Abstract: A relevant feature of networks is community structure. Detecting communities is of great importance in understanding, analyzing, and organizing networks, as well as in making informed decisions. Many approaches have been proposed for detecting community structure in networks, but few methods have been proposed for testing the statistical significance of detected community structures. In this paper, we describe a statistical framework for modularity-based network community detection. Under this framework, a hypothesis testing procedure is developed to determine the significance of an identified community structure. The proposed modularity is shown to be consistent under a degree-corrected stochastic block model framework. Several synthetic and real networks are used to demonstrate the effectiveness of our method.

Key words and phrases: Community detection, consistency, degree-corrected stochastic block model, hypothesis testing, modularity function.