Hello, I'm using Boost.Graph version 1.53.0. I'm trying to write some graph algorithms and I want to minimize the requirements of the input graph. I have a question about Boost.Graph concepts. I wrote a very simple code as follows: typedef boost::adjacency_list< boost::vecS, boost::vecS, boost::bidirectionalS> G; int main() { G g; boost::add_edge(0, 1, g); auto res = boost::edge(0, 1, g); // Why can I call it? std::cout << std::boolalpha << res.second << std::endl; boost::graph_traits<G>::edge_descriptor e = res.first; std::cout << boost::source(e, g) << "," << boost::target(e, g) << std::endl; } It works, but I don't understand why I can call boost::edge(). According to the following document, AdjacencyMatrix concept provides Direct Edge Access functionality, so I can call edge(u,v,g) : http://www.boost.org/doc/libs/1_53_0/libs/graph/doc/AdjacencyMatrix.html The class template adjacency_list is a model of VertexAndEdgeListGraph, MutablePropertyGraph, CopyConstructible, Assignable, and Serializable. http://www.boost.org/doc/libs/1_53_0/libs/graph/doc/adjacency_list.html So, adjacency_list is not satisfied AdjacencyMatrix concept. I checked which function template is called, then I found the following function is called: boost/graph/detail/adjacency_list.hpp:1582 template <class Config, class Base> inline std::pair<typename Config::edge_descriptor, bool> edge(typename Config::vertex_descriptor u, typename Config::vertex_descriptor v, const adj_list_helper<Config, Base>& g_) { typedef typename Config::graph_type Graph; typedef typename Config::StoredEdge StoredEdge; const Graph& cg = static_cast<const Graph&>(g_); typedef typename Config::out_edge_iterator out_edge_iterator; const typename Config::OutEdgeList& el = cg.out_edge_list(u); typename Config::OutEdgeList::const_iterator it = graph_detail:: find(el, StoredEdge(v)); return std::make_pair( typename Config::edge_descriptor (u, v, (it == el.end() ? 0 : &(*it).get_property())), (it != el.end())); } Also, I found the following document: http://www.boost.org/doc/libs/1_53_0/libs/graph/doc/using_adjacency_list.htm... This document describes that: edge() The time complexity for this operation is O(E/V) when the OutEdgeList type is a Sequence and it is O(log(E/V)) when the OutEdgeList type is an AssociativeContainer. It seems that edge() is a part of the public interface of adjacency_list. But I think that it is not a part of any graph concepts. If I want to write an algorithm that depends on several graph concepts, not actual classes such as adjancency_list, I can use edge(u,v,g) only if the input graph class satisfies AdjacencyMatrix concept. Am I understanding correctly? Thanks, Taka