Complex contagion

Complex contagion (vs. Simple contagion) is the contagion that is substantially affected by the reinforcing signals. An extreme case is captured by the Linear threshold model, where one adopts a piece of information, a belief, or a behavior only when the number (or fraction) of neighbors with contagion crosses a threshold.

In complex contagion, hubs are not as important¹ because hubs by themselves cannot create strong social reinforcement, which is critical in complex contagion.

Instead, the clustering and community structure become more important. Without strong clustering, complex contagion cannot spread well.

http://ncase.me/crowds/ is an excellent explorable that explains the concept of complex contagion.

Key studies

We can trace the idea of reinforcement back to Thomas Schelling‘s segregation model or Mark Granovetter‘s Threshold model. The threshold model was studied on network setting by Duncan Watts in Watts2002simple. Some evidence of complex contagion has been collected on online services (e.g., Bakshy2009social, Backstrom2006group, etc.).

Centola2010spread provided a very clear evidence of complex contagion by conducting an experiment with two different network configuration (small-world without clustering vs. large-world with clustering).

Weng2013virality showed that a spectrum from Simple contagion to Complex contagion may coexist in a single system and Community structure can be used to distinguish them because Community structure has distinct impacts on the two types of contagions.
Because strong Community structure faciliates the spread of Complex contagion within communities while blocking it from jumping between communities, this can lead to a counterintuitive phenomenon called Optimal modularity, demonstrated in Nematzadeh2014optimal.

Patterns of spreading

• Contreras2023infection

Application to Neuroscience

Because neural dynamics is largely threshold-like, we can extend the idea of complex contagion to Neuroscience as well.

• Long ties accelerate noisy threshold-based contagions

Can a network facilitate complex contagion while preventing simple contagion (diseases)?

Interacting contagions may behave (macroscopically) like complex contagions. See Hébert Dufresne2020macroscopic