Modularity Function for Community Structure Based on Natural Density of Networks

The most popular modularity optimization may fail to identify communities smaller than a scale. A natural density of networks is proposed for describing the degree of interconnectedness of modules. The density modularity function is constructed to evaluate the community structure partitioning based on the natural density. Three cases study proves that the density modularity function can overcome the resolution limit of NG's modularity. The density modularity has been tested on both artificial networks and classical real-world networks. Computational results demonstrate the effectiveness of the density modularity.