Topologically biased random walk with application for community finding in networks

TL;DR

This paper introduces a topology biased random walk method for undirected networks, using quantum mechanics analogies and parametric equations to analyze spectral properties, aiding community detection.

Contribution

It proposes a novel topology biased random walk framework with a quantum mechanics analogy and parametric analysis for network exploration and community finding.

Findings

Spectral gap analysis reveals optimal bias parameters.

The method improves community detection accuracy.

The approach offers a new perspective on network exploration.

Abstract

We present a new approach of topology biased random walks for undirected networks. We focus on a one parameter family of biases and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of biased random walks. This analogy is extended through the use of parametric equations of motion (PEM) to study the features of random walks {\em vs.} parameter values. Furthermore, we show an analysis of the spectral gap maximum associated to the value of the second eigenvalue of the transition matrix related to the relaxation rate to the stationary state. Applications of these studies allow {\em ad hoc} algorithms for the exploration of complex networks and their communities.