Community detection based on significance optimization in complex networks

Community structure is an important topological property that extensively exists in various complex networks. In the past decade, much attention has been paid to the design of community-detection methods, while analyzing the behaviors of the methods is also of interest in theoretical research and real applications. Here, we focus on an important measure for community structure, i.e. significance (2013 Sci. Rep. 3 2930). Specifically, we study the effect of various network parameters on this measure, analyze the critical behaviors in partition transition, and then deduce the formula of the critical points and the phase diagrams theoretically. The results show that the critical number of communities in partition transition increases dramatically with the difference between inter-community and intra-community link densities, and thus significance optimization displays higher resolution in community detection than many other methods, but it also may lead to the excessive splitting of communities. By employing the Louvain algorithm to optimize the significance, we confirm the theoretical results on artificial and real-world networks, and further perform a series of comparisons with some classical methods.