Evaluating Local Community Methods in Networks

The study of complex networks [1, 2, 3] has recently arisen as a powerful tool for understanding a variety of systems, such as biological and social interactions [4, 5], technology communications and interdependencies [1, 6], and many others. The problem of detecting communities, subsets of network nodes that are densely connected amongst themselves while being sparsely connected to other nodes, has attracted a great deal of interest due to a variety of applications [7, 8, 9, 10, 11, 12]. Many techniques have been developed to find these subsets, with a broad array of costs and associated accuracies [13]. Many community-finding algorithms hinge upon maximizing a quantity known as Modularity [14, 15], often defined as: