Evolving activity cascades on socio-technological networks

Networks are the substrate on which social contagion propagates, from the growth of social movements to the adoption of innovations. In the complex networks community, it took some time to realize the difference between simple propagation—e.g., the spread of disease—in which a single active node is sufficient to trigger the activation of its neighbors, and complex contagion, in which node activation requires simultaneous exposure to multiple active neighbors. Rooted in the social science literature, complex contagion has settled as the driving mechanism for behavior cascades on social networks. However, our access to digital traces of social interaction reveals, besides and beyond complex contagion, bursty activity patterns, repeated agent activation, and occasionally a form of synchronization under the form of trending topics and hypes. Thus, the threshold model—the paramount example in the tradition of complex contagion—needs to shift from a standpoint in which agents become irreversibly active (“one-off” events), to another in which agents continuously change their state and whose activity shows oscillating patterns. Here, we review a mechanistic model that, within the logic of complex contagion, accounts as well for the temporal evolution of behavior cascades. In it, agents follow the dynamics of integrate-and-fire oscillators. The affordances of the model—and of some recent variations on it—will open a discussion and outlook for future developments.