What Stops Social Epidemics?

Abstract

Theoretical progress in understanding the dynamics of spreading processes on graphs suggests the existence of an epidemic threshold below which no epidemics form and above which epidemics spread to a significant fraction of the graph. We have observed information cascades on the social media site Digg that spread fast enough for one initial spreader to infect hundreds of people, yet end up affecting only 0.1% of the entire network. We find that two effects, previously studied in isolation, combine cooperatively to drastically limit the final size of cascades on Digg. First, because of the highly clustered structure of the Digg network, most people who are aware of a story have been exposed to it via multiple friends. This structure lowers the epidemic threshold while moderately slowing the overall growth of cascades. In addition, we find that the mechanism for social contagion on Digg points to a fundamental difference between information spread and other contagion processes: despite multiple opportunities for infection within a social group, people are less likely to become spreaders of information with repeated exposure. The consequences of this mechanism become more pronounced for more clustered graphs. Ultimately, this effect severely curtails the size of social epidemics on Digg.

Scalable Continuous-time Diffusion Framework for Network Inference and Influence Estimation

“…To begin with, for illustration, observe that online users usually get more exposed to marketing information as this is initially diffused in their community, and the influence of neighbors on that specific piece of information typically diminishes gradually with time. This is the well-known saturation effect [26,27,38,40,44]. To model this phenomenon, we employ exponential functions with learnable parameters to quantify the transmission rate between nodes [18,41].…”