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Title: Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians
Authors: Bebiano, Natália 
Providência, João da 
Xu, Wei-Ru
Keywords: entropy; graphs; Laplacian matrix; Euler-Maclaurin summation formula
Issue Date: 2022
Project: UID/FIS/04564/2019 
Laurent Mathematics Center of Sichuan Normal University and National-Local Joint Engineering Laboratory of System Credibility Automatic Verification (No. ZD20220106). 
Serial title, monograph or event: Electronic Research Archive
Volume: 30
Issue: 5
Abstract: In this note, we approximate the von Neumann and R´enyi entropies of high-dimensional graphs using the Euler-Maclaurin summation formula. The obtained estimations have a considerable degree of accuracy. The performed experiments suggest some entropy problems concerning graphs whose Laplacians are g-circulant matrices, i.e., circulant matrices with g-periodic diagonals, or quasi- Toeplitz matrices. Quasi means that in a Toeplitz matrix the first two elements in the main diagonal, and the last two, di er from the remaining diagonal entries by a perturbation.
ISSN: 2688-1594
DOI: 10.3934/era.2022094
Rights: openAccess
Appears in Collections:I&D CFis - Artigos em Revistas Internacionais
I&D CMUC - Artigos em Revistas Internacionais

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