Catching homologies by geometric entropy
Mathematical Physics
2017-12-20 v1 math.MP
Abstract
A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability to single out topological features of networks proceeding in a bottom-up manner: first we consider small size networks by analytical methods and then large size networks by numerical techniques. Two different classes of networks, the random graphs and the scale--free networks, are investigated computing their Betti numbers and then showing the capability of geometric entropy of detecting homologies.
Cite
@article{arxiv.1703.07369,
title = {Catching homologies by geometric entropy},
author = {D. Felice and R. Franzosi and S. Mancini and M. Pettini},
journal= {arXiv preprint arXiv:1703.07369},
year = {2017}
}
Comments
12 pages, 2 Figures