On the Statistical Significance of a Community Structure

The community structure typically refers to the existence of a network partition in terms of a set of non-overlapping dense sub-graphs, where each sub-graph is called a community and there are few links between different communities. The detection of community structure is able to provide additional knowledge on the organization mechanism of the network and its characteristics. Despite decades of developments in community detection algorithms, how to determine whether a given community structure is true or not in a statistically sound manner still remains unresolved. In this paper, we derive an analytical upper bound on the p p -value of a community structure under the configuration model. To demonstrate its effectiveness on community structure validation, we further develop a community detection algorithm in which the p p -value upper bound is used as the objective function. Experimental results on both real networks and simulated networks show that our algorithm outperforms prior state-of-the-art community detection methods.