Walks on weighted networks

TL;DR

This paper analyzes the behavior of random walks on weighted networks, deriving exact formulas for key metrics and comparing weight-dependent and strength-dependent walks through simulations.

Contribution

It introduces and compares weight-dependent and strength-dependent random walks, providing exact analytical expressions and simulation validation.

Findings

Weight-dependent walkers reach new areas more easily.

Exact expressions for stationary distribution and return time are derived.

Simulations confirm theoretical results.

Abstract

We investigate the dynamics of random walks on weighted networks. Assuming that the edge's weight and the node's strength are used as local information by a random walker, we study two kinds of walks, weight-dependent walk and strength-dependent walk. Exact expressions for stationary distribution and average return time are derived and confirmed by computer simulations. We calculate the distribution of average return time and the mean-square displacement for two walks on the BBV networks, and find that a weight-dependent walker can arrive at a new territory more easily than a strength-dependent one.