CLBA: A Coulomb’s law based algorithm for community detection in directed networks

Many networks in the real world are directed networks, e.g., email networks, citation networks, etc. Community structure also exists in directed networks, and community detection can help us analyze the structure and function of the network. Currently, the number of community detection algorithms proposed for directed networks is small. The common method for detecting communities in directed networks is transforming the directed network into the undirected network. However, this method ignores the information carried by directed edges, which makes the quality of detected communities poor. In this paper, we propose a community detection algorithm for directed networks, which is based on Coulomb’s law in physics, named CLBA. Moreover, we propose a new method to measure the node importance in directed networks that considers the situation of different networks in which the out-degree and in-degree of a node have different effects to the node importance. We abstract the nodes in the directed network as sets of charged particles and measure the charge of a node by its importance. Based on Coulomb’s law, we can obtain the attraction between nodes and assign the attraction as the weight to the edges, which serves as the basis for the label propagation in directed networks. We also prove that our model is consistent with the point proposed by Kim et al. in 2010 for directed networks. The CLBA algorithm not only has low time complexity, but also, experimental results on benchmark and real networks show that our algorithm can detect communities effectively and efficiently.