Improving Modularity Regularization Techniques for Estimating Structures in Complex Network

Complex systems in the real world have networks differ significantly from random graphs and have non-trivial structures. In fact, they have a community structure that needs to be recognized and recovered. The stochastic block models (SBMs) are popular models for community detection in networks, where nodes are divided into groups based on their connectivity patterns. Maximum likelihood estimation is a common method for estimating the parameters of SBMs. In this paper, a model selection for stochastic block models is presented based on the optimization of the log-likelihood function to find the best number of communities K detected by the regularized convex modularity maximization method. This work deals with many assumptions on K because it is necessary to study the behavior of the network and the best optimum K is assumed to select the best partition over the AIC, BIC metric. The proposed model selection method is presented in an algorithm that is implemented for both real and synthetic networks. This method enables the detection of networks with small communities that are more likely to provide a better fit to the observed data.