Estimating the Number of Communities in a Network

Community detection, the division of a network into dense subnetworks with only sparse connections between them, has been a topic of vigorous study in recent years. However, while there exist a range of effective methods for dividing a network into a specified number of communities, it is an open question how to determine exactly how many communities one should use. Here we describe a mathematically principled approach for finding the number of communities in a network by maximizing the integrated likelihood of the observed network structure under an appropriate generative model. We demonstrate the approach on a range of benchmark networks, both real and computer generated.