Measuring vertex centrality using the Holevo quantity

Luca Rossi, Andrea Torsello

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

3 Citations (Scopus)

Abstract

In recent years, the increasing availability of data describing the dynamics of real-world systems led to a surge of interest in the complex networks of interactions that emerge from such systems. Several measures have been introduced to analyse these networks, and among them one of the most fundamental ones is vertex centrality, which quantifies the importance of a vertex within a graph. In this paper, we propose a novel vertex centrality measure based on the quantum information theoretical concept of Holevo quantity. More specifically, we measure the importance of a vertex in terms of the variation in graph entropy before and after its removal from the graph. More specifically, we find that the centrality of a vertex v can be broken down in two parts: (1) one which is negatively correlated with the degree centrality of v, and (2) one which depends on the emergence of non-trivial structures in the graph when v is disconnected from the rest of the graph. Finally, we evaluate our centrality measure on a number of real-world as well as synthetic networks, and we compare it against a set of commonly used alternative measures.

Original languageEnglish
Title of host publicationGraph-Based Representations in Pattern Recognition - 11th IAPR-TC-15 International Workshop, GbRPR 2017, Proceedings
EditorsPasquale Foggia, Mario Vento, Cheng-Lin Liu
PublisherSpringer Verlag
Pages154-164
Number of pages11
ISBN (Print)9783319589602
DOIs
Publication statusPublished - May 2017
Externally publishedYes
Event11th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition, GbRPR 2017 - Anacapri, Italy
Duration: 16 May 201718 May 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10310 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition, GbRPR 2017
Country/TerritoryItaly
CityAnacapri
Period16/05/1718/05/17

Keywords

  • Complex networks
  • Quantum Information
  • Vertex centrality

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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