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arXiv · 1410.5459

Riemannian-geometric entropy for measuring network complexity

Roberto Franzosi·Domenico Felice·Stefano Mancini·Marco Pettini
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Abstract

A central issue of 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 to a - in principle any - network a differentiable object (a Riemannian manifold) whose volume is used to define an entropy. The effectiveness of the latter to measure networks 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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Roberto Franzosi, Domenico Felice, Stefano Mancini, Marco Pettini. 2014-10-20. Riemannian-geometric entropy for measuring network complexity. https://doi.org/10.1103/physreve.93.062317

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