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A note on the von Neumann entropy of random graphs

Du, WX; Li, XL; Li, YY; Severini, S; (2010) A note on the von Neumann entropy of random graphs. LINEAR ALGEBRA APPL , 433 (11-12) 1722 - 1725. 10.1016/j.laa.2010.06.040.

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Abstract

In this note, we consider the von Neumann entropy of a density matrix obtained by normalizing the combinatorial Laplacian of a graph by its degree sum. We prove that the von Neumann entropy of the typical Erdos-Renyi random graph saturates its upper bound. Since connected regular graphs saturate this bound as well, our result highlights a connection between randomness and regularity. A general interpretation of the von Neumann entropy of a graph is an open problem. (C) 2010 Elsevier Inc. All rights reserved.

Type:Article
Title:A note on the von Neumann entropy of random graphs
DOI:10.1016/j.laa.2010.06.040
Keywords:Graph spectra, von Neumann entropy, Laplacian
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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