Modularity Density for Evaluating Community Structure in Bipartite Networks

Bipartite networks are an important category of complex networks in human social activities. Newman and Girvan proposed a measurement called modularity to evaluate community structure in unipartite networks called modularity. Due to the success of modularity in unipartite networks, bipartite modularity is developed according to different understandings of community in bipartite networks which all contains an intrinsic scale that depends on the total sizeof links and ignores the number of nodes in the bipartite network. In addition, the size heterogeneity of communities and degree of nodes often affects the measure of community. In this work, we propose a quantitative measure forevaluatingthe partition of bipartite networks into one-to-one correspondence between different type communities basedon the concept of average bipartite modularity degree. Unlike the bipartite modularity measures previously proposed, the new measure can overcome the resolution limits. Experiments on the artificial and real-world bipartite networks validate the accuracy and reliability of our bipartite modularity density.