ModMRF: A modularity-based Markov Random Field method for community detection

Complex networks are widely used in the research of social and biological fields. Analyzing real community structure in networks is the key to the study of complex networks. Modularity optimization is one of the most popular techniques in community detection. However, due to its greedy characteristic, it leads to a large number of incorrect partitions and more communities than in reality. Existing methods use the modularity as a Hamiltonian at the finite temperature to solve the above problem. Nevertheless, modularity is not formalized as a statistical model in the method, which makes many statistical inference methods limited and cannot be used. Moreover, the method uses the sum-product version of belief propagation (BP) and its performance is not as good as the max-sum version, since it calculates per-variable marginal probabilities rather than the joint probability. To address these issues, we propose a novel Markov Random Field (MRF) method by formalizing modularity as an energy function based on the rich structures of MRF to represent properties and constraints of this problem, and use the max-sum BP to infer model parameters. In order to analyze our method and compare it with existing methods, we conducted experiments on both real-world and synthetic networks with ground-truth of communities, showing that the new method outperforms the state-of-the-art methods.