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

<abstract><p>In this note, we approximate the von Neumann and Rényi entropies of high-dimensional graphs using Euler-Maclaurin summation formula. The obtained estimations have a considerable degree accuracy. performed experiments suggest some entropy problems concerning whose Laplacians are $ g $-circulant matrices, i.e., circulant matrices with $-periodic diagonals, or quasi-Toeplitz matrices. Quasi means that in Toeplitz matrix first two elements main diagonal, last two, differ from remaining diagonal entries by perturbation.</p></abstract>