Graph of the Internet.
Law enforcement is an extremely complex line of work, as police officers have to keep up-to-date with events and people in the community, but usually from the sidelines or through second-hand information. Tools that can augment police officers' mental models of the communities they serve, especially in an ever increasing information-rich world, are critical to the future of policing.
And that's where graph theory comes in. Graph theory looks at objects (nodes) and the relationships (edges) between them. These objects could be people, computers, or buildings, while the corresponding relationships could be family ties, Internet connections, and roads. As Facebook and other social networking tools continue to bring our world closer together each day, social network applications of graph theory are becoming a hot topic. Ever hear of "six degrees of separation?" Thanks to Facebook, it's now closer to four or five.
Criminal networks are really just a specific example of social networks. Currently, law enforcement agencies use link analysis, a basic application of graph theory, to attempt to understand these networks. Link analysis produces a visual output of relationships between nodes, but "people tend to believe that actors in the center or at the top of a graph are crucially and most important." Instead, Renee van der Hulst describes a framework for using social network analysis (SNA) for crime analysis. Beyond just outputing a visual graph, SNA provides a mathematical approach to quantify the "characteristics of network activity, social roles, positions and associated social mechanisms."
A simple graph of a social network, including nodes and edges.
In 2011, researchers from Virginia Commonwealth University implemented a pilot program of SNA in the Richmond, VA Police Department to test its effectiveness. The Richmond City Police Department asked the researchers to identify the reason behind why "two groups of previously friendly males" were now engaging in a "rash of violence" against each other. The researchers mined a police informational database for details concerning twenty-four persons of interest, as well as any connections four people out.
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