A new framework for dynamical models on multiplex networks

TL;DR

This paper introduces a new theoretical framework for analyzing dynamical processes on multiplex networks, including spectral properties, convergence rates, and a generalized eigenvector centrality, with applications to real-world data.

Contribution

It develops a comprehensive model for multiplex dynamics, extending spectral analysis and centrality measures to multi-layer networks, and compares these with existing models.

Findings

Spectral properties of multiplex models are characterized both theoretically and computationally.

The framework enables calculation of convergence rates for multiplex diffusion and Markov processes.

A generalized multiplex eigenvector centrality is proposed and validated.

Abstract

Many complex systems have natural representations as multi-layer networks. While these formulations retain more information than standard single-layer network models, there is not yet a fully developed theory for computing network metrics and statistics on these objects. We introduce a family of models of multiplex processes motivated by dynamical applications and investigate the properties of their spectra both theoretically and computationally. We study special cases of multiplex diffusion and Markov dynamics, using the spectral results to compute their rates of convergence. We use our framework to define a version of multiplex eigenvector centrality, which generalizes some existing notions in the literature. Last, we compare our operator to structurally-derived models on synthetic and real-world networks, helping delineate the contexts in which the different frameworks are appropriate.