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Measuring Vertex Centrality Using the Holevo Quantity

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Graph-Based Representations in Pattern Recognition (GbRPR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10310))

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.

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Author information

Authors and Affiliations

  1. School of Engineering and Applied Science, Aston University, Birmingham, UK

    Luca Rossi

  2. DAIS, Università Ca’ Foscari Venezia, Venice, Italy

    Andrea Torsello

Authors
  1. Luca Rossi
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  2. Andrea Torsello
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Correspondence to Luca Rossi .

Editor information

Editors and Affiliations

  1. Università degli Studi di Salerno, Fisciano, Italy

    Pasquale Foggia

  2. Chinese Academy of Sciences, Beijing, China

    Cheng-Lin Liu

  3. Università degli Studi di Salerno, Fisciano, Italy

    Mario Vento

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Rossi, L., Torsello, A. (2017). Measuring Vertex Centrality Using the Holevo Quantity. In: Foggia, P., Liu, CL., Vento, M. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2017. Lecture Notes in Computer Science(), vol 10310. Springer, Cham. https://doi.org/10.1007/978-3-319-58961-9_14

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  • DOI: https://doi.org/10.1007/978-3-319-58961-9_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58960-2

  • Online ISBN: 978-3-319-58961-9

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