Catching homologies by geometric entropy
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.
Journal/Review: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
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 networksDOI: 10.1016/j.physa.2017.09.007Citations: 1data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2021-10-10References taken from IsiWeb of Knowledge: (subscribers only)Connecting to view paper tab on IsiWeb: Click hereConnecting to view citations from IsiWeb: Click here