## Approximations for von Neumann and Renyi entropies of graphs using the Euler-Maclaurin formula

Natália Bebiano, Susana Furtado, João da Providência, Wei-Ru Xu, and João P. da Providência

### Abstract

There have been many attempts of understanding graph structures by investigating graph entropies. In this article we investigate approximations for von Neumann and Rényi-$\alpha$ entropies of paths and rings, using the Euler-Maclaurin summation formula. For $\alpha$ an integer, the approximations become exact, and, in general, the obtained estimates have a remarkable degree of accuracy.

Full Text (PDF) [449 KB], BibTeX

### Key words

entropy, graphs, Laplacian matrix, Euler-Maclaurin formula

### AMS subject classifications

05C50, 81P45, 91A17

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