantified using the CS coefficient, which quantified the maximum proportion of cases with a 95% certainty that could be dropped to retain a correlation with an original centrality higher than 0.7 (by default) ( 54 ).

The students' average age was 15.54 years ( SD = 1.302); the group included 102 males and 88 females. We conducted descriptive statistics for the scores of each scale on different demographic variables. The results are shown in Table 1 , which demonstrate the number of participants in each group and the mean score and standard deviation (in the parenthesis) for each scale. Due to some missing data for some participants, the total the number of people with different conditions does not equal 190.

The descriptive statistics of the six SPS components, anxiety, and depression.

As for the network, ~41.5% of all 171 network edges were set to zero by the EBICglasso algorithms. Figure 1 presents the network of SPS components and anxiety-depression symptoms. Figure 1A displays an easily viewable circular network with weights on each edge. For example, the strongest edge (weight = 0.32) among the anxiety symptoms was between Btt 1 (“I get sort of a frightened feeling, like 'butterflies' in the stomach”) and Pnc (“I get sudden feelings of panic”). Among depression symptoms, the strongest edge (weight = 0.25) was between Chr (“I feel cheerful”) and Fnn (“I can laugh and see the funny side of things”). For SPS components, the strongest edge (weight = 0.46) was between PPO (positive problem orientation) and RPS (rational problem-solving). Figure 1B display the MDS network. Highly-related nodes appear close together, whereas weakly-related nodes appear further apart. The anxiety-depression symptoms and SPS components cluster within their own communities, and anxiety-depression nodes are closer to each other. The NPO (negative problem orientation) and AS (avoidance style) nodes are nearest to the anxiety-depression network, while other components are distant from that network.

Centrality indices

For the centrality indices, the values were scaled (i.e., normalized) relative to the largest value for each measure. Figure 2 shows the centrality indices, which are ordered by strength . For strength , Rlx (“I can sit at ease and be relaxed”) from the anxiety symptoms is the most central symptom, 2 followed by Frw (“I look forward with enjoyment to things”) from the depression symptoms and PPO (positive problem orientation) from the SPS components, indicating that these nodes had the strongest relationships to the other nodes. For closeness and betweenness , Frw again ranked the highest, indicating that it was closest to all other nodes in the network and on the shortest path between two other nodes. As for expected influence , considering the direction of the relationship (both positive and negative), Rlx and Pnc from the anxiety community was most positively and PPO most negatively influential on the whole network, indicating that Rlx may be an important risk factor and PPO an important protective factor. NPO most positively influenced the network from the SPS community, and Slw (“I feel as if I am slowed down”) did the same for the depression community.

Centrality indices for the nodes of the present network including those for strength betweenness closeness expected influence. The values are normalized to be within the range of 0–1. The full names of the abbreviations can be found in Figure 1 .

We also calculated the bridge centrality indices (see Figure 3 ). Rlx, Frw , and NPO for anxiety-depression and SPS were found to have the strongest connections (i.e., bridge strength) with other communities ( 42 ). For bridge closeness, Frw, AS , and NPO ranked the highest. For bridge betweenness, Frw, AS , and ICS comprised the top three. For bridge expected influence, Rlx, Slw , and NPO were the most influential.

Estimated bridge centrality indices for the present network, including bridge strength, bridge betweenness, bridge closeness, and bridge expected influence. The full names of the abbreviations for the nodes can be found in Figure 1 .

Stability of the centrality indices

Figure 4 shows that the average correlations dropped between the centrality indices of networks sampled with persons and the original sample. The stability levels of closeness and betweenness dropped steeply, while the stability levels of the node strength and expected influence less so. The Correlation-Stability (CS) coefficient value should preferably be above 0.5 and not be below 0.25 ( 59 ). In this research, the CS coefficient indicated that the betweenness [CS (cor = 0.7) = 0.205] was not stable, while the closeness [CS (cor = 0.7) = 0.437] was relatively stable in the subset cases. Node strength and expected influence performed best [CS (cor = 0.7) = 0.516], reaching the cutoff of 0.5 and indicating that the metric was stable. Therefore, we found that the order of node strength and expected influence were most interpretable (with some care), while the order of betweenness was not.

Average correlations between the centrality indices of networks sampled with persons and the original sample. Lines indicate the means and areas ranging from the 2.5th quantile to the 97.5th quantile.

Anchored in the network perspective ( 39 ), this study illustrated the node pathways, central indices, and central bridging indices for the SPS and anxiety-depression networks. From a “network-network” perspective, the node connections were closer within (vs. between) the anxiety-depression and SPS networks, demonstrating their relative independence from one other. This result is in keeping with previous comorbidity studies of anxiety and depression that employed network analysis ( 60 , 61 ), underscoring that the SPS network is distant from the anxiety-depression network (though the NPO and AS nodes are close to the anxiety-depression network, which can be measured by bridge closeness, as seen in Figure 3 ). Further, the SPS seems more strongly related to anxiety than depression networks, given the longer mean distance from SPS to depression. The reason could be that anxiety is more related to problems or events (the uncertainty of the future) ( 62 ) while depression is more related to self (usually accompanied by low self-esteem, low self-efficacy, and hopelessness) ( 63 ). This explanation is reasonable but required further verifications. The MDS structure is a useful tool for displaying the spatial relationships of nodes, and thus its use should be encouraged in the future.

From a “nodes-in-network” perspective, the node centrality indices revealed that the NPO node from SPS and Rlx and Frw from anxiety-depression were likely to be the most central in the entire SPS-anxiety-depression network. Considering that mood disorders affect how people look at and deal with problems, it is appropriate to put anxiety, depression, and SPS components into a single network. In terms of clinical implications, from our results, we can infer that therapy will yield the greatest rewards by modifying NPO , encouraging relaxation training, and enhancing the expectation of enjoyment for coming things. In addition, the NPO and AS nodes are nearest to the anxiety-depression network, especial to the anxiety symptoms. Therefore, we may even consider that NPO and AS (very close to each other) are innate components of anxiety, as anxious people are worried about the future but do not positively view the problem and do not actively cope with the problem ( 64 ). However, this hypothesis requires further confirmation.

From a “network-node-network” perspective, the results of bridge centrality found that the NPO in SPS community had the strongest association (for both bridge strength and bridge closeness) with the anxiety-depression network, echoing previous research that NPO most strongly contributes to anxiety and depression. However, PPO is located away from the anxiety-depression network and the most negatively correlated ( 65 ), as can be seen from the low levels of bridge expected influence and bridge closeness. Furthermore, the RPS node is strongly connected with PPO but valued low in the four indices of bridge centrality, indicating its unimportance because both of them should “stay away” from the network which is main consists of negative nodes ( 66 ). In short, PPO is the protective and NPO the risk factor for the anxiety-depression network. In clinical settings, encouraging PPO and discouraging NPO would be an effective approach to reducing symptoms of anxiety and depression.

Some limitations of this research will direct future research. First, a cross-sectional design was adopted to build the SPS and anxiety-depression networks. Therefore, this study could not be used to ascertain whether anxiety-depression symptoms impact SPS components or vice versa. Thus, future work will adopt a longitudinal approach with repeated measures of anxiety-depression and SPS components to clarify the causal relationship between anxiety-depression and SPS components. Second, it is probable that the detected potential pathways among the components are limited to the SPSI-R and HADS scales applied. Self-report tools for the SPSI-R and anxiety-depression usually vary in their constructs. This diversity limits the connections that can be found in terms of network structure. Nevertheless, the scales we used are broadly employed; they were carefully implemented based on their psychometric constructs and applicability for adolescents. Therefore, the present research adds to the literature of how among adolescents, anxiety-depression symptoms may be associated with SPS components. This study may also act as an incentive for future research applying other scales for SPS and anxiety-depression to ascertain the stability of these novel findings.

Data availability statement

Ethics statement.

The studies involving human participants were reviewed and approved by Ethics Committee of Wenzhou Seventh People's Hospital. Written informed consent to participate in this study was provided by the participants' legal guardian/next of kin.

Author contributions

Q-NR conceived and designed the experiments. W-JY and CC performed the experiments. ZL, Q-NR, and W-JY wrote and revised the manuscript. ZL gave financial support. All authors contributed to the article and approved the submitted version.

This research was supported by the Medicine and Health Science and Technology Project of Zhejiang, China (No. 2019KY669), and Wenzhou Science and Technology Project of Zhejiang, China (Y20210112).

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

1 Following, the node labels with abbreviations will be in italics.

2 Rlx (“I can sit at ease and be relaxed”) and Frw (“I look forward with enjoyment to things”) are not symptoms per se , but for measuring the symptoms “restless” and “pessimistic” using reverse questions.

• Systematic Review
• Open access
• Published: 05 September 2024

Exploring the use of social network analysis methods in process improvement within healthcare organizations: a scoping review

• Troy Francis 1 , 2 , 3 ,
• Morgan Davidson 1 ,
• Laura Senese 1 ,
• Lianne Jeffs 1 ,
• Reza Yousefi-Nooraie 4 ,
• Mathieu Ouimet 5 ,
• Valeria Rac 1 , 3   na1 &
• Patricia Trbovich 1 , 2   na1  

BMC Health Services Research volume  24 , Article number:  1030 ( 2024 ) Cite this article

Metrics details

Communication breakdowns among healthcare providers have been identified as a significant cause of preventable adverse events, including harm to patients. A large proportion of studies investigating communication in healthcare organizations lack the necessary understanding of social networks to make meaningful improvements. Process Improvement in healthcare (systematic approach of identifying, analyzing, and enhancing workflows) is needed to improve quality and patient safety. This review aimed to characterize the use of SNA methods in Process Improvement within healthcare organizations.

Relevant studies were identified through a systematic search of seven databases from inception - October 2022. No limits were placed on study design or language. The reviewers independently charted data from eligible full-text studies using a standardized data abstraction form and resolved discrepancies by consensus. The abstracted information was synthesized quantitatively and narratively.

Upon full-text review, 38 unique articles were included. Most studies were published between 2015 and 2021 (26, 68%). Studies focused primarily on physicians and nursing staff. The majority of identified studies were descriptive and cross-sectional, with 5 studies using longitudinal experimental study designs. SNA studies in healthcare focusing on process improvement spanned three themes: Organizational structure (e.g., hierarchical structures, professional boundaries, geographical dispersion, technology limitations that impact communication and collaboration), team performance (e.g., communication patterns and information flow among providers., and influential actors (e.g., key individuals or roles within healthcare teams who serve as central connectors or influencers in communication and decision-making processes).

Conclusions

SNA methods can characterize Process Improvement through mapping, quantifying, and visualizing social relations, revealing inefficiencies, which can then be targeted to develop interventions to enhance communication, foster collaboration, and improve patient safety.

Peer Review reports

Introduction

Adverse events, including medical errors, diagnostic errors, and preventable complications, continue to affect millions of patients globally, leading to severe morbidity, mortality, and substantial avoidable healthcare costs [ 1 , 2 ]. Among the many factors contributing to avoidable adverse events, breakdowns in communication have been identified as a leading cause [ 3 , 4 , 5 ]. Lapses in communication during care coordination and patient handoffs can lead to inadequate patient follow-up, delayed care, increased healthcare costs, and provider burnout, leading to an increased risk of adverse events [ 4 , 6 ].

Many studies have highlighted that investigating the underlying causes and consequences of poor communication is necessary to improve the delivery of high-quality care [ 3 , 4 , 6 , 7 ]. However, a large proportion of studies investigating communication in healthcare organizations lack the necessary understanding of social structures (interconnected relationships of social groups e.g., who speaks to who, for what purpose, using what mechanism) and coordination structures (e.g., how information gets transferred or transitioned between people or services) to make meaningful improvements and reduce adverse events [ 8 , 9 ]. For example, the surgical safety checklist (SSC) is a tool meant to enhance patient safety by coordinating care delivery and improving inter-professional communication [ 10 ]. Yet, many studies report conflicting results on the impact of the SSC due to a lack of mutual understanding of communication among team members (e.g., who is responsible for leading a specific checklist pause point) and coordination (e.g., what team members should be present during specific pause points) structures ( 11 , 12 , 13 ). Effective communication among healthcare providers is challenging due to the complex nature of tasks performed and the numerous healthcare providers embedded within hierarchical structures. While the effective use of Process Improvement or Quality Improvement (QI; framework to systematically improve processes and systems in healthcare) interventions rely on understanding the social interactions and relationships within organizations, little attention has been paid to how social networks can be used to improve the effectiveness of communication and coordination in healthcare.

A social network is a set of social entities, actors or nodes (individuals, groups, organizations) connected by similarities, social relations, interactions, or flows (information) [ 14 ]. Analyzing professional communication structures (e.g., observed formal advice-seeking or giving related to work situations) within healthcare organizations’ social networks is important in understanding how best to inform interventions by identifying which network structures promote or inhibit behavior change [ 15 ]. The use of social network analysis (SNA) can provide insight into the social relationships, interactions, and tasks involved within sociotechnical systems. SNA metrics are quantitative measures used to analyze the structure, relationships, and dynamics within social networks through quantifying network behavior [ 16 ]. Network metrics reflect centrality , which refers to a family of measures where each represent different conceptualizations of nodal importance within a network, and cohesion measures, which examine the extent to which nodes within a network are connected [ 14 , 17 ]. These metrics provide an understanding of the structure of social networks through identifying influential nodes, information flow, communities, and cliques [ 18 ]. SNA has been shown to improve professional communication and interprofessional relationships by revealing gaps in communication and identifying influential social entities and communication channels [ 14 , 15 , 19 ]. By indicating which social entities are effective in the flow of communication, organizations can leverage their skills to disseminate important information effectively and foster positive inter-professional relationships [ 19 , 20 ]. Additionally, through identifying gaps in communication between different teams or departments organizations can work to prevent misunderstandings, adverse events, and the duplication of efforts resulting in a more collaborative work environment with stronger interprofessional relationships [ 14 , 21 ]. Through understanding social networks, SNA can be effective in designing, implementing, and evaluating interventions needed to improve professional communication and coordination in healthcare [ 15 , 22 ].

The aim of this review was to characterize the existing literature to assess SNA methods ability to identify, analyze, and improve processes (Process Improvement) related to patient care within healthcare organizations.

The scoping review was conducted using Arksey and O’Malley’s modified six-step framework [ 23 , 24 ]. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews (PRISMA-ScR) standards were used to guide the reporting of this review [ 25 ]. The PRISMA-ScR checklist is shown in the Appendix.

Information sources and search strategy

In collaboration with a research librarian (JB), relevant studies were identified through a systematic search of the MEDLINE (Ovid), Embase, Psychinfo, AMED (Allied and Complementary Medicine), CINAHL, Cochrane Library and Web of Science databases from inception – 16 October 2022. The database search was supplemented with hand searching of reference lists of included reviews. Grey literature was searched using Google Custom Search Engine strategies to narrow search results and allow for more targeted results [ 26 , 27 ]. Searched websites included the International Network for Social Network Analysis, American Evaluation Association Social Network Analysis Technical Interest Group, and the International Sunbelt Social Networks Conference proceedings archives. The search strategy for the social network analysis concept was adapted from Sabot et al.’s systematic review of Social Network Analysis and healthcare settings [ 22 ]. Truncation search terms were used to search inclusive and key terms for these concepts can be found in the supplemental appendix.

Eligibility criteria

A screening checklist developed by Sabot et al., 2017 was modified to guide the review of this study [ 22 , 28 ]. A “no” response to any of the study inclusion criteria (Appendix) was a reason for exclusion from the scoping review. “Healthcare providers” were classified as physicians, physician’s assistants, nurses, midwives, pharmacists, pharmacy technicians, clinical officers, counselors, allied health professionals, and other individuals involved in professional networks (e.g., administrative support staff, management). “Professional communication” was defined as observed formal professional advice-seeking or giving related to hypothetical or actual work situations or patients [ 22 ]. Healthcare organizations were defined as a building or mobile enclosure in which human medical, dental, psychiatric, nursing, obstetrical, or surgical care is provided. Healthcare organizations can include but are not limited to, hospitals, nursing homes, limited care facilities, medical and dental offices, and ambulatory care centers [ 29 ]. Studies had to report the use of SNA in the design of the study (e.g., social network mapping, evaluation of network properties or structure, or analysis of network actors) [ 22 ]. Additionally, to be included studies were required to use systematic data-guided activities (e.g., aims and measures) to achieve improvement or use an iterative development and testing process (i.e., Lean Management, Six Sigma, Plan-Do-Study-Act (PDSA) cycles, or Root Cause Analysis) [ 30 , 31 ]. Studies where network relations were defined solely by patient sharing were excluded, as this only predicts person-to-person communication in a minority of instances [ 32 ]. Abstracts and conference proceedings were considered if details of their methodology and results were published. No limits were placed on study design, language, or publication period.

Study selection and screening process

Study selection and screening employed an iterative process involving searching the literature, refining the search strategy, and reviewing articles for study inclusion. The titles and abstracts of all identified references were independently examined for inclusion by three reviewers (T.F, M.D, and L.S) using the Covidence software platform for systematic reviews [ 33 ]. Full texts of potentially eligible studies were retrieved by the reviewers (T.F, M.D, and L.S), who determined study eligibility using a standardized inclusion screening checklist. Inter-rater reliability was assessed at each phase of the scoping review between reviewers and disagreements were resolved by consensus with input from a fourth author (L.J).

Charting the data

Data from eligible full-text studies was charted by the reviewers (T.F, M.D, L.S) independently using a standardized data abstraction form in Covidence to obtain key items of information from the primary research reports. Discrepancies among reviewers were resolved by consensus. The data abstraction form captured information on key study characteristics (e.g., author, year of publication, location of study, study design, aim of study, type of healthcare facility/provider), SNA-related information (e.g., SNA purpose, data collection methodology, software, SNA metrics) and reported on the implications of using SNA (e.g., social network mapping, assessment of network members or structures).

Collating, summarizing, and reporting the results

A narrative synthesis was performed to describe the study characteristics, SNA methodology, and SNA metrics. The stages of the narrative synthesis included: (1) developing the preliminary synthesis, (2) comparing themes within and between studies, and (3) thematic classification [ 34 ]. Detailed text data on SNA characteristics and implications were reviewed, re-categorized, and analyzed thematically. In line with our objectives, the thematic analysis focused on identifying SNA methods used to improve communication and coordination in healthcare organizations. To categorize the approaches, we conducted further distillation of overarching approaches. We took notes throughout the review and analysis stages, documenting emerging trends and ideas to facilitate further review and discussion among the review team. The extracted data was tabulated in descriptive formats and narrative summaries were provided.

The literature search generated 5084 potentially eligible studies after deduplication, of which 4936 were excluded based on title and abstract, leaving 148 full-text articles to be reviewed. The PRISMA-ScR flow diagram outlining the breakdown of studies can be found in Fig.  1 . Upon full-text review, 44 reports of 38 studies were included for data abstraction. Six studies [ 4 , 35 , 36 , 37 , 38 , 39 ] had multiple records and were truncated into single studies.

PRISMA-ScR flow diagram

Study characteristics

The characteristics of the included studies are shown in Table  1 . Many studies were recently published between 2015 and 2021 (26, 68%) and were primarily located in the United States (26, 68%). 67% of studies occurred within a hospital (25, 66%) and most studies (15, 39%) were set in Internal medicine (gastroenterology, oncology, cardiology, nephrology, respirology, telemetry, or acute care). Studies employed multidisciplinary healthcare providers, however many studies focused on physicians (endocrinologists, oncologists, plastic surgeons, neurologists, anesthesiologists, intensivists, generalists; 27, 71%) and nursing staff (registered nurse, nurse practitioner, practical nurse; nursing assistants; 27, 71%). Most studies employed an observational study design, with 5 studies utilizing longitudinal quasi-experimental design [ 40 , 41 , 42 , 43 , 44 ]. Five studies used mixed-methods designs [ 35 , 36 , 45 , 46 , 47 ] with integrated qualitative and quantitative data, and a further 6 studies used multi-method designs [ 48 , 49 , 50 , 51 , 52 , 53 ] using a combination of independent qualitative and quantitative data. Twenty-four studies reported using quantitative data only [ 3 , 4 , 6 , 40 , 41 , 42 , 43 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 ] and the remaining 2 studies used qualitative methods [ 71 , 72 ].

Table  2 provides an overview of the aims and findings of the included studies and Table  3 outlines the use of SNA methodology and reflects the data collection methods, software, and SNA metrics included in each study. A wide range of network visualization software was used with studies giving preferences towards UCINET [ 36 , 40 , 48 , 54 , 57 , 58 , 59 , 66 , 67 , 68 , 70 , 72 , 73 ], Organization Risk Analyzer (ORA) [ 4 , 55 , 74 , 75 ], and Open-Sourced R Software [ 42 , 49 , 53 , 63 , 65 , 76 ]. Five out of the 38 studies did not visualize their networks through social network mapping and only provided a descriptive assessment of network structures or analysis of network members [ 3 , 40 , 57 , 68 , 76 ]. Two studies did not explicitly report SNA metrics [ 47 , 61 ]. Table  4 provides a comprehensive breakdown of the SNA metrics selected in each study and their application to healthcare networks. There were many network metrics used throughout the studies, however, most studies primarily employed Degree Centrality, Betweenness Centrality, and Density. Twenty-six studies used Degree Centrality as a measure of reach and importance [ 3 , 4 , 6 , 35 , 36 , 41 , 43 , 44 , 45 , 46 , 48 , 49 , 51 , 54 , 55 , 56 , 57 , 58 , 59 , 62 , 63 , 64 , 65 , 67 , 69 , 70 ], 20 studies used Density to measure network cohesion [ 6 , 35 , 36 , 41 , 43 , 44 , 45 , 48 , 53 , 54 , 55 , 57 , 58 , 62 , 63 , 69 , 70 , 71 , 72 , 77 ], and 19 studies used Betweenness Centrality as a measure of influence and brokerage [ 3 , 4 , 36 , 44 , 45 , 46 , 49 , 51 , 52 , 55 , 56 , 57 , 59 , 60 , 62 , 63 , 65 , 66 , 69 ].

* Some articles were assigned to more than one category.

Listed in descending frequency, however “Other” is always at the bottom.

Application and findings of SNA

SNA has been used in healthcare to measure the number of connections (i.e., interactions, tasks), the centrality of providers (i.e., degree, betweenness, and closeness), and network cohesion (i.e., density, clustering). It has helped us to understand essential themes like organizational structure, team performance, and influential actors in healthcare.

a) Organizational Structure.

SNA has been used to better understand how organizational structures (e.g., management roles, groupings of tasks and employees) influence communication and coordination, thereby informing opportunities for improvement. Nine studies showed how SNA was used to redesign hospital organizational structures [ 35 , 36 , 41 , 45 , 46 , 53 , 66 , 69 , 72 ]. For example, Samarth et al. [ 69 ] applied SNA to improve the throughput of their surgical patients, which revealed a hierarchical network coordination structure in their post-anesthesia care unit (PACU) wherein the Charge Nurse channeled all communication downstream, thereby becoming a bottleneck resulting in patient delays. This led to a redesign of their organizational network to a more democratic structure where coordination was performed by an integrated information technology (IT) system which was available to all team members, reducing the dependence on the charge nurse [ 69 ]. Additionally, Alhaider et al. [ 52 ] demonstrated how SNA could be used to investigate system-wide communication in patient flow management and identify process improvement within the healthcare system. Applying SNA within the Distributed Situation Awareness (DSA) framework helped identify bottlenecks in patient flow and the roles that were most likely to experience communication or transaction overload while acquiring and disseminating situational awareness. The DSA model provided a characterization of patient flow and a blueprint for healthcare facilities to consider when modifying their organizational structure to improve communication and coordination. Spitzer-Shohat et al. [ 36 ] used SNA to understand how their organizational structure could help implement disparity reduction interventions to improve care. The SNA unveiled that their subregional management had a high degree of centrality (i.e., many connections), and as such, they were targeted to spread information about the interventions [ 36 ].

A specialized application of SNA involves identifying how IT can enhance or transform organizational communication and coordination. Three studies used SNA to understand how providers from different professions and units communicate across various modes (e.g., in-person, phone, electronic medical record) [ 4 , 48 , 69 ]. For example, SNA highlighted that IT could help improve communication efficiencies during in-person patient handoffs. More specifically, SNA showed that IT could support the redesign of the social network patterns by removing redundant communication exchanges and support emergent and non-linear information flow [ 4 , 69 ]. Six studies used electronic health records (EHR) data to map the network structure of professionals involved in care to show that improving the design of IT can support communication leading to more frequent information sharing among professional groups [ 6 , 47 , 51 , 56 , 60 , 63 ]. Nengliang et al. [ 56 ] demonstrated that EHR log data could be used within an SNA to map the network structure of all healthcare providers and examine the connectivity, centrality, and clustering of networks that emerged from interactions between providers who shared patients. In turn, this data revealed the dynamic nature of care teams and areas (inpatient and outpatient) for collaborative improvement [ 56 ]. Another study used SNA to help contrast low and high IT implementations; they found that the high IT sophistication care homes had more robust and integrated communication strategies requiring fewer face-to-face interactions between providers to verify orders or report patient status compared to the low IT sophistication nursing home [ 47 ].

b) Team Performance.

Sixteen studies used SNA to examine poor team communication and coordination by highlighting the inefficiencies in health networks [ 3 , 36 , 41 , 43 , 53 , 54 , 55 , 57 , 58 , 61 , 64 , 65 , 67 , 68 , 70 , 71 ]. SNA identified that these inefficiencies stem from: teams being overburdened due to workload [ 54 , 61 ], conflict between team roles [ 36 ], lack of leadership [ 43 , 58 ], and fragmented interprofessional relationships [ 57 , 65 , 70 ]. For example, poor team performance in hospital emergency departments has resulted in congestion and increased length of stay with patients having prolonged discharges. SNA allowed for an exploration of the possible causes of inefficiencies resulting in access blocks and determined that the number of healthcare providers and interactions between them, and the centralization of providers within the network affected the performance and quality of emergency departments [ 54 ]. Grippa et al. [ 3 ] used SNA and determined that the most efficient and effective healthcare teams focused more inwardly (internal team operation) and were less connected to external members. Additionally, SNA highlighted that effective teams communicated using only one or two mediums (e.g., in-person, email, instant messaging media) instead of dispersing time on multiple media applications.

SNA has been used to diagnose possible reasons for team inefficiencies and to identify potential design solutions to improve team performance [ 3 , 35 , 42 , 53 , 64 , 67 , 68 , 71 ]. A study used SNA to identify that some experienced staff (who frequently mentor other staff) may have too many connections (high degree of centrality), leading to interruptions or distractions and impacting performance and coordination [ 54 ]. However, a different study, identified that staff with a high degree of centrality have the benefit of improving team performance by leveraging their social networks to be change agents and lead others to replicate desired behaviors (e.g., when a provider may forget to implement a desired change but gets reminded by a team member) [ 62 ]. Lastly, analyzing network cohesion helped identify fragmentation and cliques in the network which may reflect a lack of collaboration and interprofessional relations. For instance, denser (more connections) communication networks with more clustering (groups of connections) are associated with more rapid diffusion of information. Additionally, the connections between providers in dense networks can provide social support (reinforcement) to team members that strengthen their commitment to follow desired behaviors and increase the likelihood that deviations from those actions will be noted by their peers [ 62 ].

c) Influential Actors.

SNA was used to identify influential actors who could act as brokers (an individual who occupies a specific structural position in systems of exchange) [ 3 , 49 , 64 ] who could become opinion leaders (an individual who holds significant influence over others’ attitudes/beliefs) [ 62 ], champions (an individual who actively supports innovation and its promotion/implementation) [ 40 ] or a change agent (an early adopter of an intervention who supports the dissemination of its use) [ 44 ] based off measures of social influence within a network. Studies showed that influential actors in social networks can inform behavioral interventions needed to improve professional communication or coordination [ 3 , 40 , 49 , 62 , 64 ]. For example, Meltzer et al. [ 62 ] used SNA to identify influential physicians to join a QI team and highlighted that having members with connections external to the team is most important when disseminating information, while within team relationships matter most when coordination, knowledge sharing, and within-group communication are most important. When creating an interdisciplinary team, betweenness centrality (node that frequently lies on the shortest path in a network) may be a useful network metric for prospectively identifying team members that may help to facilitate coordination within and across units / professional groups. Providers with a high betweenness have been found to be leaders and active participants in task-related groups [ 68 ]. Hurtado et al. [ 40 ] used SNA to identify and recruit champions who were used to deploy a QI intervention (safe patient handling education program) to advance safety in critical access hospitals. The champion-centered approach resulted in improved safety outcomes (increase in safety participation/compliance and decrease in patient-assist injuries) after one year. Additionally, Lee et al. [ 44 ] used SNA to assess the use of peer-identified and management-selected change agents on improving hand hygiene behavior in acute healthcare. No significant differences were reported between the two groups; however providers expressed a preference for hierarchical leadership styles highlighting the need to understand organizational culture before designing changes to the system.

This scoping review presents a comprehensive overview of the existing literature looking at the use and impact of SNA methodology on Process Improvement within healthcare organizations. Our search strategy included a wide range of databases and placed no restrictions on study design, language, or publication period. When examining the expanding body of literature represented in our identified 38 studies, SNA methods were used to detect essential work processes in organizations, reveal bottlenecks in workflow, offer insight into resource allocation, evaluate team performance, identify influential providers, and monitor the effectiveness of process improvements over time. By analyzing the communication and relationships between management roles, employee groupings, and task allocation, SNA provides insights that can help identify areas for improvement related to patient throughput, diffusion of information, and the uptake of technology (e.g., IT systems). Studies highlighted that healthcare team performance can be hampered by inefficiencies related to being overburdened due to workload, conflicts between team roles, lack of leadership, and fragmented interprofessional relationships. To address these inefficiencies, SNA can leverage network outcomes related to connectedness (e.g., degree, betweenness, closeness) and use knowledge of the network structure (e.g., density, clustering coefficient, fragmentation) to create targeted interventions to mitigate these problems. Additionally, inefficiencies in social networks can be mitigated by identifying influential actors who serve as change agents and can be utilized as opinion leaders or champions to improve the efficiency of information exchange and the uptake of behavioral interventions.

Comparison With Past Literature (Study Design and Data Collection).

Our review stands out from previous studies due to its unique focus on the application of SNA methods in Process Improvement within healthcare organizations. Our primary objective was to investigate how healthcare organizations utilize SNA techniques to improve system-level coordination and enhance the overall quality of care provided to patients. In their research study, Sabot et al. [ 22 ] aimed to investigate the various SNA methods employed to examine professional communication and performance among healthcare professionals. Their study delved into the diverse range of SNA techniques used to gain insights into the complex network dynamics and interactions among providers. In more recent studies, Saatchi et al. [ 78 ] focused on exploring the adoption and implementation of network interventions in healthcare settings. This study provided insights into the effectiveness of network interventions (in which contexts they are successful and for whom), their potential benefits (increased volume of communication), and the challenges associated with their adoption in practice. Additionally, Rostami et al. [ 79 ] focused on advancing quantitative SNA techniques and investigated the application of community detection algorithms in healthcare. This study offers a comprehensive categorization of SNA community detection algorithms and explores potential approaches to overcome gaps and challenges in their use. Previous reviews primarily included observational and cross-sectional study designs with no comparator arms, which made determining the value of using SNA methods difficult as there was no comparison of social networks over time and no comparable head-to-head data. Our review identified 5 quasi-experimental studies [ 40 , 41 , 42 , 43 , 44 ] which used longitudinal or pre-post study designs. In each of these studies SNA was used to review a system which delivered clinical care to identify sources of variation and areas for process improvement at an individual and organizational level. The quasi-experimental studies were published within the last 5 years, indicating that SNA methodology is still in development and opportunities for experimental and longitudinal study designs are forthcoming. Using experimental and longitudinal SNA methods would enable causal inference of healthcare interventions or policies leading to improved generalizability of results.

When performing SNA there is a variety of qualitative (interviews, focus groups, observations) and quantitative (surveys, document artifacts, information systems) methods that researchers can use to map social networks, assess network structures, and analyze team actors. However, previous literature reviews have outlined an overreliance on descriptive SNA methods, which lack the contextual factors needed to interpret how a network reached a given structure. There has been a growing body of evidence advocating for the use of mixed-method social network data collection [ 80 ]. Our review has highlighted an increased uptake of mixed-method (integration of qualitative and quantitative methods and data) and multi-method (independent use of quantitative and qualitative methods) SNA study designs [ 81 ].

Knowledge Gaps and Future Research.

This scoping review highlights many practical uses of SNA; however, within most studies, little attention has been paid to leveraging SNA theory to help explain why networks have the structures they do [ 21 ]. For example, social boundaries between professional groups (e.g., Physicians, Nurses, Pharmacists) can inhibit the development of interprofessional networks though the creation of cliques leading to strong communication and coordination within groups, but fragmented communication across professional groups [ 21 , 82 , 83 ]. A potential explanation for the scarcity of studies assessing the reasons behind the structures of networks could be attributed to the primarily quantitative SNA methods used. Few studies used a qualitative or mixed-method design, indicating a limited understanding of the contextual factors associated with social networks. SNA can reveal the informal structures within organizations and underscores the importance of understanding that not all influential relationships between healthcare providers are found on formal organizational charts, and that informal networks can significantly influence communication and coordination [ 84 ]. The lack of robust study designs (mixed-method or multi-method) may also reflect the use of SNA by researchers more so as a technique than a methodology with theoretical underpinnings.

The value of using SNA to inform research and disseminate evidence-based interventions and policies has been discussed in the literature extensively. However, very few studies have used research on complex systems and network theory to examine how HCWs can act as change agents, interacting within and between hubs in organizations to disseminate knowledge [ 85 ]. Future research should apply complexity science to SNA to reconceptualize knowledge translation and think of the process as interdependent and relationship-centric to support sustainable translation [ 85 ]. Only a small group of included articles have highlighted how leveraging influential actors as change agents such as opinion leaders or champions can be advantageous in improving professional communication or coordination [ 3 , 40 , 44 , 49 , 62 , 64 ]. This review identified two studies [ 40 , 44 ] which utilized SNA and a champion-centered approach to support the successful implementation of a QI intervention resulting in improved safety outcomes. The use of champions is very prevalent in healthcare; however, success rates vary widely, likely due to the poor selection of champion candidates or organizational culture [ 40 , 44 ]. In many cases healthcare workers selected to be champions are volunteered and do not hold enough social influence to change the behaviors of their colleagues. In the future SNA methods should be used to identify influential champions or opinion leaders embedded within their social networks who can influence knowledge transfer and facilitate coordination leading to process improvements.

Future research should identify how SNA methods can leverage health informatics and the large amounts of data stored within healthcare organizations. Even though past studies have used SNA to enhance organizational communication and coordination using IT [ 47 , 56 , 69 ], applying SNA to artificial intelligence and machine learning (ML) algorithms has not received much attention [ 86 ]. Integrating ML algorithms into community detection techniques has showcased the diverse ways SNA can be utilized in healthcare to monitor disease diagnosis, track outbreaks, and analyze HCW networks [ 79 ].

Limitations of the Review.

This review has some limitations that should be acknowledged. First, we excluded studies of provider friendship networks, which theoretically may have contained some professional communication. Secondly, we excluded studies where network relations were defined solely by patient sharing, as this has only been shown to predict person-to-person communication in a minority of instances. Lastly, studies were required to incorporate a Process Improvement component. Different terms were used to describe Process Improvement in the literature, making it challenging to devise a search strategy that would yield sufficient articles for review while also utilizing SNA methods. As a result, studies that utilized SNA methods but did not explicitly examine a process or system for delivering clinical care to identify sources of variation and areas for improvement were excluded.

SNA methods can be used to characterize Process Improvements through mapping, quantifying, and visualizing social relations revealing inefficiencies, which can then be targeted to develop interventions to enhance communication, foster collaboration, and improve patient safety. However, healthcare organizations still lack an understanding of the benefit of using SNA methods to reduce adverse events due to a lack of experimental studies. By emphasizing the importance of understanding professional communication and coordination within healthcare teams, units, and organizations, our review underscores the relationship between organizational structures and the potential of influential actors and emerging IT technologies to mitigate adverse events and improve patient safety.

Data availability

All data generated or analyzed during this study are included in this published article [and its supplementary information files].

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Acknowledgements

The authors would like to thank Joanna Bielecki for her assistance in developing the search strategy and Sonia Pinkney for her valuable feedback and suggestions in refining this manuscript.

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Valeria Rac and Patricia Trbovich contributed equally to this work.

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Institute of Health Policy, Management and Evaluation, Dalla Lana School of Public Health, University of Toronto, Toronto, Canada

Troy Francis, Morgan Davidson, Laura Senese, Lianne Jeffs, Valeria Rac & Patricia Trbovich

HumanEra, Research and Innovation, North York General Hospital, Toronto, ON, Canada

Troy Francis & Patricia Trbovich

Program for Health System and Technology Evaluation, Toronto General Hospital Research Institute, University Health Network, Toronto, ON, Canada

Troy Francis & Valeria Rac

Department of Public Health Sciences, University of Rochester, New York, USA

Reza Yousefi-Nooraie

Department of Political Science, Université Laval, Quebec, Canada

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All authors were involved in conceptualizing the research project. TF, MD, and LS were involved in data curation and project administration. TF was involved in the formal analysis and visualization. TF, MD, LS, LJ, RYN, MO, VR, and PT were involved in the methodology and writing the original draft. PT, LJ, and VR provided supervision and leadership. All authors reviewed the manuscript.

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Francis, T., Davidson, M., Senese, L. et al. Exploring the use of social network analysis methods in process improvement within healthcare organizations: a scoping review. BMC Health Serv Res 24 , 1030 (2024). https://doi.org/10.1186/s12913-024-11475-1

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Evaluation of stress, bio-psycho-social response and coping strategies during the practical training in nursing students: a cross sectional study

• Müjgan Solak   ORCID: orcid.org/0000-0001-6201-3139 1 ,
• Sevcan Topçu   ORCID: orcid.org/0000-0002-6228-1720 2 ,
• Zuhal Emlek Sert   ORCID: orcid.org/0000-0002-2809-5617 2 ,
• Satı Doğan   ORCID: orcid.org/0000-0002-9935-3265 3 &
• Fatma Savan   ORCID: orcid.org/0000-0002-4846-9129 2  

BMC Nursing volume  23 , Article number:  610 ( 2024 ) Cite this article

Metrics details

The aim of the study was to identify stress level, bio-psycho-social response and coping behavior of nursing students during the practical training.

A cross-sectional study was carried out with the 1st, 2nd, 3rd, 4th-year nursing students ( n  = 1181) between September 2018-may 2019. Data was collected using by Socio-Demographic Questionnaire, The Student Nurse Stress Index, The Bio-Psycho-Social Response Scale and Coping Behavior Inventory.

The fourth-grade nursing students’ stress level was found to be statistically significantly higher than of other graders. Nursing students have shown emotional symptoms and social-behavioral symptoms the most. To cope with stress, nursing students used the strategies transference, staying optimistic, problem-solving and avoidance, respectively.

Conclusions

These findings highlight the need to routinely evaluate nursing students for stress, bio-psycho-social response, and coping strategies during practical training. Thus, counseling units can be constituted by the nursing schools, and nursing students who have higher stress levels and inadequate coping strategies benefit from these units.

Peer Review reports

According to Lazarus and Folkman’s transactional theory of stress and coping, stress is a two-way process. Stress is defined as exposure to stimuli (as harmful, threatening, or challenging) that exceed the individual’s coping capacity [ 1 ]. There is a complex transaction between individual subjective reactions to stressors and stressors produced by the environment complex transaction. Transactional theory consists of cognitive appraisal, and coping. After a primary appraisal of the threat or challenge is made, a secondary appraisal process of identifying and selecting available coping options is made. Coping processes produce an outcome, which is reappraised as favorable, unfavorable, or unresolved [ 1 , 2 ].

Stress is accepted as a disease of the 20th century that affects many professions [ 3 ]. Health professionals, especially nurses encounter higher levels of stress and stress factors when their level of exposure to stress and the number of stress-sources are evaluated [ 4 ]. For nurses, stress starts from the beginning of training period and they experience the negative effects of stress on health for many years [ 5 , 6 , 7 ].

Nursing students experience different levels of stress both during their theoretical and practical training [ 8 , 9 ]. Sources of theoretical stress are constantly subjected to examinations, assignments about courses, length of lecture time despite the lack of free times and preparation process before practical evaluations [ 10 , 11 , 12 ]. But sources of practical training stress comprise of the followings; starting to practice for the first-time, clinical evaluations, feeling inadequate in practice, scaring to give patients any harm, caring for patients, relationships with healthcare workers, friends and patients [ 13 , 14 ]. Although nursing students experience stress due to many reasons both in practical and theoretical settings, practical training periods are expressed as periods in which nursing students experience the highest levels of stress [ 15 , 16 ].

Stress can sometimes be a source of motivation, however, high stress can affect coping, self-confidence, concentration, motivation, academic performance [ 9 , 17 ]. In addition, high stress levels may cause students to experience health problems such as hypertension, heart diseases, nutritional disorders, stammering, nausea, vomiting, exhaustion and depression [ 5 , 6 ]. It is stated that nursing students experience higher levels of stress and relevant physical and psychosocial symptoms when compared with the students of other health-related disciplines [ 15 , 18 ].

This situation makes coping strategies crucial for stress management. Coping is defined as constantly changing cognitive and behavioral efforts to manage specific external and/or internal demands that are appraised as taxing or exceeding the resources of the person [ 1 ]. The impact of stress on health depends on the adequacy of coping strategies that play a vital role in managing the stress [ 6 ]. As a strategy to cope with stress, nursing students prefer problem solving the most [ 8 , 11 , 19 ] and avoiding the least [ 5 , 6 , 8 ].

It was found in previous studies that the stress levels of nursing students differed according to classes. It is reported that stress levels are higher in nursing students in the upper grades and the initial clinical practice affects their stress levels [ 20 , 21 , 22 ]. In order to reduce the stress and its negative effects in nursing students, first of all, to determine their stress levels, their responses to stress, coping strategies and the factors affecting their stress levels is very important.

Research questions

What are the stress levels, bio-psycho-social responses, and coping behavior of nursing students during the practical training?

Which variables affect the stress level of nursing students?

A cross-sectional design was used.

Procedure and samples

The study’s population consisted of 1st, 2nd, 3rd, and 4th-year students [ n  = 1181] of nursing school. A cross-sectional study was conducted between September 2018-May 2019.Since it was aimed to reach the entire population, no sample selection method was used. The inclusion criteria for the study were (1) voluntary acceptance of study participation (2) being during the period of practical training. The number of students was 300 for first grade, 309 for second grade, 285 for third grade and 287 for fourth grade. All of the students [ n  = 996] who meet inclusion criteria are included in the study. The response rate of the questionnaires is 84%. ( n  = 996/1181).

Data was collected during the practical training for each grade. The Faculty of Nursing has an integrated education system. The integrated education system is based on holistic learning. It enables the student to see the big picture instead of learning small parts and subject areas are associated according to a subject. The integrated education programme, which includes a structuring from health to disease, is organised to include basic knowledge, attitudes and skills related to the subjects related to care. In the first, second and third years of the integrated education programme, courses are conducted as modules, active education methods are used, and skills training is provided in laboratories and clinics. The fourth year is organised as an internship programme. Practical training starts to in the second term of the first year in the Faculty of Nursing. 1st-year students have practical training consist of 13 h per week for one month in Primary and Secondary Schools. 2nd and 3rd-year students have practical training in Hospitals and Primary Care. The practical training of 2st-year students in the third semester consists of 24 h per week for one month in dermatology, otolaryngology clinics, eye clinics, etc. In the fourth semester, their practical training includes 24 h per week for two months in İnternal Medicine and Surgery clinics. The practical training of 3rd-year students comprises 24 h per week for three months in pediatrics, obstetrics (fifth semester) clinics and psychiatry clinics, primary care (sixth semester). 4th-year students (internship) are in practical training (eight different nursing fields fundamentals of nursing, internal nursing, surgery nursing, pediatric nursing, obstetric and gynecological nursing, psychiatric nursing, public health nursing) during the seventh and eighth semesters. They have practical training 32 h per week each semester.

Data collection tools

Data was collected using by Socio-Demographic Questionnaire, The Student Nurse Stress Index (SNSI), The Bio-Psycho-Social Response Scale (BPSRS) and Coping Behavior Inventory (CBI) Socio-Demographic Questionnaire consists of seven questions such as age, gender, grade, employment status, smoking status, choosing nursing profession willingly and academic status.

The student nurse stress index (SNSI): SNSI that developed by Jones & Johnstone (1999), consisted of 22 items, and four subscales which include academic load, clinical concerns, personal problems, and interface worries [ 23 ]. SNSI is a five-point Likert-type scale ranging from 1 [not stressful] to 5 [extremely stressful]. The Turkish validity and reliability study was conducted by Sarıkoç, Demiralp, Oksuz, Pazar, [ 24 ]. Its Cronbach α coefficient was 0.86. Turkish version of the scale consists of four subscales as personal problems, clinical concerns, interface worries, and academic load. The higher scores obtained from SNSI indicate the high-stress level.

The bio-psycho-social response scale (BPSRS): The BPSRS, developed by Sheu, Lin, Hwang (2002), consist of 21 items and three subscales about symptoms relating to the students’ physical, psychological and social health [ 25 ]. BPSRS five-point Likert-type scale from 0 to 4. Its Cronbach’s alpha coefficient was 0.90. A higher score indicated the presence of more symptoms and poorer physio-psychosocial status [ 25 ]. The Turkish validity and reliability study was conducted by Karaca et al. [ 26 ]. The Cronbach’s alpha coefficient of the Turkish version was found to be 0.91 [ 26 ].

Coping behavior inventory (CBI): The original version of CBI that developed by Sheu, Lin, Hwang, (2002), consists of 19 items and four subscales as avoidance, problem solving, stay optimistic and transference [ 25 ]. The scale is a five-point Likert-type scale from 0 to 4. Its Cronbach’s alpha coefficient was 0.76. A higher score in one factor indicated more frequent use of this type of coping behavior [ 25 ]. The Turkish validity and reliability study was conducted by Karaca et al. (2015) and its Cronbach’s alpha coefficient was 0.69 [ 26 ].

Data analysis

The data were evaluated using the SPSS 21 (Statistical Package for the Social Sciences). Descriptive statistics was used as mean and standard deviation. One way anova test was used to compare scale scores (SNSI, BPSRS, CBI) according to graders. Multiple regression analysis was used to determine the variables (gender, employment status, smoking status, willingness of the choice of the nursing profession, academic achievement status) affecting stress level. For all effects, we used the standard significance level of α = 0.05.

Ethical considerations

This study was approved by Ege University Scientific Research and Publication Ethics Committee (Approval Number: 56/2018). The participants received information about the research objectives and procedures, and their written permission was obtained by means of informed consent form before data collection.

The mean age of nursing students is 21.32 ± 1.57 years. Of the students, 91.9% are females and 26.5% are freshmen, and 5% are working outside the school (Table  1 ).

When nursing students’ total and subscale SNSI mean scores were compared, a statistically significant difference was found between the mean scores of total SNSI and academic loads, interface worries and clinical concerns subscale (Table  2 ). The first grade nursing students’ mean score of academic load subscale was found to be statistically significantly higher than of second and third graders ( p  < 0.05). The third and fourth grade nursing students’ interface worries subscale scores were also statistically significantly higher than of the first and second graders. In the clinical concerns subscale, the second and fourth grade nursing students had significantly higher clinical anxiety than the other graders and the first-year nursing students had lower clinical concerns than other graders. When the total SNSI mean scores were compared, fourth grade nursing students’ stress level was found to be statistically significantly higher than of other graders, and the first grade nursing students’ stress level was statistically lower than of other graders.

It was established that nursing students have shown emotional symptoms and social-behavioral symptoms the most, whereas physical symptoms were shown the least (Table  3 ). When the total and subscale mean scores of BPSRS were compared according to nursing students’ grades, a statistically significant difference was detected in subscales of total BPSRS, emotional symptoms and social behavioral symptoms. In the emotional symptoms subscale, the first year nursing students had less emotional symptoms than other graders. In the social behavioral symptoms subscale, the mean scores of fourth grade nursing students were found to be significantly higher than of other graders. When total BPSRS mean scores were compared, it was observed that the fourth grade students had more bio-psycho-social behavioral symptoms than the first grade students.

It was found that to cope with stress, nursing students used the strategies transference, staying optimistic, problem-solving and avoidance, respectively (Table  4 ). When nursing students’ behaviors related to coping with stress were evaluated according to grades, no statistically significant difference was found between the subscale scores of avoidance, staying optimistic and transference, whereas only the problem-solving subscale was statistically significant. In the problem-solving subscale, the problem-solving skills have increased significantly as the class increased ( F  = 72.63; p  = 0.00).

The relationship between nursing students’ stress level and gender, willingness to choose nursing profession, smoking status, employment status and academic achievement status was evaluated using regression analysis (Table  5 ). The extent to which nursing students’ stress levels were predicted by variables such as gender ( β =-0.22, p  = 0.00), choosing nursing profession willingly ( β =-0.27, p  = 0.00), smoking status ( β  = 0.28, p  = 0.00), employment status ( β  = 0.14, p  = 0.00) and academic achievement status ( β =-0.34, p  = 0.00) was determined by applying linear multiple regression. As a result of this process was detected as R  = 0.84, R2  = 0.70, and 70% of the total variance on stress level was explained by these variables. The stress level was found significantly higher in female students, working students, smokers, those who did not want to choose the nursing profession and those with low academic achievement.

One of the most important stress factors for nursing students is practical training periods especially an initial period of practical training [ 21 ]. It is stated that nursing students experience more stress in clinical practice periods than other periods [ 16 , 21 ]. In the literature, studies investigating the effects of grade on the stress level of nursing students have shown mixed results. Eswi, Radi, Youssri reported that there was no relationship between grade and stress level [ 27 ]. In a study conducted by Shaban, Khater, Akhu-Zaheya, it was found that nursing students were more sensitive to stress due to reasons such as transition to university life, managing their own needs and gaining new social skills, especially during the first years of education. In this study, unlike other studies, the first-year nursing students’ stress level was found lower than of other graders [ 6 ]. Aedh, Elfaki & Mohamed, reported that nursing students who are in the second year of nursing education have experienced higher level of stress than other grades [ 28 ]. In this study, although the second grade was not the highest stress level group, the stress level showed a rapid increase compared to the first grade and the clinical concerns subscale scores were found higher than other grades. Third and fourth grade nursing students’ mean interface worries scores were found high the other grades. Several studies have similarly reported that, nursing students’ stress level was found higher in the last period of nursing education compared to other periods [ 15 , 22 ]. In a qualitative study conducted by Admi et al. (2018) it was found that conflict between professional beliefs and the reality of hospital practice were stressors for final year students [ 19 ]. In the study conducted by Bhat (2021) et al. it was reported that training on invasive procedures (safe catheter etc.) should be standardised in undergraduate education and this should be made part of the annual or biannual compulsory training for healthcare personnel [ 29 ]. Similarly, in this study, the stress level of fourth-grade nursing students was found higher than of other graders, and fourth-grade nursing students’ mean scores of clinical concerns and interface worries were higher than of other graders. The results of our study indicate that the first-grade nursing students had problems adapting to the intensive pace of nursing education and that they experienced stress; accordingly, second-grade nursing students who first-time took to practical training and fourth-grade nursing students who had the longest practical training period also experienced stress due to practical training.

In several studies found that nursing students experienced higher levels of stress, physical and psychological symptoms than the students in other health disciplines [ 6 , 30 ]. Chen & Hung reported that nursing students demonstrated physical symptoms toward stress mostly, and social-behavioral symptoms the least [ 8 ]. In the study carried out by Kassem & Abdou, when the bio-psycho-social responses experienced by nursing students were evaluated, it was found that emotional symptoms were the most common and social-behavioral symptoms were the least [ 11 ]. In another study conducted by Durmuş & Gerçek with nursing students, it that bio-psycho-social responses were found to be occurred mostly in fourth grade students [ 31 ]. In all classes, the most often emotional symptoms were observed in nursing students followed by social behavior symptoms and physical symptoms respectively [ 31 ]. The present study showed that nursing students demonstrated emotional symptoms and social-behavioral symptoms the most, whereas physical symptoms were demonstrated the least, and these results were consistent with results from most of previous similar studies. It was found that fourth-grade nursing students experienced more Bio-Psycho-Social Responses than freshmen and emotional symptoms were higher in second, third and fourth grade nursing students and social behavioral symptoms were higher in fourth-grade nursing students. This difference may be explained by the fact that because fourth-grade nursing students’ stress levels were higher than of other graders, they showed more Bio-Psycho-Social Responses.

Durmuş & Gerçek found that first, and the third-year nursing students have usually used strategies for coping with stress such as stay optimistic and avoidance, respectively [ 31 ]. Also, the same study showed that second and fourth-year nursing students have used problem-solving most [ 31 ]. Many studies found that nursing students have generally used problem solving as a coping strategy [ 5 , 8 , 11 , 19 , 32 ] and the avoidance at least [ 5 , 6 , 8 ]. Sheu, Lin, Hwang reported that using effective ways of coping with the problem will facilitate returning to stable status by allowing reduction of negative consequences of stress [ 25 ]. The present study showed that nursing students most often used transference and least avoidance strategies to cope with stress, and as the students’ grade levels increased, also the level of using problem-solving skills increased. This situation indicates that the problem-solving competencies involving in nursing education are being provided to the students. The fourth grade of nursing students who has highest practical-training hours possess problem-solving skills more than other grades because of the positive effects of the practical applications encountered in a large number of complicated situations on the problem-solving skills of the nursing students.

In the present study, when the interaction between nursing students’ stress level and gender, working status, smoking status, willingness to choose nursing profession and academic achievement status was evaluated, it was found that female students, employees, smokers, those that have chosen nursing profession unwillingly, and those with low academic achievement had significantly higher stress levels. It was reported in different studies that academic success [11,20,], gender [ 20 , 21 , 33 ] have affected students’ stress levels and also their working hours outside of nursing education have affected their stress level [ 11 ]. Although it is important for all students to reduce stressors and to provide support for the use of coping mechanisms; especially female students, employees, smokers, those that choose the nursing profession unwillingly, and those with poor academic achievement should be supported more.

Limitations

This study has some limitations. Unlike other nursing schools in our country, this research was carried out in a nursing school where an integrated education system was applied. The findings could be specific to this college of nursing. Therefore, the generalizability of results may be limited. Besides, the small number of male students is another limitation of the study. SNSI, BPSRS, and CBI are a self-reported questionnaire. This can lead to social desirability bias in respondents.

Reccommendations

It is recommended that long-term studies be conducted to understand the long-term effects of stress experienced during nursing education and to develop sustainable support mechanisms. Support mechanisms may decrease stress levels and their negative effects on nursing students and can promote nursing students’ well-being and academic success, especially during practical training. Exploring what is nursing students of stress levels and coping strategies during education, can inform post-graduation preventive strategies. Also, evaluating the current stress levels and coping strategies in different nursing education programs is crucial for identifying gaps and areas for improvement. Interventional and qualitative studies are crucial to providing concrete recommendations for educational institutions and policymakers to address stress among nursing students.

According to results of the present study, the stress levels of fourth-grade nursing students were higher than of other graders and causes of stress varied as regards grades. The higher level of stress in the senior nursing students that have the maximum responsibilities and stay times of practical training and the bio-psycho-social responses given by students associated depending on this stress indicate that those clinical practices are one of the main sources of stress for nursing students. Due to the nature of nursing education and nursing practices, students use their problem solving skills as a coping strategy. However, the presence of stress-related emotional and social-behavioral symptoms in nursing students indicates that they cannot cope with stress sufficiently. Internship, which is the preparation period for the transition to professional life for nursing, is the period in which nursing students experience the most stress. Students’ learning to cope with stress in this period will enable them to use these strategies in their professional lives. Nursing schools can consider this period as an opportunity period to reduce and cope with stress, which is one of the important risk factors for nurses.

To develop stress management and the stress-coping mechanism of nursing students, it was recommended that courses or counseling units should be available, nursing educators should support students in the clinical areas, receive regular feedback from the students about practical training, and cooperate with clinical nurses to increase nursing students’ clinical compliance. Also, in particular, female students, working students, smokers, those that have chosen nursing profession unwillingly, and those with low academic achievement should be encouraged to receive individualized or group support for stress management and in coping with stress.

Data availability

The data that support the findings of this study are not openly available due to reasons of sensitivity and are available from the corresponding author upon reasonable request.

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M. S Conception and design, data acquisition, data analysis and interpretation, writing, give final approvals. S. T Conception and design, data acquisition, data analysis, writing, give final approvals. Z. E. S Data acquisition, data interpretation, give final approvals. S. D Data acquisition, data analysis, give final approvals. F. S Conception, writing, give final approvals.

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• 3+ years of demonstrated skill and experience using CODEX/PhenoCycler.
• Possess deep knowledge and expertise in immunology, biology, and multi-omics applications in translational research across various disease areas such as oncology (ONC), immuno-oncology (IO), immunity-driven diseases, and related treatment strategies.
• Understanding sample preparation, instrument optimization, and data analysis.
• Interest in bioinformatics and experience with software.
• Ability to identify and troubleshoot critical issues.
• Detail-orientated

Why Novartis: Our purpose is to reimagine medicine to improve and extend people’s lives and our vision is to become the most valued and trusted medicines company in the world. How can we achieve this? With our people. It is our associates that drive us each day to reach our ambitions. Be a part of this mission and join us! Learn more here: https://www.novartis.com/about/strategy/people-and-culture

You’ll receive: You can find everything you need to know about our benefits and rewards in the Novartis Life Handbook: https://www.novartis.com/careers/benefits-rewards

Commitment to Diversity and Inclusion / EEO: The Novartis Group of Companies are Equal Opportunity Employers and take pride in maintaining a diverse environment. We do not discriminate in recruitment, hiring, training, promotion or other employment practices for reasons of race, color, religion, gender, national origin, age, sexual orientation, gender identity or expression, marital or veteran status, disability, or any other legally protected status. We are committed to building diverse teams, representative of the patients and communities we serve, and we strive to create an inclusive workplace that cultivates bold innovation through collaboration and empowers our people to unleash their full potential.

Novartis Compensation and Benefit Summary: The pay range for this position at commencement of employment is expected to be between $112,800 to $186,000/year; however, while salary ranges are effective from 1/1/24 through 12/31/24, fluctuations in the job market may necessitate adjustments to pay ranges during this period. Further, final pay determinations will depend on various factors, including, but not limited to geographical location, experience level, knowledge, skills, and abilities. The total compensation package for this position may also include other elements, including a sign-on bonus, restricted stock units, and discretionary awards in addition to a full range of medical, financial, and/or other benefits (including 401(k) eligibility and various paid time off benefits, such as vacation, sick time, and parental leave), dependent on the position offered. Details of participation in these benefit plans will be provided if an employee receives an offer of employment. If hired, employee will be in an “at-will position” and the Company reserves the right to modify base salary (as well as any other discretionary payment or compensation program) at any time, including for reasons related to individual performance, Company or individual department/team performance, and market factors.

Join our Novartis Network: If this role is not suitable to your experience or career goals but you wish to stay connected to hear more about Novartis and our career opportunities, join the Novartis Network here: https://talentnetwork.novartis.com/network

Commitment to Diversity and Inclusion: Novartis is committed to building an outstanding, inclusive work environment and diverse teams' representative of the patients and communities we serve.

Why Novartis: Helping people with disease and their families takes more than innovative science. It takes a community of smart, passionate people like you. Collaborating, supporting and inspiring each other. Combining to achieve breakthroughs that change patients’ lives. Ready to create a brighter future together? https://www.novartis.com/about/strategy/people-and-culture

Join our Novartis Network: Not the right Novartis role for you? Sign up to our talent community to stay connected and learn about suitable career opportunities as soon as they come up: https://talentnetwork.novartis.com/network

Benefits and Rewards: Read our handbook to learn about all the ways we’ll help you thrive personally and professionally: https://www.novartis.com/careers/benefits-rewards

EEO Statement:

The Novartis Group of Companies are Equal Opportunity Employers who are focused on building and advancing a culture of inclusion that values and celebrates individual differences, uniqueness, backgrounds and perspectives. We do not discriminate in recruitment, hiring, training, promotion or other employment practices for reasons of race, color, religion, sex, national origin, age, sexual orientation, gender identity or expression, marital or veteran status, disability, or any other legally protected status. We are committed to fostering a diverse and inclusive workplace that reflects the world around us and connects us to the patients, customers and communities we serve.

Accessibility & Reasonable Accommodations

The Novartis Group of Companies are committed to working with and providing reasonable accommodation to individuals with disabilities. If, because of a medical condition or disability, you need a reasonable accommodation for any part of the application process, or to perform the essential functions of a position, please send an e-mail to [email protected] or call +1(877)395-2339 and let us know the nature of your request and your contact information. Please include the job requisition number in your message.