A history sensitive cascade model in diffusion networks

Diffusion is a process by which information, viruses, ideas and new behavior spread over social networks. The traditional independent cascade model gives activated nodes a one-time chance to activate each of its neighboring nodes with some probability. This paper extends the traditional cascade model to be history dependent. We propose a new model called the History Sensitive Cascade Model (HSCM) that allows activated nodes to receive more than a one-time chance to activate their neighbors. HSCM provides 1) a polynomial algorithm for calculating the probability of activity for any arbitrary node at any arbitrary time in tree structure graphs, and 2) a Markov model for calculating the probability in general graphs. Finally, we perform an empirical study on HSCM under different network settings. These simulations have showed its power to observe and explain the emergent phenomena in the macro level when changing parameters in the micro level.

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