diff --git a/lemon/concepts/graph.h b/lemon/concepts/graph.h
--- a/lemon/concepts/graph.h
+++ b/lemon/concepts/graph.h
@@ -497,12 +497,11 @@
         InArcIt& operator++() { return *this; }
       };
 
-      /// \brief Read write map of the nodes to type \c T.
+      /// \brief Reference map of the nodes to type \c T.
       ///
-      /// ReadWrite map of the nodes to type \c T.
-      /// \sa Reference
+      /// Reference map of the nodes to type \c T.
       template<class T>
-      class NodeMap : public ReadWriteMap< Node, T >
+      class NodeMap : public ReferenceMap<Node, T, T&, const T&>
       {
       public:
 
@@ -513,7 +512,8 @@
 
       private:
         ///Copy constructor
-        NodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }
+        NodeMap(const NodeMap& nm) :
+          ReferenceMap<Node, T, T&, const T&>(nm) { }
         ///Assignment operator
         template <typename CMap>
         NodeMap& operator=(const CMap&) {
@@ -522,12 +522,11 @@
         }
       };
 
-      /// \brief Read write map of the directed arcs to type \c T.
+      /// \brief Reference map of the arcs to type \c T.
       ///
-      /// Reference map of the directed arcs to type \c T.
-      /// \sa Reference
+      /// Reference map of the arcs to type \c T.
       template<class T>
-      class ArcMap : public ReadWriteMap<Arc,T>
+      class ArcMap : public ReferenceMap<Arc, T, T&, const T&>
       {
       public:
 
@@ -537,7 +536,8 @@
         ArcMap(const Graph&, T) { }
       private:
         ///Copy constructor
-        ArcMap(const ArcMap& em) : ReadWriteMap<Arc,T>(em) { }
+        ArcMap(const ArcMap& em) :
+          ReferenceMap<Arc, T, T&, const T&>(em) { }
         ///Assignment operator
         template <typename CMap>
         ArcMap& operator=(const CMap&) {
@@ -546,12 +546,11 @@
         }
       };
 
-      /// Read write map of the edges to type \c T.
+      /// Reference map of the edges to type \c T.
 
-      /// Reference map of the arcs to type \c T.
-      /// \sa Reference
+      /// Reference map of the edges to type \c T.
       template<class T>
-      class EdgeMap : public ReadWriteMap<Edge,T>
+      class EdgeMap : public ReferenceMap<Edge, T, T&, const T&>
       {
       public:
 
@@ -561,7 +560,8 @@
         EdgeMap(const Graph&, T) { }
       private:
         ///Copy constructor
-        EdgeMap(const EdgeMap& em) : ReadWriteMap<Edge,T>(em) {}
+        EdgeMap(const EdgeMap& em) :
+          ReferenceMap<Edge, T, T&, const T&>(em) {}
         ///Assignment operator
         template <typename CMap>
         EdgeMap& operator=(const CMap&) {
@@ -748,6 +748,7 @@
       template <typename _Graph>
       struct Constraints {
         void constraints() {
+          checkConcept<BaseGraphComponent, _Graph>();
           checkConcept<IterableGraphComponent<>, _Graph>();
           checkConcept<IDableGraphComponent<>, _Graph>();
           checkConcept<MappableGraphComponent<>, _Graph>();