The role of network topology on extremism propagation with the relative agreement opinion dynamics

In Deffuant et al. (J. Artif. Soc. Soc. Simulation 5 (2002) 4), we proposed a simple model of opinion dynamics, which we used to simulate the influence of extremists in a population. Simulations were run without any specific interaction structure and varying the simulation parameters, we observed different attractors such as predominance of centrism or of extremism. We even observed in certain conditions, that the whole population drifts to one extreme of the opinion, even if initially there are an equal number of extremists at each extreme of the opinion axis. In the present paper, we study the influence of the social networks on the presence of such a dynamical behavior. In particular, we use small-world networks with variable connectivity and randomness of the connections. We find that the drift to a single extreme appears only beyond a critical level of connectivity, which decreases when the randomness increases.