Takehisa Hasegawa, Koji Nemoto
We study a multistage independent cascade (MIC) model in complex networks. This model is parameterized by two probabilities: T1 is the probability that a node adopting a fad increases the awareness of a neighboring susceptible node until it abandons the fad, and T2 is the probability that an adopter directly causes a susceptible node to adopt the fad. We formulate a framework of tree approximation for the MIC model on an uncorrelated network with an arbitrary given degree distribution. As an application, we study this model on a random regular network with degree k=6 to show that it has a rich phase diagram including continuous and discontinuous transition lines for the percolation of fads as well as a continuous transition line for the percolation of susceptible nodes. In particular, the percolation transition of fads is discontinuous (continuous) when T1 is larger (smaller) than a certain value. Furthermore, the phase boundaries drastically change by assigning a finite fraction of initial adopters. We discuss this sensitivity by both tree approximation and numerical simulation.
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http://arxiv.org/abs/1212.5547
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