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Sociology and Psychology behind Graph Theory and Social Networks

In “Graph Theory and Social Networks: A technical Comment on Connectedness and Connectivity” by J. A. Barnes, Barnes combines, reiterates, and cites the works of multiple sociologists, graph theorists, and psychologists to create a sort of rudimentary understanding of how we can apply graphs and graph theory to understand the different levels of connection in a social network and the different levels of thinking behind human social decision making.

The main application of graph theory that Barnes recognizes in the study of sociology, and talks about in the paper, is the idea of connectedness which is an idea that we discuss and work with often in class—this is especially true in the more recent lectures and homework(s). The main example that Barnes sorts out and looks at is the idea of how completeness and connectedness in a graph that represents a social network or another network of humans can help to topologically identify social cliques and to create algorithms for identifying these social cliques given another set of data (other than a graph). This is especially relevant to the way we analyze graphs in class. When we analyzed social network graphs in class we enumerated multiple properties to analyze them. We applied the notion of strong triadic closure to understand when a group of friends is a stable. We analyzed when a graph is strongly connected if there does not exist a bridge or a singly connected path that can disconnect the entire graph if it were to be removed. These are all notions that Barnes discusses in his analysis of social networks.

One rather interesting idea that Barnes talks about that we have not discussed in class is the idea of representing a social network graph, or any graph with data in general, as a matrix. Barnes talks about the benefits of representing graph data as a matrix as having the ability to add, multiply, and transform the data in various ways. This is really interesting because Barnes talks about how some people implicitly interpret matrix data better than they do graph data so that a matrix sometimes helps make the identifications of where social cliques or social networks are in a larger graph of data, easier to make.

Finishing our discussion of matrices and graph data we have to get into the meet of the discussion which is connectivity and connectedness. Although it is difficult to establish a concrete definition for these terms that all graph theorists can agree upon, Barnes tries his best to summarize the main ideas discussed when graph theorists generally talk about these terms. Here is his enumeration:

“(1) The existence or absence of any kind of link between two points, or the probability of the existence of a link;

(2) The length of the shortest link between two points;

(3) The number of genuinely different links between two points;

(4) The directional or orientational properties of existing links.”

All of these are topics that we have gone over in class for example, point number 1 refers to how we talked about the likeliness of a bond/link to form given a current setup of a graph or subgraph.

The psychology side of Barnes’s paper is also very, very interesting. Barnes cites a psychologist named Kurt Lewin who talks about how regions and their connectedness and how this relates to human behavioral patterns in a social setting. Lewin says a region in a graph is connected “if every point in it can be connected to every other point of it by a path which lies entirely within the region.” This is exactly what we discussed in the last homework when we were asked to find connected parts of the graph. In Lewin’s interpretation of the psychological graph he creates cells/regions as parts of the person or situations that a person would be in and the social processes that the person is involved in. He frames the paths as temporal sequences of actions or states and that under this framework the shortest path quickly becomes the most pleasant set of events or actions for a person to experience/take. This helps setup a criterion for choices and thinking that a person might undergo which has countless applications. For example one application would be to understand and analyze the spread of a rumor amongst a social network/group of people.

Moreover what we can really get a understanding of from Barnes’s paper is that the ideas and techniques we learn in class really do have fascinating real world applications in multiple fields of study. We practice things like finding a simply connected part of a graph or seeing when a graph is strongly connected but we never know what these things actually mean. Seeing how these applications can extend to areas like sociology and psychology is quite remarkable. Seeing how graph theory is actually a critically important tool for sociologists and psychologists is really quite cool.

 

Source: 

http://m.soc.sagepub.com/content/3/2/215.short

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