Node and layer eigenvector centralities for multiplex networks

TL;DR

This paper introduces a novel eigenvector centrality measure for multiplex networks based on tensor analysis, ensuring existence and uniqueness, and compares it with existing measures through extensive numerical experiments.

Contribution

It proposes a new eigenvector centrality definition for multiplex networks using tensor-based Perron eigenvectors, with proven existence and uniqueness.

Findings

The new centrality measure is mathematically well-defined under mild conditions.

Numerical experiments show the new measure's effectiveness and differences from existing centralities.

Comparison results highlight the advantages of the proposed approach.

Abstract

Eigenvector-based centrality measures are among the most popular centrality measures in network science. The underlying idea is intuitive and the mathematical description is extremely simple in the framework of standard, mono-layer networks. Moreover, several efficient computational tools are available for their computation. Moving up in dimensionality, several efforts have been made in the past to describe an eigenvector-based centrality measure that generalizes Bonacich index to the case of multiplex networks. In this work, we propose a new definition of eigenvector centrality that relies on the Perron eigenvector of a multi-homogeneous map defined in terms of the tensor describing the network. We prove that existence and uniqueness of such centrality are guaranteed under very mild assumptions on the multiplex network. Extensive numerical studies are proposed to test the newly introduced centrality measure and to compare it to other existing eigenvector-based centralities.