Computing exact P-values for community detection

Community detection is one of the most important issues in modern network science. Although numerous community detection algorithms have been proposed during the past decades, how to assess the statistical significance of one single community analytically and exactly still remains an open problem. In this paper, we present an analytical solution to calculate the exact p-value of a single community with the Erdös–Rényi model. Meanwhile, we propose a local search method for finding statistically significant communities based on the p-value minimization. Experimental results on both real networks and simulated networks demonstrate that our method is able to effectively detect true communities from different types of networks.