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Imagine a world where people constantly try to pass through walls and cars suddenly leave the roads and drive into rivers. Although this is unrealistic, most simulations for mobile ad hoc networks so far are based on the so called "random walk" of mobile objects, which are not constrained by their surrounding spatial environments. In this paper we propose a novel graph-based mobility model, which provides a more realistic movement than the random walk model by reflecting the spatial constraints in the real world. We analyzed three commonly used ad hoc network routing protocols, DSDV, DSR and AODV with both a random walk-based and our graph-based mobility model. Our simulation results show that the spatial constraints have a strong impact on the performance of ad hoc routing protocols.