Community detection and its applications in understanding dynamics of social networks

Abstract

Besides the maximization of modularity and its generalized version, an alternative approach to detect communities is the statistical inference to fit the generative graph model to the observed network data. The degree-corrected stochastic block model is one such random graph model, generating different network partitions, ranging from traditional assortative communities to disassortative structures. It does not impose any constraints on the mixing pattern of the resulting block assignments, thus the return of the traditional assortative community structures is not guaranteed. On top of the degree-corrected stochastic block model, we propose a generative random graph model which puts a constraint on nodes' internal degree ratio. This model stabilizes the inference of block model, avoiding inference algorithms like Markov chain Monte Carlo to get trapped in the local optima of the log-likelihood. Unlike the modularity maximization algorithm which always attempts to find traditional assortative communities, in this regularized model, one single regularization parameter controls the mixing patterns discovered from the given network.