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Spectral coarse graining for random walk in bipartite networks
Many real-world networks display a natural bipartite structure, while
analyzing or visualizing large bipartite networks is one of the most
challenges. As a result, it is necessary to reduce the complexity of large
bipartite systems and preserve the functionality at the same time. We observe,
however, the existing coarse graining methods for binary networks fail to work
in the bipartite networks. In this paper, we use the spectral analysis to
design a coarse graining scheme specifically for bipartite networks and keep
their random walk properties unchanged. Numerical analysis on artificial and
real-world bipartite networks indicates that our coarse graining scheme could
obtain much smaller networks from large ones, keeping most of the relevant
spectral properties. Finally, we further validate the coarse graining method by
directly comparing the mean first passage time between the original network and
the reduced one.Comment: 7 pages, 3 figure
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