The Speed of Innovation Diffusion in Complex Social Networks

H. Peyton Young , Department of Economics,  University of Oxford , UK

New technologies typically gain a foothold through the actions of a few innovators, and then diffuse more rapidly as more and more people come into contact with prior adopters.
Much of the prior literature focuses on the rate of diffusion as a function of the topology of a given network. Here we derive “topology-free” bounds on the expected waiting time until a given fraction of the population has adopted the innovation.
The bounds depend on the perceived benefits from using the innovation, and on spillover effects from neighbors’ adoption decisions, but they do not depend on the network structure per se. In particular, the bounds hold for directed and undirected networks of arbitrary size whose structure may be evolving over time.