Friday, September 21, 2012

There Will Be Graphs: Part Four of a Series

By: Evan D. Robertson, Project Associate.

So far this series has used social network analysis techniques to analyze a variety of different economic data sets that are decidedly not social networks. The next few parts of this series will transition to using social network analysis for its intended purpose, to examine social networks. Before delving into social networks crucial to our local economy, it seems prudent to give a brief introduction into the concepts underpinning social network analysis.

At its most basic components a social network is comprised of actors and relational ties. An actor is an individual within a social network while a relational tie is something that connects two or more actors together. While networks can become increasingly complex as you add more actors into the analysis, it is important to keep in mind the simple composition of the network, a social network merely represents connections between individuals. Or rather, it is an elaborate game of connect-the-dots. However, to handle the increasingly large nature of these data sets social scientists have added a myriad of terms and analysis techniques to simplify their investigations. We’ll go through a few of these now, but first a graph!

The preceding graph represents a fictitious social network. The network is composed of seven actors (also called vertices) with eight rational relations (also called edges). The actors are arranged in two cliques highlighted in the following way: Clique 1 indicated by blue squares and Clique 2 represented by lime green circles. A clique is a subgroup of actors who are all directly connected to one another and no additional member exists who is also connected to all members of the clique.* Think high school, with the various groups coalescing in the halls. The clique used by social network analysts and the clique that we intuitively know is nearly the same. Another important concept shown in the graph is the network bridge, displayed by the red triangle. This individual, fictitious as he or she is, plays a pivotal role within the social network.

The network bridge plays a vital connecting role within the context of the social network. For example, let’s imagine that the above network represented a group of doctors attempting to cure a disease of a patient. The two cliques might then represent two different specialty groups that need to communicate with one another in order to diagnose an illness. The network bridge would represent the patient’s primary doctor coordinating the patient’s care by relaying information between both specialty groups. Without this connection, this network bridge, the two different specialty cliques will almost invariably (as has been my experience) come up with two different illnesses plaguing the patient. The diagnoses would almost inevitably be related to the specialist’s area of expertise. If the clique is a group of Nephrologists then something is wrong with your kidneys, if they happen to be Neurologists then it’s all in your head.

While the example network is composed of a relatively few number of actors, most social networks consist of a much larger number of people with a myriad of connections between them. For instance, Facebook had 955 million active users at the end of July 2012. Attempting to understand this social network (i.e. individuals who use Facebook) would be a complex task, especially if you were trying to develop conclusions about the Facebook community. Social network analysts have developed a few tools to describe and generalize large social networks.

Density and betweenness centrality are two measures aimed at inferring the overall structure of the social network as well as the importance of individual actors within the boarder social context. Network density measures the connectedness between all actors in a social network. The above graph has a network density of 0.38 where a value of 1.00 would indicate that every individual is connected to every other individual and a value of 0.00 would have indicate that all the actors in the social network aren’t connected to one another. Thus, the overall structure of our example network is rather divided since less than half of the networks total possible connections have been made.

Whereas density measures the overall structure of the social network, betweenness centrality measures the position of an individual actor in the network. More specifically, betweenness centrality is the degree to which an individual is able to tie various actors in the social network together. The network bridge, highlighted by the red triangle above, has a high betweenness centrality (9.00) compared to other individuals in the social network because he or she links two cliques together, thus, all actors in either clique must go through this individual first in order to communicate with members of the other clique.

No matter how large a social network can get (say one-seventh of the world’s population), the tools for analyzing a social network and the concepts behind the analysis are relatively straight forward. You have individuals (actors), you have the connection between actors (relational ties), and you have tools to measure the overall connectedness of the network (density) and an individual’s connectedness in the overall network (betweenness centrality). With this in mind, the following blogs will utilize these concepts and tools to draw conclusions regarding various social networks.

* Hawe, P., Webster, C., and Shiell, A. (2004). A Glossary of Terms for Navigating the Field of Social Network Analysis. Journal of Epidemiology and Community Health, 58 (12), 971-975.