The short answer is that you can't. The connectivity matrix simply describes the geometry of the network, not the dynamics of the degrees of freedom that live on the network. It's the dynamics that determines the ``diffusion related parameters'', namely from the two-point correlation function of the dynamical degrees of freedom, that describe how the individuals interact.

Of course in many interesting situations interactions relate the two-point correlation function with the other correlation functions-the distribution isn't a Gaussian.

In that case what matters are the relations between the correlation functions and how these can be used to obtain information on the probability distribution, therefore on the properties of the two-point correlation function, from which the diffusive properties can be deduced.

This Preprint Neural Monte Carlo Renormalization Group