A measure of dissimilarity between diffusive processes on networks

TL;DR

This paper introduces a spectral dissimilarity measure based on eigenvalues and eigenvectors of the normalized Laplacian to compare diffusive processes on networks, capturing differences in dynamics due to structural modifications.

Contribution

It proposes a novel framework for quantifying differences in diffusive processes on networks using spectral properties, applicable to various network modifications and random walk types.

Findings

Effective in distinguishing diffusive dynamics due to network modifications

Applicable to degree-biased and reset random walks

Provides a general tool for analyzing complex network processes

Abstract

In this paper, we present a framework to compare the differences in the occupation probabilities of two random walk processes, which can be generated by modifications of the network or the transition probabilities between the nodes of the same network. We explore a dissimilarity measure defined in terms of the eigenvalues and eigenvectors of the normalized Laplacian of each process. This formalism is implemented to examine differences in the diffusive dynamics described by circulant matrices, the effect of new edges, and the rewiring in networks as well as to evaluate divergences in the transport in degree-biased random walks and random walks with stochastic reset. Our results provide a general tool to compare dynamical processes on networks considering the evolution of states and capturing the complexity of these structures.