A temporal network version of watts’s cascade model

Threshold models of cascades in the social and economical sciences explain the spread of opinion and innovation as an effect of social influence. In threshold cascade models, fads or innovation spread between agents as determined by their interactions to other agents and their personal threshold of resistance. Typically, these models do not account for structure in the timing of interaction between the units. In this work, we extend a model of social cascades by Duncan Watts to temporal interaction networks. In our model, we assume agents are influenced by their friends and acquaintances at certain time into the past. That is, the influence of the past ages and becomes unimportant. Thus, our modified cascade model has an effective time window of influence. We explore two types of thresholds—thresholds to fractions of the neighbors, or absolute numbers. We try our model on six empirical datasets and compare them with null models.