Characterization of multiple topological scales in multiplex networks through supra-Laplacian eigengaps

TL;DR

This paper investigates the spectral properties of multiplex networks, revealing how gaps in the supra-Laplacian spectrum characterize different structural phases and topological scales, with implications for understanding their dynamics.

Contribution

It introduces a spectral method based on supra-Laplacian eigengaps to identify and characterize multiple topological phases in multiplex networks.

Findings

Identification of spectral gaps corresponding to different phases

Explanation of topological scales via quotient graphs

Insights into dynamical implications of spectral gaps

Abstract

Multilayer networks have been the subject of intense research during the last few years, as they represent better the interdependent nature of many real world systems. Here, we address the question of describing the three different structural phases in which a multiplex network might exist. We show that each phase can be characterized by the presence of gaps in the spectrum of the supra-Laplacian of the multiplex network. We therefore unveil the existence of different topological scales in the system, whose relation characterizes each phase. Moreover, by capitalizing on the coarse-grained representation that is given in terms of quotient graphs, we explain the mechanisms that produce those gaps as well as their dynamical consequences.