Complex Contagions and the Weakness of Long Ties

The strength of weak ties is that they tend to be long – they connect socially distant locations. Recent research on “small worlds” shows that remarkably few long ties are needed to give large and highly clustered populations the “degrees of separation” of a random network, in which information can rapidly diffuse. We test whether this “strength of weak ties” generalizes from simple to complex contagions – those in which the credibility of information or the willingness to adopt an innovation requires independent confirmation or reinforcement from multiple sources. Using Watts and Strogatz’s original small world model, we demonstrate that as thresholds increase, more random ties are needed to speed up complex contagions and fewer random ties are needed to preclude diffusion entirely. Results show that contagions requiring strong social reinforcement – such as the spread of collective action, social movements, and risky innovations – depend primarily on the width of bridges between otherwise distant locations, not just their length. Wide bridges are a characteristic feature of many spatial networks, which may account in part for the widely observed tendency for social movements to diffuse spatially.