Multiple Resolution Community Structure Analysis

Detecting community structure is fundamental for uncovering the links between topological structure and function in complex networks. A popular method now widely used relies on the optimization of a quantity called modularity. But modularity optimization has a fundamental drawback: there exists a resolution limit which depends on the total size of the network and on the degree of interconnectedness of the modules. Resultantly there are tendencies to merge smaller modules. Intuitively the considered module is relative to the local structure, and is not relative to the total size of the network. In this paper, firstly, we give an simple explanation from the theoretic point of view that why the resolution limit depends on the total size of the network which seems to violate the intuition. Secondly, in order to address the issue of the resolution limit we propose a quantitative function MQλ with a tuning parameter λ (−1 6 λ 6 1/2) which contains modularity as a special case at λ = 0. In particular, MQ 1 2 optimization ensures the partition not to merge the smaller modules in any complex network. Numerical results show that the proposed method has been validated using synthetic networks, discovering the predefined structures at all scales and its applications to some real social networks can correctly identify the number of communities.