Theory of Rumour Spreading in Complex Social Networks

TL;DR

This paper develops a stochastic model for rumour spreading on complex social networks, analyzing how network topology influences the threshold, speed, and reach of rumours, especially highlighting the vulnerability of scale-free networks.

Contribution

It introduces a general rumour spreading model and derives mean-field equations to analyze dynamics on various complex networks, including scale-free networks with degree correlations.

Findings

Rumours cannot propagate below a critical spreading rate in homogeneous networks.

Scale-free networks have a vanishing threshold as size increases, making them highly susceptible.

Rumour spread is faster and more extensive in scale-free networks, especially with assortative degree correlations.

Abstract

We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular those mediated by the Internet). We use analytical and numerical solutions of these equations to examine the threshold behavior and dynamics of the model on several models of such networks: random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumour spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumour, however, depends on the interplay between network topology and the rumour spreading rate. Our results show that scale-free social networks are prone to the spreading of rumours, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale information dissemination algorithms on the Internet.