Temporal Evolution of Social Innovation

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.