  We introduce a heterogeneous network structure into the Bass diffusion model,
in order to study the diffusion times of innovation or information in networks
with a scale-free structure, typical of regions where diffusion is sensitive to
geographic and logistic influences (like for instance Alpine regions). We
consider both the diffusion peak times of the total population and of the link
classes. In the familiar trickle-down processes the adoption curve of the hubs
is found to anticipate the total adoption in a predictable way. In a major
departure from the standard model, we model a trickle-up process by introducing
heterogeneous publicity coefficients (which can also be negative for the hubs,
thus turning them into stiflers) and a stochastic term which represents the
erratic generation of innovation at the periphery of the network. The results
confirm the robustness of the Bass model and expand considerably its range of
applicability.
