Open AccessApproximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians
Author(s) -
Natália Bebiano,
J. da Providência,
Wei-Ru Xu
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022094
Subject(s) - circulant matrix , toeplitz matrix , mathematics , diagonal , von neumann entropy , combinatorics , pure mathematics , discrete mathematics , physics , geometry , quantum mechanics , quantum entanglement , quantum
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.