Edge centrality via the Holevo quantity

Joshua Lockhart, Giorgia Minello, Luca Rossi, Simone Severini, Andrea Torsello

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

5 Citations (Scopus)

Abstract

In the study of complex networks, vertex centrality measures are used to identify the most important vertices within a graph. A related problem is that of measuring the centrality of an edge. In this paper, we propose a novel edge centrality index rooted in quantum information. More specifically, we measure the importance of an edge in terms of the contribution that it gives to the Von Neumann entropy of the graph. We show that this can be computed in terms of the Holevo quantity, a well known quantum information theoretical measure. While computing the Von Neumann entropy and hence the Holevo quantity requires computing the spectrum of the graph Laplacian, we show how to obtain a simplified measure through a quadratic approximation of the Shannon entropy. This in turns shows that the proposed centrality measure is strongly correlated with the negative degree centrality on the line graph. We evaluate our centrality measure through an extensive set of experiments on real-world as well as synthetic networks, and we compare it against commonly used alternative measures.

Original languageEnglish
Title of host publicationStructural, Syntactic, and Statistical Pattern Recognition - Joint IAPR International Workshop S+SSPR 2016, Proceedings
EditorsBattista Biggio, Richard Wilson, Marco Loog, Francisco Escolano, Antonio Robles-Kelly
PublisherSpringer Verlag
Pages143-152
Number of pages10
ISBN (Print)9783319490540
DOIs
Publication statusPublished - Nov 2016
Externally publishedYes
EventJoint IAPR International Workshops on Structural and Syntactic Pattern Recognition, SSPR 2016 - Merida, Mexico
Duration: 29 Nov 20162 Dec 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10029 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceJoint IAPR International Workshops on Structural and Syntactic Pattern Recognition, SSPR 2016
Country/TerritoryMexico
CityMerida
Period29/11/162/12/16

Keywords

  • Complex networks
  • Edge centrality
  • Holevo quantity
  • Quantum information

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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