Perron communicability and sensitivity of multilayer networks

TL;DR

This paper analyzes how the communicability of multilayer networks responds to changes in edge weights by examining the Perron root of the supra-adjacency matrix, providing insights for optimizing network robustness.

Contribution

It introduces a method to assess the sensitivity of multilayer network communicability to edge perturbations using Perron root analysis.

Findings

Identifies which edges to strengthen to enhance communicability.

Determines edges that can be reduced or removed without significant impact.

Provides a framework for network robustness optimization.

Abstract

Modeling complex systems that consist of different types of objects leads to multilayer networks, where nodes in the different layers represent different kind of objects. Nodes are connected by edges, which have positive weights. A multilayer network is associated with a supra-adjacency matrix. This paper investigates the sensitivity of the communicability in a multilayer network to perturbations of the network by studying the sensitivity of the Perron root of the supra-adjacency matrix. Our analysis sheds light on which edge weights to make larger to increase the communicability of the network, and which edge weights can be made smaller or set to zero without affecting the communicability significantly.