Critical phenomena in complex contagions

Why do some contagions “go viral” and others do not? Research on “small world” networks (Watts and Strogatz, 1998) shows how a very small number of long-range ties that bridge between clusters can allow contagions to spread almost as rapidly as on a random network of equal density. Recent research shows how long-range ties that accelerate the spread of information and disease can impede the spread of complex contagions—behaviors, beliefs and preferences that diffuse via contact with multiple adopters ( Centola and Macy, 2007). In confirming this result analytically and extending the analysis from small world to power law networks, we discovered that complex contagions require a critical mass of infected nodes that corresponds to a phase transition in the ability of the contagion to take advantage of the “shortcuts” created by long-range ties. We demonstrate how this critical mass is related to the dynamics of the contagion process and identify implications for modeling behaviors that spread via social influence, such as viral marketing and social movements.

► We show that social contagions typically require a critical mass of infected nodes that corresponds to a phase transition in the ability of the contagion to take advantage of the “shortcuts” created by long-range ties.
► We derive the value of the critical mass analytically, and show how the value depends on network topology and the network externality of the contagion.
► We conclude by identifying implications for modeling behaviors that spread via social influence, such as viral marketing and social movements.