A deterministic model for history sensitive cascade in diffusion networks

This paper studies information diffusion in networks. Traditional models are all history insensitive, i.e. only giving activated nodes a one-time chance to activate each of its neighboring nodes with some probability. But history dependent interactions between people are often observed in real world. This paper 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 is a deterministic model to decide the probability of activity for any arbitrary node at any arbitrary time step. In particular, we provide 1) a polynomial algorithm for calculating this probability in tree structure graphs, and 2) a Markov model for calculating the probability in general graphs. This paper makes a theoretical contribution on studying the information diffusion problem.