Phase transition for the Maki-Thompson rumour model on a small-world network

Abstract

We consider the Maki-Thompson model for the stochastic propagation of a rumour within a population. We extend the original hypothesis of homogenously mixed population by allowing for a small-world network embedding the model. This structure is realized starting from a $k$-regular ring and by inserting, in the average, $c$ additional links in such a way that $k$ and $c$ are tuneable parameter for the population architecture. We prove that this system exhibits a transition between regimes of localization (where the final number of stiflers is at most logarithmic in the population size) and propagation (where the final number of stiflers grows algebraically with the population size) at a finite value of the network parameter $c$. A quantitative estimate for the critical value of $c$ is obtained via extensive numerical simulations.

24 pages, 4 figures

References in corpus (5)

• Theory of Rumour Spreading in Complex Social Networks
• On the behaviour of a rumour process with random stifling
• Criticality in diluted ferromagnet
• Universal features of information spreading efficiency on $d$-dimensional lattices
• A large deviations principle for the Maki-Thompson rumour model

Cited by in corpus (4)

• From subcritical behavior to elusive transitions in rumor models
• The Maki-Thompson rumor model on infinite Cayley trees
• Stochastic rumors on random trees
• Statistical inference for unknown parameters of stochastic SIS epidemics on complete graphs