A spectral method to find communities in bipartite networks

Community detection in complex networks that aims to find partitions of networks with dense intra-edges and sparse inter-edges, has recently attracted lots of interest in many fields. Specially, bipartite networks composed of two different types of vertices are the common representations for many real-world networks, such as actor-film, consumer-product networks, etc. In this paper, we show that optimizing Barber's bipartite modularity, which is widely used to evaluate partitions of bipartite networks, can be reformulated as a spectral problem with appropriate relaxations. We further propose a new method combining singular value decomposition(SVD) and BRIM algorithm to obtain an optimal community partition. Compared with many other algorithms, the new method can give us a more detailed and comprehensive view of the original bipartite network for different cluster numbers k. We test our method on both synthetic networks and two benchmark data sets. Experimental results show that, our method is not only capable to extract a community partition with a larger bipartite modularity, but also converge to the exact underlying community partition when k is appropriately set, which helps to alleviate the resolution limit issue to some extent.