A process of rumor scotching on finite populations

Rumor spreading is a ubiquitous phenomenon in social and technological networks. Traditional models consider that the rumor is propagated by pairwise interactions between spreaders and ignorants. Spreaders can become stiflers only after contacting spreaders or stiflers. Here we propose a model that considers the traditional assumptions, but stiflers are active and try to scotch the rumor to the spreaders. An analytical treatment based on the theory of convergence of density dependent Markov chains is developed to analyze how the final proportion of ignorants behaves asymptotically in a finite homogeneously mixing population. We perform Monte Carlo simulations in random graphs and scale-free networks and verify that the results obtained for homogeneously mixing populations can be approximated for random graphs, but are not suitable for scale-free networks. Furthermore, regarding the process on a heterogeneous mixing population, we obtain a set of differential equations that describes the time evolution of the probability that an individual is in each state. Our model can be applied to study systems in which informed agents try to stop the rumor propagation. In addition, our results can be considered to develop optimal information dissemination strategies and approaches to control rumor propagation.Comment: 13 pages, 11 figure

Controversy-seeking fuels rumor-telling activity in polarized opinion networks

Rumors have ignited revolutions, undermined the trust in political parties, or threatened the stability of human societies. Such destructive potential has been significantly enhanced by the development of on-line social networks. Several theoretical and computational studies have been devoted to understanding the dynamics and to control rumor spreading. In the present work, a model of rumor-telling in opinion polarized networks was investigated through extensive computer simulations. The key mechanism is the coupling between ones' opinions and their leaning to spread a given information, either by supporting or opposing its content. We report that a highly modular topology of polarized networks strongly impairs rumor spreading, but the couplings between agent's opinions and their spreading/stifling rates can either further inhibit or, conversely, foster information propagation, depending on the nature of those couplings. In particular, a controversy-seeking mechanism, in which agents are stimulated to postpone their transitions to the stiffer state upon interactions with other agents of confronting opinions, enhances the rumor spreading. Therefore such a mechanism is capable of overcoming the propagation bottlenecks imposed by loosely connected modular structures.Comment: 11 pages, 7 figure

How asynchrony affects rumor spreading time

International audienceIn standard randomized (push-pull) rumor spreading, nodes communicate in synchronized rounds. In each round every node contacts a random neighbor in order to exchange the rumor (i.e., either push the rumor to its neighbor or pull it from the neighbor). A natural asynchronous variant of this algorithm is one where each node has an independent Poisson clock with rate 1, and every node contacts a random neighbor whenever its clock ticks. This asynchronous variant is arguably a more realistic model in various settings, including message broadcasting in communication networks, and information dissemination in social networks. In this paper we study how asynchrony affects the rumor spreading time, that is, the time before a rumor originated at a single node spreads to all nodes in the graph. Our first result states that the asynchronous push-pull rumor spreading time is asymptotically bounded by the standard synchronous time. Precisely, we show that for any graph G on n nodes, where the synchronous push-pull protocol informs all nodes within T (G) rounds with high probability, the asynchronous protocol needs at most time O(T (G) + log n) to inform all nodes with high probability. On the other hand, we show that the expected synchronous push-pull rumor spreading time is bounded by O(√ n) times the expected asynchronous time. These results improve upon the bounds for both directions shown recently by Acan et al. (PODC 2015). An interesting implication of our first result is that in regular graphs, the weaker push-only variant of synchronous rumor spreading has the same asymptotic performance as the synchronous push-pull algorithm