In a first paragraph we present briefly the Relative Agreement Model, the addition of extremists within the population and the main results corresponding to the totally connected case. We then describe the first simulations done on a regular grid with a Von Neumann and a De Moore neighborhood. Significant changes occur in comparison with the totally connected case as for instance the disappearance of the single extreme convergence. Aiming at understanding it, we then explore the behavior of the model between regular grids and fully connected networks. We use a Small-World topology that enables us to tune both the average connectivity of the network and the level of noise within the network, from a regular network to a totally random one. The simulations show that there is a critical level of connectivity beyond which the drift to a single extreme appears. We then discuss the observed behavior of our model.