  Using a mean-field network formulation of the Bass innovation diffusion model
and exact results by Fotouhi and Rabbat on the degree correlations of
Barabasi-Albert networks, we compute the times of the diffusion peak and
compare them with those on scale-free networks which have the same scale-free
exponent but different assortativity properties. We compare our results with
those obtained by Caldarelli et al. for the SIS epidemic model with the
spectral method applied to adjacency matrices. It turns out that diffusion
times on finite Barabasi-Albert networks are at a minimum. This may be due to a
little-known property of these networks: although the value of the
assortativity coefficient is close to zero, they look disassortative if one
considers only a bounded range of degrees, including the smallest ones, and
slightly assortative on the range of the higher degrees. We also find that if
the trickle-down character of the diffusion process is enhanced by a larger
initial stimulus on the hubs (via a inhomogeneous linear term in the Bass
model), the relative difference between the diffusion times for BA networks and
uncorrelated networks is even larger, reaching for instance the 34% in a
typical case on a network with $10^4$ nodes.
