than once, since it is not necessarily known before transitioning to a vertex that it has already been explored. As graphs become more dense, this redundancy becomes more prevalent, causing computation time to increase; as graphs become more sparse, the opposite holds true.

Thus, it is usually necessary to remember which vertices have already been explored by the algorithm, so that vertices are revisited as infrequently as possible (or in the worst case, to prevent the traversal from continuing indefinitely).