Spectral coarse graining for random walk in bipartite networks

TL;DR

This paper introduces a spectral coarse graining method tailored for bipartite networks that reduces their size while preserving key random walk properties, validated through numerical experiments on real-world data.

Contribution

The paper proposes a novel spectral coarse graining scheme specifically designed for bipartite networks, addressing limitations of existing methods for binary networks.

Findings

Reduces large bipartite networks to smaller ones while retaining spectral properties.

Maintains the random walk characteristics, such as mean first passage time.

Effective on both artificial and real-world bipartite networks.

Abstract

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.