Node and layer eigenvector centralities for multiplex networks

Francesco Tudisco, Francesca Arrigo, Antoine Gautier

Research output: Contribution to journalArticle

9 Citations (Scopus)

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.
LanguageEnglish
Pages853–876
Number of pages24
JournalSIAM Journal on Applied Mathematics
Volume78
Issue number2
Early online date20 Mar 2018
DOIs
Publication statusE-pub ahead of print - 20 Mar 2018

Fingerprint

Centrality
Eigenvalues and eigenfunctions
Eigenvector
Vertex of a graph
Network layers
Tensors
Dimensionality
Numerical Study
Intuitive
Existence and Uniqueness
Tensor
Generalise

Keywords

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

Cite this

Tudisco, Francesco ; Arrigo, Francesca ; Gautier, Antoine. / Node and layer eigenvector centralities for multiplex networks. In: SIAM Journal on Applied Mathematics . 2018 ; Vol. 78, No. 2. pp. 853–876.
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Node and layer eigenvector centralities for multiplex networks. / Tudisco, Francesco; Arrigo, Francesca; Gautier, Antoine.

In: SIAM Journal on Applied Mathematics , Vol. 78, No. 2, 20.03.2018, p. 853–876.

Research output: Contribution to journalArticle

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