Understanding complex networks with community-nding algorithms

In a complex network, edges between nodes are often distributed non-uniformly, leading to the formation of hierarchical community structures. However, finding community structure in dense networks has proven to be a difficult task. We study current community-finding algorithms on a small but dense social network from the California Institute of Technology, formed on www.thefacebook.com. Using knowledge of the school’s undergraduate Housing system, we assess the capabilities of modularity-maximizing algorithms, which we find to work decently, and singlelinkage clustering, which we find to work poorly. We also propose a new agglomerative algorithm for constructing overlapping communities using local shells, and implement methods for visualizing overlap between communities.