Mining for spatially-near communities in geo-located social networks

Current approaches to community detection in social networks often ignore the spatial location of the nodes. In this paper, we look to extract spatially-near communities in a social network. We introduce a new metric to measure the quality of a community partition in a geolocated social networks called "spatially-near modularity" a value that increases based on aspects of the network structure but decreases based on the distance between nodes in the communities. We then look to find an optimal partition with respect to this measure - which should be an "ideal" community with respect to both social ties and geographic location. Though an NP-hard problem, we introduce two heuristic algorithms that attempt to maximize this measure and outperform non-geographic community finding by an order of magnitude. Applications to counter-terrorism are also discussed.