Hello all. It is clear for me the reason for template parameter CombineFunction in dijkstra_shortest_paths. For instance, prim_minimum_spanning_tree makes use of it to correct compute the MST. Basically, in Dijkstra's it is something like this: distance = distance of vertex v + weight of edge e; And in Prim's only the weight is considered: distance = weight of edge e; This is reflected on the argument used for the CombineFunction in Prim's function (from file prim_minimum_spanning_tree.hpp): prim_minimum_spanning_tree(...) { typedef typename property_traits<WeightMap>::value_type W; std::less<W> compare; detail::_project2nd<W,W> combine; dijkstra_shortest_paths(...); } Where _project2nd is: template <class U, class V> struct _project2nd { V operator()(U, V v) const { return v; } }; However, it is not clear the reason of the CompareFunction template parameter (which is a predicate). First, because, I don't see a situation where not using std::less<Some_type> would make any sence, because of the way the Dijkstra's algorithm is constructed. Second, because the value_type of the DistanceMap must be the same of the value_type of WeightMap (according to the documentation). Therefore, why the following two lines of code in Prim's implementation (from the function I pointed at beginning of the email)? typedef typename property_traits<WeightMap>::value_type W; std::less<W> compare; Since, in Dijkstra's algorithm the only difference is that DistanceMap is used as an argument for the definition of the value_type from property_traits. Am I loosing something here? If yes, would anyone explain it to me? Thank you, Leandro.