Multilayer networks: metrics and spectral properties

TL;DR

This paper reviews key metrics and spectral properties of multilayer networks, providing a comprehensive framework for analyzing complex systems with multiple interaction layers and their dynamical behaviors.

Contribution

It offers a unified overview of metrics and spectral tools for multilayer networks, including applications to real-world systems, advancing the understanding of their dynamics.

Findings

Spectral properties relate to critical phenomena in multilayer systems

Metrics enable detailed characterization of multilayer topologies

Framework applied to real-world multilayer networks

Abstract

Multilayer networks represent systems in which there are several topological levels each one representing one kind of interaction or interdependency between the systems' elements. These networks have attracted a lot of attention recently because their study allows considering different dynamical modes concurrently. Here, we revise the main concepts and tools developed up to date. Specifically, we focus on several metrics for multilayer network characterization as well as on the spectral properties of the system, which ultimately enable for the dynamical characterization of several critical phenomena. The theoretical framework is also applied for description of real-world multilayer systems.