Local modularity for community detection in complex networks

Community detection is a topic of interest in the study of complex networks such as the protein-protein interaction networks and metabolic networks. In recent years, various methods were proposed to detect community structures of the networks. Here, a kind of local modularity with tunable parameter is derived from the Newman-Girvan modularity by a special self-loop strategy that depends on the community division of the networks. By the self-loop strategy, one can easily control the definition of modularity, and the resulting modularity can be optimized by using the existing modularity optimization algorithms. The local modularity is used as the target function for community detection, and a self-consistent method is proposed for the optimization of the local modularity. We analyze the behaviors of the local modularity and show the validity of the local modularity in detecting community structures on various networks.