Complex Contagion 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 effect of long ties generalizes from simple to complex contagions – those in which the credibility of information or the willingness to adopt an innovation requires independent confirmation from multiple sources. Using Watts and Strogatz’s original small world model, we demonstrate that long ties may not only fail to speed up complex contagions, they can even preclude diffusion entirely. Results suggest that the spread of collective actions, social movements, and risky innovations benefit not from ties that are long but from bridges that are wide enough to transmit strong social reinforcement. Balance theory shows how wide bridges might also form in evolving networks, but this turns out to have surprisingly little effect on the propagation of complex contagions. We find that hybrid contagions, which have high thresholds for some nodes and low-thresholds for others, can propagate on perturbed networks if the latter are sufficiently numerous. However, for purely complex contagions, propagation depends decisively on wide bridges, a characteristic feature of spatial networks. This may account in part for the widely observed tendency for social movements to diffuse spatially.