The maximum likelihood method for detecting communities in communication networks

The community detection in social and communication networks is an important problem in many applied fields: biology, sociology, social networks. This is especially true for networks that are represented by large graphs. In this paper, we propose a method for community detection based on the maximum likelihood method for the random formation of a network with given parameters of the tightness of connections within the community and between different communities. A numerical algorithm for finding the maximum of the objective function over all possible network partitions is described. The algorithm is implemented and tested on real networks of small dimension.