Riemannian-geometric entropy for measuring network complexity
Authors: Franzosi R., Felice D., Mancini S., Pettini M.
Autors Affiliation: QSTAR and INO-CNR, largo Enrico Fermi 2, I-50125 Firenze, Italy;
School of Science and Technology, University of Camerino, I-62032 Camerino, Italy;
INFN-Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy;
Aix-Marseille University, Marseille, France;
CNRS Centre de Physique Théorique UMR7332, 13288 Marseille, France
Abstract: A central issue in the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate with a-in principle, any-network a differentiable object (a Riemannian manifold) whose volume is used to define the entropy. The effectiveness of the latter in measuring network complexity is successfully proved through its capability of detecting a classical phase transition occurring in both random graphs and scale-free networks, as well as of characterizing small exponential random graphs, configuration models, and real networks.
Journal/Review: PHYSICAL REVIEW E
Volume: 93 (6) Pages from: 062317 to: 062317
More Information: We are indebted to R. Quax for providing us with data on power-law random graphs. We also thank M. Rasetti for useful discussions. This work was supported by the Seventh Framework Programme for Research of the European Commission under FET-Proactive Grant TOPDRIM (FP7-ICT-318121).KeyWords: Entropy; Geometry; Graph theory, Configuration model; Geometric entropy; Information geometry; Network complexity; Quantitative characterization; Random graphs; Real networks; Riemannian manifold, Complex networksDOI: 10.1103/PhysRevE.93.062317Citations: 8data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2020-10-18References taken from IsiWeb of Knowledge: (subscribers only)Connecting to view paper tab on IsiWeb: Click hereConnecting to view citations from IsiWeb: Click here