Concepts and Measurements in Social Network Analysis
We live in an interconnected world, more so now than ever. Our social networks influence our beliefs and behaviors in ways that are often not obvious to us. In this dynamic and rapidly evolving landscape, understanding the intricacies of social networks is not only a matter of personal awareness but a crucial skill in navigating the complexities of the 21st century.
Social network analysis (SNA) introduces a powerful set of concepts and measurements for understanding relational structures across many contexts. Because of this versatility, network analysis has many practical applications: explaining the performance of organizations or organizational systems; understanding the balance of ecological systems and predicting extinctions; and producing search and other online recommendation engines.
What is a Network?
A network refers to any system that can be expressed in terms of some type or types of relationship among some set of nodes. A set of nodes connected by a set of edges is called a graph. The number of edges connected to a given node is called that node’s degree. In the context of social networks, “nodes” usually refer to actors and “edges” to relationships or connections between actors.
Key Concepts
To begin analyzing social networks, there are a few key conceptual distinctions that are useful:
Directed vs. Undirected Graphs
Often, edges on a network graph have no arrows, because the relationships they represent are bidirectional: that is, one person can’t have the relationship without the other one having it, too. Graphs like this are called undirected graphs. In networks where the relationships only go in one direction, the graph is called a directed graph.
In-degree and Out-degree
In a directed graph, in-degree refers to the number of ties a node receives (i.e. the number of edges terminating in that node). Out degree refers to the number of ties a node sends (i.e. the number of edges originating in that node).
Symmetric vs. Asymmetric ties
Ties can also be symmetric or asymmetric. A symmetric relation is one that necessarily goes in both directions (e.g., a mutual friendship), while an asymmetric relation occurs when one node interacts with another without reciprocation (ex. admiration or unreturned calls). Undirected graphs consist of symmetric ties while directed graphs consist of asymmetric ties.
Complementary vs. Elective Asymmetries
Network analysis can reveal the status structure of a network based on whether asymmetries are complementary (ex. Student-teacher relationship) or elective (ex. following someone on social media without reciprocation).
Symmetry vs. Reciprocation
The distinction between the two can be a bit fuzzy, but it’s important to keep in mind that symmetry is about a kind of relation wherever it might occur, while reciprocity is about a kind of tie between two specific nodes. If a kind of tie is symmetric, you don’t need an arrow because it has to go both ways by definition. If the tie is “attended the same meeting” or “shook hands,” then the relationship has to be mutual, regardless of how two people feel about each other. Reciprocity is only relevant if a tie is asymmetric.
Binary vs. Weighted Ties
Often, ties in social networks are depicted as binary either present or absent. Sometimes this reflects a binary reality. At other times it simplifies in a way that makes graphic representation or statistical operations easier. Other times, however, one wants to measure the strength of a tie, or the intensity or frequency of interaction between nodes, such as the closeness of a friendship or frequency of communication.
Weak Ties vs. Strong Ties
Strong ties refer to close, frequent interactions, such as close friendships, while weak ties are more casual, distant connections. Weak ties often serve as bridges between different social groups, facilitating the spread of new information while strong ties promote trust and reciprocity.
One vs. Two-Mode Networks
In a one-mode network, all nodes are of the same type (e.g., people). In a two-mode network (also called a bi-partite network), there are two different types of nodes, such as people and organizations, where edges indicate a relationship between the two types (e.g., membership in an organization).
Multiplex Networks and Multiplex Ties
The social world is often complex and nodes might share multiple types of relationships simultaneously. In multiplex networks, nodes may share multiple types of relationships. For example, two people might be colleagues, friends, and neighbors, creating multiplex ties that reflect the complexity of their interactions.
Compound Ties
A multiplex network can be transformed into a single-tie network by creating compound ties that combine different types of relationships. For example, in a network of coworkers or fellow students, one relationship might be "enjoys spending time with," while another could be "feels very competitive with." Instead of representing these as separate ties in a multiplex network, we can create a new tie—termed a "frenemy" tie—between individuals who both enjoy each other's company and experience competition. This new "frenemy" connection is an example of a compound relation, encapsulating multiple dimensions of their interaction.
Adjacency Matrices / Sociomatrices
Adjacency matrices store network information in a concise format that can easily be analyzed statistically using matrix algebra. In a simple adjacency matrix, each actor has a row and a column. Where a tie (edge) exists between two actors, a 1 appears in the cell formed by the intersection of their respective rows and columns. Where no tie exists, the cell contains a 0. If the nodes in this matrix are people, this is simply called a “sociomatrix.”
Path Distance
A “path” in a network is the sequence of edges leading from one node to another. The number of edges between two nodes on a given path is considered distance. Related, the length of the shortest path between two nodes is commonly called the “geodesic distance.”
Key Measurement: Centrality
One of the many metrics that SNA allows you to measure is centrality. Often, we care about which nodes hold the most power, influence the flow of information, or occupy strategic positions that connect different parts of a network. Centrality enables you to quantify this influence, with different types of centrality measures reflecting a unique aspect of centrality. The four most common measures of centrality are:
Degree Centrality (Popularity): This measure based centrality on the amount of in-degree links between nodes – the higher the in-degree, the more central.
Weighted Centrality (Eigenvector): Degree centrality can be enhanced by weighting each incoming tie according to the degree centrality of the actor sending it. The intuition behind this concept is that an individual holds higher status if their friends are popular, and they possess more power if their friends are influential rather than insignificant. One of the most famous applications of this measure is the Google PageRank algorithm.
Betweenness Centrality (Bridging): This measures how often a node lies on the shortest path between other nodes in a network (referred to as a “geodesic path”). Nodes with high betweenness centrality are important because they control the flow of information or resources in the network. Chicago, for example, is a key hub in the U.S. rail network. Many rail routes pass through Chicago, connecting different parts of the country. This position gives Chicago businesses access to many markets, showing how a central location in a network can lead to more opportunities and influence.
Closeness Centrality (Reachability): Similar to betweenness centrality, closeness centrality is related to the idea that if you are on a shorter path, information and other resources will be routed through you.
However, this is concerned with the mean length of the geodesics from a given node to all other nodes. This measure helps understand which nodes would be the most influential in spreading something through a social network.
Conclusion
Lazer et. al highlights sociologist Robert Merton’s famous claim that the social sciences have not produced an Einstein because it has not yet found its Kepler. In other words, the social sciences lacked the empirical foundations to construct great theories. Over half a decade after Merton’s landmark book Social Theory and Social Structure (1949), sociologist Duncan Watts, a pioneer of the study of social networks wrote “…by rendering the unmeasurable measurable, the technological revolution in mobile, Web, and Internet communications has the potential to revolutionize our understanding of ourselves and how we interact. Merton was right: social science still has not found its Kepler. But three hundred years after Alexander Pope argued that the proper study of mankind should lie not in the heavens but in ourselves, we have finally found our telescope.”
The concepts and measurements of social network analysis are revolutionizing how we understand the broader structures that shape our society, akin to the invention of the telescope that revolutionized astronomy or how the microscope revolutionized biology. With the increased availability of data from mobile devices and the internet, we can now track human behavior in ways that were once unimaginable.
References
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Newman, M. E. J. Networks: An Introduction. Oxford University Press, 2010.
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Lazer, D., Hargittai, E., Freelon, D. et al. Meaningful measures of human society in the twenty-first century. Nature 595, 189–196 (2021). https://doi.org/10.1038/s41586-021-03660-7