How does innovation spread across a network? We give an overview of the sociological theory on the diffusion of innovation in a social system. We then study the linear threshold model for innovation on a network. An initial seed set adopts a new behavior. The remaining vertices adopt the behavoir when a specified fraction of its neighbors have adopted the behavior. We characterize when we get a complete cascade in the network, meaning that every vertex adopts the new behavior after the diffusion process completes.
