## Abstract

We propose a multistage version of the independent cascade model, which we call a multistage independent cascade (MIC) model, on networks. This model is parameterized by two probabilities: the probability T_{1} that a node adopting a fad increases the awareness of a neighboring susceptible node and the probability T_{2} that an adopter directly causes a susceptible node to adopt the fad. We formulate a tree approximation for the MIC model on an uncorrelated network with an arbitrary degree distribution p_{k}. Applied on a random regular network with degree k=6, this model exhibits a rich phase diagram, including continuous and discontinuous transition lines for fad percolation and a continuous transition line for the percolation of susceptible nodes. In particular, the percolation transition of fads is discontinuous (continuous) when T_{1} is larger (smaller) than a certain value. A similar discontinuous transition is observed in random graphs and scale-free networks. Furthermore, assigning a finite fraction of initial adopters dramatically changes the phase boundaries.

Original language | English |
---|---|

Article number | P11024 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2014 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2014 Nov 1 |

## Keywords

- interacting agent models
- networks
- percolation problems (theory)
- random graphs

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty