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Title: Quantifying networks complexity from information geometry viewpoint

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.
Authors:
;  [1] ;  [2] ;  [3]
  1. School of Science and Technology, University of Camerino, I-62032 Camerino (Italy)
  2. (Italy)
  3. Centre de Physique Théorique, UMR7332, and Aix-Marseille University, Luminy Case 907, 13288 Marseille (France)
Publication Date:
OSTI Identifier:
22250811
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATIONS; ENTROPY; GEOMETRY; INFORMATION; METRICS; RANDOMNESS; SPACE; STATISTICAL MECHANICS; STATISTICAL MODELS