Dynamics and stability of edges and communities in social networks

Abstract

We study social and criminal networks, with a focus on how users and communities of such networks interact with one another, and the impact that such interactions have on the community structures of such networks. We first conducted a study on the crime rates present in different community areas across the city of Chicago, and we were able to identify and predict which community areas have the highest crime rates. In this study, we did not have information about how these community areas interacted with one another. This led us into the study of the Gowalla network, where we analyzed how members of the Gowalla network interacted with one another, and how the modifications of such interactions can break the structure of the original Gowalla network. Such modifications involve the addition and removal of edges from the network, which then led us into our third study, which was creating a synthetic network generator to rewire, with the extent defined by a parameter, edges of the given real-world network. When repeated, this rewiring process adds and removes edges from many generated synthetic versions of the original network. Consequently, all generated networks are also statistically similar to each other. We found that the networks generated using this approach often had community structures different from the one that the original network had. This led us into our final study of measuring the entropy and uncertainty present in the generated networks' community structures. Repeating rewiring enables us to identify the generated network with the lowest community structure uncertainty. Such a network and its corresponding community structure can be used as the best rewired version of ground truth structure alternative to the original network. Finally, we found that predicting the community structure with the lowest cost of this network uncertainty lowers not only this cost but also uncertainty itself. The cost function can be defined according to the requirements of the applications.