TY - JOUR

T1 - Discontinuous transition of a multistage independent cascade model on networks

AU - Hasegawa, Takehisa

AU - Nemoto, Koji

N1 - Publisher Copyright:
© 2014 IOP Publishing Ltd and SISSA Medialab srl.

PY - 2014/11/1

Y1 - 2014/11/1

N2 - 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 T1 that a node adopting a fad increases the awareness of a neighboring susceptible node and the probability T2 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 pk. 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 T1 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.

AB - 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 T1 that a node adopting a fad increases the awareness of a neighboring susceptible node and the probability T2 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 pk. 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 T1 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.

KW - interacting agent models

KW - networks

KW - percolation problems (theory)

KW - random graphs

UR - http://www.scopus.com/inward/record.url?scp=84914690062&partnerID=8YFLogxK

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U2 - 10.1088/1742-5468/2014/11/P11024

DO - 10.1088/1742-5468/2014/11/P11024

M3 - Review article

AN - SCOPUS:84914690062

VL - 2014

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 11

M1 - P11024

ER -