title: Riemannian-geometric entropy for measuring network complexity.
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.
authors.affiliation: QSTAR and INO-CNR, largo Enrico Fermi 2, I-50125 Firenze, Italy.
authors.forename: Roberto
authors.initials: R
authors.lastname: Franzosi
authors.affiliation: School of Science and Technology, University of Camerino, I-62032 Camerino, Italy.|INFN-Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy.
authors.forename: Domenico
authors.initials: D
authors.lastname: Felice
authors.affiliation: School of Science and Technology, University of Camerino, I-62032 Camerino, Italy.|INFN-Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy.
authors.forename: Stefano
authors.initials: S
authors.lastname: Mancini
authors.affiliation: Aix-Marseille University, Marseille, France.|CNRS Centre de Physique Théorique UMR7332, 13288 Marseille, France.
authors.forename: Marco
authors.initials: M
authors.lastname: Pettini