Null model and community structure in heterogeneous networks

Finding different types of communities has become a research hot spot in network science. Plenty of the real-world systems containing different types of objects and relationships can be perfectly described as the heterogeneous networks. However, most of the current research on community detection is applied for the homogeneous networks, while there is no effective function to quantify the quality of the community structure in heterogeneous networks. In this paper, we first propose the null model with the same heterogeneous node degree distribution of the original heterogeneous networks. The probability of there being an edge between two nodes is given to build the modularity function of the heterogeneous networks. Based on our modularity function, a fast algorithm of community detection is proposed for the large scale heterogeneous networks. We use the algorithm to detect the communities in the real-world twitter event networks. The experimental results show that our method perform better than other exciting algorithms and demonstrate that the modularity function of the heterogeneous networks is an effective parameter that can be used to quantify the quality of the community structure in heterogeneous networks.