Catching homologies by geometric entropy

Year: 2018

Authors: Felice D., Franzosi R., Mancini S., Pettini M.

Autors Affiliation: School of Science and Technology, University of Camerino, I-62032 Camerino, Italy; INFN-Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy; QSTAR and INO-CNR, largo Enrico Fermi 2, I-50125 Firenze, Italy; Aix-Marseille University, Marseille, France; CNRS Centre de Physique Théorique UMR7332, 13288 Marseille, France

Abstract: A geometric entropy is defined in terms of 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. (C) 2017 Elsevier B.V. All rights reserved.


Volume: 491      Pages from: 666  to: 677

KeyWords: Entropy; Geometry; Large scale systems; Numerical methods; Topology, Analytical method; Bottom-up manner; Differential geometry; Geometric entropy; Large-size networks; Numerical techniques; Statistical manifolds; Topological features, Complex networks
DOI: 10.1016/j.physa.2017.09.007

Citations: 1
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