A Tensor-Based Framework for Studying Eigenvector Multicentrality in Multilayer Networks

TL;DR

This paper introduces a tensor-based framework for analyzing eigenvector multicentrality in multilayer networks, enabling better understanding of interlayer influence and node importance across complex interconnected systems.

Contribution

It presents a novel tensor-based approach for studying multicentrality, incorporating interlayer influence and providing algorithms for practical computation.

Findings

Framework effectively quantifies interlayer influence.

Algorithms successfully compute eigenvector multicentrality.

Application to empirical networks validates the approach.

Abstract

Centrality is widely recognized as one of the most critical measures to provide insight in the structure and function of complex networks. While various centrality measures have been proposed for single-layer networks, a general framework for studying centrality in multilayer networks (i.e., multicentrality) is still lacking. In this study, a tensor-based framework is introduced to study eigenvector multicentrality, which enables the quantification of the impact of interlayer influence on multicentrality, providing a systematic way to describe how multicentrality propagates across different layers. This framework can leverage prior knowledge about the interplay among layers to better characterize multicentrality for varying scenarios. Two interesting cases are presented to illustrate how to model multilayer influence by choosing appropriate functions of interlayer influence and design algorithms to calculate eigenvector multicentrality. This framework is applied to analyze several empirical multilayer networks, and the results corroborate that it can quantify the influence among layers and multicentrality of nodes effectively.