@article{Bebiano2022, 
author = {Natália Bebiano and João da Providência and Wei-Ru Xu},
title = {Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {5},
pages = {1864-1880},
keywords = {entropy, graphs, Laplacian matrix, Euler-Maclaurin summation formula},
url = {https://www.sciopen.com/article/10.3934/era.2022094},
doi = {10.3934/era.2022094},
abstract = {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.}
}