Network Analysis

Network Visualizations, Community Structure, and Tie Formation in the Creation of Social Capital

This project used several network analysis techniques to explore different relationship types that exist in the fictional TV series "The Boys", as well as how the network structure emerges through tie formation. Techniques for this project included: network diagrams and visualizations, measures of actor prominence and centralization, community detection algorithms to detect clustering, and Exponential Random Graph models to determine how individuals form networks in the aggregate.

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Business Relationships: Loss of a Loved One due to a Superhero

This is a network diagram of the business relationships in the fictional world. From such visualizations, network types and overall structure can be discerned. This network is quite dense and transitive. This nodes are colored according to whether or not they have lost someone they care about at the hands of a superhero. The premise of this series is humans who have been wronged by superheroes conspiring to bring them down; thus, it is expected that this attribute of the characters would influence the structure of relationships. It does appear to do so; the people who have lost someone because of a superhero seem to cluster together to some extent, and the superheroes themselves, not having lost someone, seem to also band together.

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Community Detection Algorithms

Community detection algorithms provide network analysts with various ways in which network clustering and groups can be divided. The algoritms determine the best fitting groups within the network, and by numbering the nodes with a certain nodal attribute, it is possible to see how well the algorithms clustered similar nodes. This diagram has the three shaded clusters found by the two best fitting algorithms, as well as nodes that are numbered according to whther or not they have lost a loved one because of a superhero. It is clear how the algorithms created clusters comprised of mostly similar nodes; a 1 denotes a character who has not lost someone and a 2 denotes a character who has. These algorithms are useful in visualizing and determining how clustered, or lack thereof, a network is.

Vertex Attributes Represented in Network Visualizations

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ERGM

This is the output of an Exponential Random Graph model. These can be used to predict tie formation in a network in hopes of generating the actual network structure based on various model specifications that reflect tie-generative social processes. I include a number of nodal-level predictors, like gender and race, as well as dyadic-level predictors, such as if a pair of connected nodes shares the same attitudes towards suoerheroes or not. Thirdly, it is important to include a structural term in the model to see if processes like triadic closure are occurring between three nodes more than what would be expected by chance. All of these predictors work to simulate the actual structure that can be observed in network diagram. In this case, many of the predictors used were not signifcant in predicting tie formation, except for attitudes about superheroes, gender, and triadic closure.

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Simulations

Above are the various iterations of the network that were generated by a sequence of ERGMs that I specified. The first one is completely random with edges placed between nodes totally by chance. The second diagram is the network that was generated by the most specified ERGM. The third diagram is the actual network diagram of the business ties in this fictional world. Clearly, the best specified ERGM is not all that similar looking to the real network. Thus, my ERGM is not a great representation of the influences of tie formation in this network. However, there is certainly a change in structure from the first to the second so identifying better predictors would most likely improve the ERGM.

Reflection

This project highlighted above was my first exposure to network analysis and was exceptionally rewarding. A major focus of the course was examining how social capital is created within social networks and how this social capital is then diffused throughout the network. Network strucutre can be quite illuminating in how it allows us to see pathways through which information may or may not flow. Many advantages stem from being well-connected, however, nodes located proximate to other networks also benefit from different forms of social capital. The elements exhibited above help to determine influential members of networks who weild power because of the social capital they glean from their network positions.

Perhaps the biggest theme of studying network analysis was distinguishing between how individuals are affected by their network postion at the individual level compared to determining how nodes at the individual level aggregate to form the overall network structure. Thanks to tools like ERGMs, as discussed above, such tie-generative social processes can be modelled to see if they are influencing or predictive of tie formation in a network. A comprehensive exploration of a social network can be produced using all of these network analysis tools in hopes of determining who has influence in a network and how this is structurally possible, as well as why a network has the structure that it does.