Node and layer eigenvector centralities for multiplex networks

Francesco Tudisco, Francesca Arrigo, Antoine Gautier

Research output: Contribution to journalArticle

15 Citations (Scopus)
22 Downloads (Pure)

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 entrality measure that generalizes the 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.
Original languageEnglish
Pages (from-to)853–876
Number of pages24
JournalSIAM Journal on Applied Mathematics
Volume78
Issue number2
DOIs
Publication statusPublished - 20 Mar 2018

Keywords

  • networks
  • multiplex
  • multilayer
  • eigenvector
  • centrality
  • multi-homogeneous map
  • Perron–Frobenius theory

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