Measuring vertex centrality using the Holevo quantity

Rossi, Luca and Torsello, Andrea (2017). Measuring vertex centrality using the Holevo quantity. IN: Graph-based representations in pattern recognition : 11th IAPR-TC-15 international workshop, GbRPR 2017. Proceedings. Foggia, Pasquale; Liu, Cheng-Lin and Vento, Mario (eds) Lecture Notes in Computer Science . Cham (CH): Springer.

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.

Publication DOI: https://doi.org/10.1007/978-3-319-58961-9_14
Divisions: Engineering & Applied Sciences
Engineering & Applied Sciences > Computer science research group
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Event Title: 11th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition, GbRPR 2017
Event Type: Other
Event Dates: 2017-05-16 - 2017-05-18
Uncontrolled Keywords: complex networks,quantum Information,vertex centrality,Theoretical Computer Science,Computer Science(all)
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
Published Date: 2017
Authors: Rossi, Luca ( 0000-0002-6116-9761)
Torsello, Andrea

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