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.
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Physical Review E , American Physical Society (APS), 2016, 〈10.1103/PhysRevE.93.062317〉
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Roberto Franzosi, Domenico Felice, Stefano Mancini, Marco Pettini. Riemannian-geometric entropy for measuring network complexity. Physical Review E , American Physical Society (APS), 2016, 〈10.1103/PhysRevE.93.062317〉. 〈hal-01361918〉

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