Many state-of-the-art heuristic planners derive their heuristic function by relaxing the planning task at hand, where the relaxation is to assume that all delete lists are empty. Looking at a collection of planning benchmarks, we measure topological properties of state spaces with respect to that relaxation. The results suggest that, given the heuristic based on the relaxation, many planning benchmarks are simple in structure. This sheds light on the recent success of heuristic planners employing local search.