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Article Dans Une Revue Journal of Mathematical Physics Année : 2014

Quantifying Networks Complexity from Information Geometry Viewpoint

Résumé

We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as weighted edges among vertices. We then associate to the parameter space a statistical manifold endowed with a Riemannian metric structure (that of Fisher-Rao). Going on, in analogy with the microcanonical definition of entropy in Statistical Mechanics, we introduce an entropic measure of networks complexity. We prove that it is invariant under networks isomorphism. Above all, considering networks as simplicial complexes, we evaluate this entropy on simplexes and find that it monotonically increases with their dimension.

Dates et versions

hal-01252500 , version 1 (07-01-2016)

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Domenico Felice, Stefano Mancini, Marco Pettini. Quantifying Networks Complexity from Information Geometry Viewpoint. Journal of Mathematical Physics, 2014, 55 (4), pp.043505. ⟨10.1063/1.4870616⟩. ⟨hal-01252500⟩
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