title: Algorithm to cover all edges given starting node
body: <p>Working on an algorithm for a game I am developing with a friend and we got stuck. Currently, we have a cyclic undirected graph, and we are trying to find the quickest path from starting node S that covers every edge. We are not looking for a tour and there can be repeated edges. </p>
  
  <p>Any ideas on an algorithm or approximation? I'm sure this problem is NP-hard, but I don't believe it's TSP.</p>