Significance-based community detection in weighted networks

Community detection is the process of grouping strongly connected nodes in a net-work. Many community detection methods for un-weighted networks have a theoreticalbasis in a null model, which provides an interpretation of resulting communities in termsof statistical significance. In this paper, we introduce a null for sparse weighted networkscalled the continuous configuration model. We prove a Central Limit Theorem for sums ofedge weights under the model, and propose a community extraction method called CCMEwhich combines this result with an iterative multiple testing framework. To benchmarkthe method, we provide a simulation framework that incorporates the continuous config-uration model as a way to plant null or “background” nodes in weighted networks withcommunities. We show CCME to be competitive with existing methods in accuratelyidentifying both disjoint and overlapping communities, while being particularly effectivein ignoring background nodes when they exist. We present two real-world data sets withpotential background nodes and analyze them with CCME, yielding results that corre-spond to known features of the data.