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Node centrality for continuous-time quantum walks

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Title of host publicationStructural, Syntactic, and Statistical Pattern Recognition
DatePublished - 2014
Pages103-112
Number of pages10
PublisherSpringer-Verlag
Volume8621 LNCS
Original languageEnglish
ISBN (Print)9783662444146

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8621 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Abstract

The study of complex networks has recently attracted increasing interest because of the large variety of systems that can be modeled using graphs. A fundamental operation in the analysis of complex networks is that of measuring the centrality of a vertex. In this paper, we propose to measure vertex centrality using a continuous-time quantum walk. More specifically, we relate the importance of a vertex to the influence that its initial phase has on the interference patterns that emerge during the quantum walk evolution. To this end, we make use of the quantum Jensen-Shannon divergence between two suitably defined quantum states. We investigate how the importance varies as we change the initial state of the walk and the Hamiltonian of the system. We find that, for a suitable combination of the two, the importance of a vertex is almost linearly correlated with its degree. Finally, we evaluate the proposed measure on two commonly used networks.

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© Springer Verlag 2014. This is an author produced version of a paper accepted for publication in Lecture Notes in Computer Science. Uploaded in accordance with the publisher's self-archiving policy.

    Research areas

  • Complex Network, Quantum Jensen-Shannon Divergence, Quantum Walk, Vertex Centrality

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