For an adjaceny_list which uses sets for its edges, edge(u, v, g) is supposed to be O(log(E/V)), as you would expect for a lookup in a set. (See http://www.boost.org/libs/graph/doc/using_adjacency_list.html#sec:choosing-g....) But in fact it is linear in the number of out edges. This is because in graph/detail/adjacency_list.hpp (line 1325 in revision 1.113), in the edge_dispatch function that handles the disallow_parallel_edge_tag case, the code reads: i = std::find(g.out_edge_list(u).begin(), g.out_edge_list(u).end(), StoredEdge(v)), when it should probably be: i = g.out_edge_list(u).find(StoredEdge(v)), as it was in revisions 1.59 and previous. As an aside, it's not that obvious from the documentation that adjacency_list supports edge(u, v, g). AFAICT it's defined only in the AdjacencyMatrix concept, which adjacency_list is not documented as being a model of. [This is a repost - the original was in message 31695 on the 21st of January. But I foolishly reported two different problems with the same subject & in the same thread, only one of which was addressed. I'm assuming the other one was overlooked and so repeating it. I apologise if this assumption is incorrect.] - Alan