Role of persistent cascades in diffusion.

We define a structural property of real-world large-scale communication networks consisting of the recurring patterns of communication among individuals, which we term persistent cascades. Using methods of inexact tree matching and agglomerative clustering, we group these patterns into classes which we claim represent some underlying way in which individuals tend to disseminate information. We extend methods from epidemic modeling to offer a way to analytically model this recurring structure in a random network, and comparing to the data, we find that the real cascading structure is significantly larger and more recurrent than the random model. We find that the cascades reveal a habitual hierarchy of spreading, alternative roles in weekday vs weekend spreading, and the existence of hidden spreaders. Finally, we show that cascade membership increases the likelihood of receiving information spreading through the network through simulation on the real order of communication events.