Community Detection in Social Networks by using Bayesian network and Expectation Maximization technique

Community detection in complex networks has attracted a lot of attention in recent years. Communities play special roles in the structure-function relationship; therefore, detecting communities can be a way to identify substructures that could correspond to important functions. Social networks can be formalized by a statistical model in which interactions between actors are generated based on some assumptions. We adopt the idea and introduce a statistical model of the interactions between social network's actors, and we use Bayesian network (probabilistic graphical model) to show the relation between model variables. Through the use Expectation Maximization (EM) algorithm, we drive estimates for the model parameters and propose a community detection algorithm based on the EM estimates. The proposed algorithm works well with directed and undirected networks, and with weighted and un-weighted networks. The algorithm yields very promising results when applied to the community detection problem.