Riemannian-geometric entropy for measuring network complexity

Year: 2016

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.


Volume: 93 (6)      Pages from: 062317-1  to: 062317-11

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 networks
DOI: 10.1103/PhysRevE.93.062317

Citations: 9
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