When agents interact and adapt in a network, the spread of behavior is often modeled as a type of cascade. At the heart of many of these models is a form of threshold-based contagion, in which an individual's probability of changing state depends on the number of neighbors who have done so. We analyze a basic formulation of this threshold contagion process, and show that the relative sizes of cascades can depend in subtle ways on the structure of the underlying network: small shifts in the distribution of thresholds can favor graphs with a maximally clustered structure, those with a maximally branching structure, or even intermediate hybrids.

The talk is based on joint work with Larry Blume, David Easley, Bobby Kleinberg, and Eva Tardos.