Domenico Felice

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.

Hamilton-Jacobi approach to potential functions in information geometry

The search for a potential function

Riemannian-geometric entropy for measuring network complexity.

S

Information Geometric Complexity of a Trivariate Gaussian Statistical Model

allowing to reconstruct a given metric tensor

Information geometric methods for complexity

g

The volume of Gaussian states by information geometry

and a given symmetric covariant tensor

Gaussian Network’s Dynamics Reflected into Geometric Entropy

T

Catching homologies by geometric entropy

on a manifold

Aspects of Geodesical Motion with Fisher-Rao Metric: Classical and Quantum

\mathcal{M}

The Volume of Two-Qubit States by Information Geometry

is formulated as the Hamilton-Jacobi problem associated with a canonically defined Lagrangian on