Spectral coarse-graining of complex networks

TL;DR

This paper introduces a spectral coarse-graining method for complex networks using random walks, enabling reduction of network size while preserving key spectral properties, thus facilitating analysis of large systems.

Contribution

The authors propose a novel spectral coarse-graining scheme based on random walks that maintains essential spectral features of large networks in smaller, simplified models.

Findings

Preserves slow modes of random walks in reduced networks

Significantly decreases network size and complexity

Maintains most relevant spectral properties

Abstract

Reducing the complexity of large systems described as complex networks is key to understand them and a crucial issue is to know which properties of the initial system are preserved in the reduced one. Here we use random walks to design a coarse-graining scheme for complex networks. By construction the coarse-graining preserves the slow modes of the walk, while reducing significantly the size and the complexity of the network. In this sense our coarse-graining allows to approximate large networks by smaller ones, keeping most of their relevant spectral properties.