  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.
