A model for the spread of rumors in Barrat-Barthelemy-Vespignani (BBV) networks

Rumor propagation is a typical form of social communication and plays a significant role in social life. In this paper, we studied the process of rumor propagation by accounting for the mechanism of forgetting in Barrat-Barthelemy-Vespignani (BBV) networks. First, we derived mean-field equations for rumor propagation based on the strength of the nodes in the propagation network. We then analyzed the stability of the model to determine whether a propagation threshold existed in the BBV networks. We also conducted numerical simulations of the BBV networks and found that rumors propagate more slowly in BBV networks than in unweighted networks. The numerical simulation results also demonstrated that as the forgetting rate increases, the rumor's influence decreases in both BBV networks and unweighted networks. Finally, the simulation results confirmed that a threshold exists for rumor propagation in BBV networks, but that it was independent of the value of the stifling rate.