Quantifying Networks Complexity from Information Geometry Viewpoint

Abstract

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.

16 pages, 1 table

References in corpus (2)

• Critical phenomena in complex networks
• Networks in Motion

Cited by in corpus (10)

• Information geometric methods for complexity
• Geometric Algebra and Information Geometry for Quantum Computational Software
• Entropic dynamics on Gibbs statistical manifolds
• The volume of Gaussian states by information geometry
• Theoretical investigations of an information geometric approach to complexity
• Information geometric complexity of a trivariate Gaussian statistical model
• A geometric entropy detecting the Erdös-Rényi phase transition
• Riemannian-geometric entropy for measuring network complexity
• Information geometry and Bose-Einstein condensation
• Catching homologies by geometric entropy