Complex Contagions on Social Networks

Social interactions constitute a crucial part of everyday life.
Behavior changes, similar to rumors or viruses, spread in the social network
and become a contagion. Diseases and information can spread through a
single contact. However, in many realistic settings when agents' actions and behavioral changes are involved, it often takes multiple activated neighbors to spread a contagion. We denote this type of contagion as a complex contagion. The requirement of synergy between neighbors, intuitively, makes the spreading of a complex contagion to be more unlikely, slower, and more delicate. Enabling the successful spreading of a complex contagion requires special graph structures.
This talk will present recent mathematical results on the study of complex contagion in network models. In particular, we will highlight classes of models where complex contagions can spread quickly and provide a rigorous mathematical foundation for how.