It is a shared belief that Thomas Schelling' model of segregation is only weakly affected by the underlying spatial structure, whatever its complexity. Such a conclusion is important from an urban planning perspective as it suggests that only a very restricted range of possible actions, if any, would be able to contribute limiting social segregation, unless individual preferences are significantly modified. Our own simulations show that, using appropriate graph-based spatial structures, one can reveal significant spatial effects and thus provide alternative planning insights. Cliques in networks indeed play a significant role, reinforcing segregation effects in Schelling's model. Introducing a small amount of noise in the model permits us to reveal more precisely this effect, without modifying the global behavior of the initial model. Furthermore, we show how a logistic model describes in a concise but precise way this global behavior.