Threshold model of cascades in empirical temporal networks

Abstract

Threshold models try to explain the consequences of social influence like the spread of fads and opinions. Along with models of epidemics, they constitute a major theoretical framework of social spreading processes. In threshold models on static networks, an individual changes her state if a certain fraction of her neighbors has done the same. When there are strong correlations in the temporal aspects of contact patterns, it is useful to represent the system as a temporal network. In such a system, not only contacts but also the time of the contacts are represented explicitly. There is a consensus that bursty temporal patterns slow down disease spreading. However, as we will see, this is not a universal truth for threshold models. In this work, we propose an extension of Watts' classic threshold model to temporal networks. We do this by assuming that an agent is influenced by contacts which lie a certain time into the past. I.e., the individuals are affected by contacts within a time window. In addition to thresholds as the fraction of contacts, we also investigate the number of contacts within the time window as a basis for influence. To elucidate the model's behavior, we run the model on real and randomized empirical contact datasets.

Bursty Communication Patterns Facilitate Spreading in a Threshold-Based Epidemic Dynamics

“…Threshold models can be generalized to temporal networks in several ways. Reference [23], for example, considers a sliding window where only contacts within the window matters for the spreading. The authors examined two types of threshold rules–whether the threshold operates on all the total number of contacts with I in the interval or on the fraction of such contacts.…”

Threshold cascades with response heterogeneity in multiplex networks

“…Previous studies showed * kgoh@korea.ac.kr that, for a wide range of network densities and threshold distributions, even an extremely small seed fraction ρ 0 can activate a finite fraction of an infinite-size network, an event called a global cascade [16,17]. Recently, some studies have generalized the threshold model to temporal networks [22] and to multiplex networks [5,23]. However, cascades with heterogeneous nodal responses to their multiplex environments are not yet addressed.…”

Analyzing Temporal Networks in Social Media

“…Ref. [21] discusses this further and uses a sliding time window to represent the duration of possible influence. Ref.…”