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https://hdl.handle.net/10316/100571
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 UID/MAT/00324/2013 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. | URI: | https://hdl.handle.net/10316/100571 | ISSN: | 2688-1594 | DOI: | 10.3934/era.2022094 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais I&D CFis - Artigos em Revistas Internacionais |
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