Electronic Research Archive (Mar 2022)

Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians

  • Natália Bebiano,
  • João da Providência,
  • Wei-Ru Xu

DOI
https://doi.org/10.3934/era.2022094
Journal volume & issue
Vol. 30, no. 5
pp. 1864 – 1880

Abstract

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In this note, we approximate the von Neumann and Rényi 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, differ from the remaining diagonal entries by a perturbation.

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