Diffusion dynamics on multiplex networks

TL;DR

This paper analyzes diffusion processes on multiplex networks by constructing a supra-Laplacian matrix, using perturbative analysis to relate eigenvalues and eigenvectors to the spectral properties of individual layers, enhancing understanding of diffusion dynamics.

Contribution

It introduces a supra-Laplacian matrix for multiplex networks and provides an analytical framework linking its spectral properties to those of individual layers.

Findings

Eigenvalues and eigenvectors of the supra-Laplacian are analytically characterized.

Spectral properties of the multiplex network are related to those of single layers.

The approach improves understanding of diffusion timescales on multiplex networks.

Abstract

We study the time scales associated to diffusion processes that take place on multiplex networks, i.e. on a set of networks linked through interconnected layers. To this end, we propose the construction of a supra-Laplacian matrix, which consists of a dimensional lifting of the Laplacian matrix of each layer of the multiplex network. We use perturbative analysis to reveal analytically the structure of eigenvectors and eigenvalues of the complete network in terms of the spectral properties of the individual layers. The spectrum of the supra-Laplacian allows us to understand the physics of diffusion-like processes on top of multiplex networks.