  The Bass model, which is an effective forecasting tool for innovation
diffusion based on large collections of empirical data, assumes an homogeneous
diffusion process. We introduce a network structure into this model and we
investigate numerically the dynamics in the case of networks with link density
$P(k)=c/k^\gamma$, where $k=1, \ldots , N$. The resulting curve of the total
adoptions in time is qualitatively similar to the homogeneous Bass curve
corresponding to a case with the same average number of connections. The peak
of the adoptions, however, tends to occur earlier, particularly when $\gamma$
and $N$ are large (i.e., when there are few hubs with a large maximum number of
connections). Most interestingly, the adoption curve of the hubs anticipates
the total adoption curve in a predictable way, with peak times which can be,
for instance when $N=100$, between 10% and 60% of the total adoptions peak.
This may allow to monitor the hubs for forecasting purposes. We also consider
the case of networks with assortative and disassortative correlations and a
case of inhomogeneous advertising where the publicity terms are "targeted" on
the hubs while maintaining their total cost constant.
