Quantitative function and algorithm for community detection in bipartite networks

Community detection in complex networks is a topic of high interest in many fields. Bipartite networks are a special type of complex networks in which nodes are decomposed into two disjoint sets, and only nodes between the two sets can be connected. Bipartite networks represent diverse interaction patterns in many real-world systems, such as predator-prey networks, plant-pollinator networks, and drug-target networks. While community detection in unipartite networks has been extensively studied in the past decade, identification of modules or communities in bipartite networks is still in its early stage. Several quantitative functions proposed for evaluating the quality of bipartite network divisions are based on null models and have distinct resolution limits. In this paper, we propose a new quantitative function for community detection in bipartite networks, and demonstrate that this quantitative function is superior to the widely used Barber's bipartite modularity and other functions. Based on the new quantitative function, the bipartite network community detection problem is formulated into an integer programming model. Bipartite networks can be partitioned into reasonable overlapping communities by maximizing the quantitative function. We further develop a heuristic and adapted label propagation algorithm (BiLPA) to optimize the quantitative function in large-scale bipartite networks. BiLPA does not require any prior knowledge about the number of communities in the networks. We apply BiLPA to both artificial networks and real-world networks and demonstrate that this method can successfully identify the community structures of bipartite networks.