  Acceptance of an innovation can occur through mutliple exposures to
individuals who have already accepted it. Presented here is a model to trace
the evolution of an innovation in a social network with a preference $\lambda$,
amidst topological constraints specified mainly by connectivity, $k$ and
population size, $N_k$. With the interplay between properties of innovation and
network structure, the model attempts to explain the variations in patterns of
innovations across social networks. Time in which the propagation attains
highest velocity depends on $\lambda^{-2}k^{-2}N_{k}^{1/2}$. Dynamics in random
networks may lead or lag behind that in scale-free networks depending on the
average connectivity. Hierarchical propagation is evident across connectivity
classes within scale-free networks, as well as across random networks with
distinct topological indices. For highly preferred innovations, the hierarchy
observed within scale-free networks tends to be insignificant. The results have
implications for administering innovations in finite size networks.
