Comparing local modularity optimization for detecting communities in networks

Community detection is one important problem in network theory, and many methods have been proposed for detecting community structures in the networks. Given quality functions for evaluating community structures, community detection can be considered as one kind of optimization problem, such as modularity optimization, therefore, optimization of quality functions has been one of the most popular strategies for community detection. In this paper, we introduced two kinds of local modularity functions for community detection, and the self-consistent method is introduced to optimize the local modularity for detecting communities in the networks. We analyze the behaviors of the modularity optimizations, and compare the performance of them in community detection. The results confirm the superiority of the local modularity in detecting community structures, especially on large-size and heterogeneous networks.