Graph Product Multilayer Networks: Spectral Properties and Applications

TL;DR

This paper develops the theoretical spectral properties of graph product multilayer networks (GPMNs) and explores their applications in epidemic modeling, propagation analysis, and higher-order network properties.

Contribution

It introduces a unified spectral framework for GPMNs derived from various graph products, extending to nonsimple and generalized cases.

Findings

Spectral relationships between GPMNs and factor networks established.

Applications demonstrated in epidemic threshold prediction.

Analysis of propagation and self-similar network properties.

Abstract

This paper aims to establish theoretical foundations of graph product multilayer networks (GPMNs), a family of multilayer networks that can be obtained as a graph product of two or more factor networks. Cartesian, direct (tensor), and strong product operators are considered, and then generalized. We first describe mathematical relationships between GPMNs and their factor networks regarding their degree/strength, adjacency, and Laplacian spectra, and then show that those relationships can still hold for nonsimple and generalized GPMNs. Applications of GPMNs are discussed in three areas: predicting epidemic thresholds, modeling propagation in nontrivial space and time, and analyzing higher-order properties of self-similar networks. Directions of future research are also discussed.