Density-based modularity for evaluating community structure in bipartite networks

• We illustrate the harmful resolution limit of the traditional bipartite modularities.
• We present density based modularity for bipartite network community detecting.
• We verify our density based modularity has no drawback of resolution limit.
• The optimization on density based modularity as a non-linear programming.
• We empirically illustrate the accuracy and reliability of our density based modularity.

A bipartite network is an important type of complex network in human social activities. Newman defined modularity as a measurement for evaluating community structure in unipartite networks. Due to the success of modularity in unipartite networks, bipartite modularities were developed according to different understandings of community in bipartite networks. However, these modularity measurements are subject to resolution limits that could reduce the quality of community partitioning. These modularity measurements contain an intrinsic scale that depends on the total size of links and ignores the number of nodes in a bipartite network. In this paper, we first illustrate such resolution limits of traditional bipartite modularities using several examples of bipartite networks. Next, we propose a quantitative measurement called density-based modularity to evaluate community partitioning in bipartite networks. We verify that optimization of the density-based modularity proposed has no resolution limit. By optimizing this density-based modularity, we can partition the network into the appropriate communities. Experiments on synthetic and real-world bipartite networks verify the accuracy and reliability of our bipartite density-based modularity.