Spectral coarse graining for random walks in bipartite networks.

Many real-world networks display a natural bipartite structure, yet analyzing and visualizing large bipartite networks is one of the open challenges in complex network research. A practical approach to this problem would be to reduce the complexity of the bipartite system while at the same time preserve its functionality. However, we find that existing coarse graining methods for monopartite networks usually fail for bipartite networks. In this paper, we use spectral analysis to design a coarse graining scheme specific for bipartite networks, which keeps their random walk properties unchanged. Numerical analysis on both artificial and real-world networks indicates that our coarse graining can better preserve most of the relevant spectral properties of the network. We validate our coarse graining method by directly comparing the mean first passage time of the walker in the original network and the reduced one.