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arXiv · 1703.07369

Catching homologies by geometric entropy

D. Felice·R. Franzosi·S. Mancini·M. Pettini
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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.

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D. Felice, R. Franzosi, S. Mancini, M. Pettini. 2017-03-21. Catching homologies by geometric entropy. https://doi.org/10.1016/j.physa.2017.09.007

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