Community identification in networks with unbalanced structure

Community (module) structure is a common and important property of many types of networks, such as social networks and biological networks. Several classes of algorithms have been proposed for community structure detection and identification, including clustering techniques, modularity optimization, and other methods. Among these methods, the modularity optimization method has attracted a great deal of attention and much related research has been published. However, the existing modularity optimization method does not perform well in the presence of unbalanced community structures. In this paper, we introduce a metric to characterize the community structure better than other metrics in this situation, and we propose a method to infer the number of communities, which may solve the resolution limit problem. We then develop an algorithm for community structure identification based on eigendecompositions, and we give both simulated and real data examples to illustrate the better performance of our approach.