diff --git a/include/nwgraph/adjacency.hpp b/include/nwgraph/adjacency.hpp
index 5d9c4c34..38638a00 100644
--- a/include/nwgraph/adjacency.hpp
+++ b/include/nwgraph/adjacency.hpp
@@ -85,7 +85,7 @@ class index_adjacency : public unipartite_graph_base, public indexed_struct_of_a
    * @brief Constructor of index_adjacency. Require the type of the graph to be unipartite.
    * Create an empty index_adjacency.
    */
-  index_adjacency(std::array<size_t, 1> N, size_t M = 0) requires(std::is_same<unipartite_graph_base, unipartite_graph_base>::value) : unipartite_graph_base(N), base(N[0], M) {}
+  index_adjacency(std::array<size_t, 1> N, size_t M = 0) requires(std::is_same<unipartite_graph_base, unipartite_graph_base>::value) : unipartite_graph_base(N[0]), base(N[0], M) {}
 
   template <class ExecutionPolicy = std::execution::parallel_unsequenced_policy>
   index_adjacency(index_edge_list<vertex_id_type, unipartite_graph_base, directedness::directed, Attributes...>& A,
diff --git a/include/nwgraph/edge_list.hpp b/include/nwgraph/edge_list.hpp
index e284ebb2..615e9e3d 100644
--- a/include/nwgraph/edge_list.hpp
+++ b/include/nwgraph/edge_list.hpp
@@ -74,7 +74,7 @@ class index_edge_list : public graph_base_t, public struct_of_arrays<vertex_id,
   using vertex_id_type = vertex_id;
   using base           = struct_of_arrays<vertex_id_type, vertex_id_type, Attributes...>;
   using element        = std::tuple<vertex_id_type, vertex_id_type, Attributes...>;
-  using reference      = base::reference;
+  using reference      = typename base::reference;
 
 
   static const directedness edge_directedness = direct;
diff --git a/include/nwgraph/graph_concepts.hpp b/include/nwgraph/graph_concepts.hpp
index 1c1669f0..daa656d8 100644
--- a/include/nwgraph/graph_concepts.hpp
+++ b/include/nwgraph/graph_concepts.hpp
@@ -54,9 +54,10 @@ DECL_TAG_INVOKE(target);
  *
  */
 template <typename G>
-concept graph = std::copyable<G> && requires(G g) {
-  typename vertex_id_t<G>;
-  { num_vertices(g) } -> std::convertible_to<std::ranges::range_difference_t<G>>;
+concept graph = std::copyable<std::remove_cvref_t<G>>
+              && has_vertex_id<G>
+              && requires(G g) {
+                  { num_vertices(g) } -> std::convertible_to<std::ranges::range_difference_t<G>>;
 };
 
 template <typename G>
diff --git a/include/nwgraph/graph_traits.hpp b/include/nwgraph/graph_traits.hpp
index 3c746bd2..949f2676 100644
--- a/include/nwgraph/graph_traits.hpp
+++ b/include/nwgraph/graph_traits.hpp
@@ -34,7 +34,12 @@ struct graph_traits {
 };
 
 template <typename G>
-using vertex_id_t = typename graph_traits<G>::vertex_id_type;
+using vertex_id_t = typename graph_traits<std::remove_cvref_t<G>>::vertex_id_type;
+
+template <typename G>
+concept has_vertex_id = requires {
+    typename graph_traits<std::remove_cvref_t<G>>;
+};
 
 // template <typename G>
 // using vertex_size_t = typename graph_traits<G>::vertex_size_type;