Graph Theory and Criminology
http://www.core77.com/posts/22462/Visualizing-Criminal-Networks-to-Help-Police-Solve-Crime
While graph theory has immediate connections to friendships and interactions in social media, the analysis of networks can have other surprising applications, including as a tool for solving real-time crime cases. A few years ago, the Richmond City Police Department tested a social network analysis program which not only provided visual representations of networks, but also statistical metrics to characterize nodes by their number of edges, centrality in a group, connectedness to other nodes. The graphs, developed from information on the police database, used positive links to represent relations with family, friends, and criminal partners, and negative links to represent hostile or violent relations.
In this particular test, the police connected a sudden onset of violence between different groups to series of well connected, but unbalanced regions of the network. This pointed towards tense relationships that were likely a cause of the investigated crimes. The study shows how the principles of triadic closure and balanced versus unbalanced networks can be applied to make predictions about the behavior of individuals in a group, in this case criminal behavior. Aside from allowing the police to identify the people involved in particular crime, network visualizations can also help police to associate related cases that initially appear to be independent of each other.
Network graphs are especially useful to the police during investigations when they may be working with incomplete information, as they can pick out the people who are most likely to have access to the information that they are looking for. Even networks constructed with the data already in the police database revealed connections that would have been difficult to discover without the use of analytical tools. This application of graph theory demonstrates the importance of not just collecting data, but also representing and analyzing it.