This question may be better served at cs.SE, but I am not very familiar with CS lingo, so I'm hoping the maths community would be able to answer it as well...
I have an undirected graph, and I am interested in finding all vertices in the graph exactly $k$ steps away from a given vertex. In other words, I want to compute the set of all vertices such that the closest path is $k$ steps away.
Is there such an algorithm, or is there an obvious modification to a different algorithm? I'm sure that something like Djikstra's algorithm can solve it brute force by computing the shortest path to each vertex, but I'm hoping that there is something more cleverer that doesn't resort to brute-forciness.