diff --git a/BGL/include/CGAL/boost/graph/graph_traits_HalfedgeDS.h b/BGL/include/CGAL/boost/graph/graph_traits_HalfedgeDS.h
index 1c8e90bb683..b6e764277ef 100644
--- a/BGL/include/CGAL/boost/graph/graph_traits_HalfedgeDS.h
+++ b/BGL/include/CGAL/boost/graph/graph_traits_HalfedgeDS.h
@@ -137,7 +137,9 @@ struct HDS_edge {
 
   friend  std::size_t hash_value(const HDS_edge&  i)
   {
-    return hash_value(i.halfedge());
+    if (i.halfedge()==Halfedge_handle()) return 0;
+    return hash_value(i.halfedge()<i.halfedge()->opposite()?
+                      i.halfedge():i.halfedge()->opposite());
   }
 
 private:
@@ -153,6 +155,7 @@ namespace handle{
     operator()(const HDS_edge<Halfedge_handle>& edge)
     {
       Halfedge_handle he = edge.halfedge();
+      if (he==Halfedge_handle()) return 0;
       if ( he < he->opposite() )
         return Hash_functor<Halfedge_handle>()(he);
       return Hash_functor<Halfedge_handle>()(he->opposite());
@@ -240,7 +243,9 @@ namespace std {
     std::size_t operator()(const CGAL::internal::HDS_edge<H>& e) const
     {
       std::hash<H> fct;
-      return fct(e.halfedge());
+      if (e.halfedge()==H()) return 0;
+      return fct(e.halfedge()<e.halfedge()->opposite()?
+                 e.halfedge():e.halfedge()->opposite());
     }
   };
 
diff --git a/BGL/include/CGAL/boost/graph/graph_traits_Triangulation_2.h b/BGL/include/CGAL/boost/graph/graph_traits_Triangulation_2.h
index 6d5d426bbf0..8cea712b933 100644
--- a/BGL/include/CGAL/boost/graph/graph_traits_Triangulation_2.h
+++ b/BGL/include/CGAL/boost/graph/graph_traits_Triangulation_2.h
@@ -74,7 +74,9 @@ public:
 
   friend std::size_t hash_value(const Edge& e)
   {
-    return hash_value(e.first);
+    if (e.first==Face_handle()) return 0;
+    return hash_value(e.first<e.first->neighbor(e.second)?
+                      e.first:e.first->neighbor(e.second));
   }
 
   bool operator==(const Edge& other) const
@@ -846,7 +848,6 @@ namespace std {
   struct hash<CGAL::detail::Edge<T,EdgeBase> > {
     std::size_t operator()(const CGAL::detail::Edge<T,EdgeBase>& e) const
     {
-      std::cerr << "Triangulation_2::Edge HashFct" << std::endl;
       return hash_value(e);
     }
   }; 
@@ -855,7 +856,6 @@ namespace std {
   struct hash<CGAL::detail::T2_halfedge_descriptor<Tr> > {
     std::size_t operator()(const CGAL::detail::T2_halfedge_descriptor<Tr>& e) const
     {
-      std::cerr << "Triangulation_2::halfedge_descriptor HashFct" << std::endl;
       return hash_value(e);
     }
   };
diff --git a/Hash_map/test/Hash_map/Hash.cpp b/Hash_map/test/Hash_map/Hash.cpp
index 36e99a99eeb..3d6b15e91db 100644
--- a/Hash_map/test/Hash_map/Hash.cpp
+++ b/Hash_map/test/Hash_map/Hash.cpp
@@ -12,6 +12,8 @@
 #include <CGAL/boost/graph/graph_traits_Triangulation_2.h>
 #include <map>
 #include <boost/unordered_map.hpp>
+#include <boost/foreach.hpp>
+#include <CGAL/boost/graph/helpers.h>
 
 
 typedef CGAL::Simple_cartesian<double> Kernel;
@@ -21,10 +23,10 @@ typedef CGAL::Arrangement_2<Arrangement_traits_2> Arrangement_2;
 typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
 typedef CGAL::Surface_mesh<Kernel::Point_3> Surface_mesh;
 typedef CGAL::Triangulation_2<Kernel> Triangulation_2;
-#ifdef CGAL_LINKED_WITH_TBB  
-typedef CGAL::Triangulation_data_structure_3< 
-    CGAL::Triangulation_vertex_base_3<Kernel>, 
-    CGAL::Triangulation_cell_base_3<Kernel>, 
+#ifdef CGAL_LINKED_WITH_TBB
+typedef CGAL::Triangulation_data_structure_3<
+    CGAL::Triangulation_vertex_base_3<Kernel>,
+    CGAL::Triangulation_cell_base_3<Kernel>,
     CGAL::Parallel_tag>                          Tds;
 typedef CGAL::Delaunay_triangulation_3<Kernel, Tds> Triangulation_3;
 #endif
@@ -80,6 +82,29 @@ fct3(const P& )
   U[vd] = 12;
 }
 
+template <class P>
+void test_edge_hash_and_null(const P& p)
+{
+  typedef boost::graph_traits<P> GT;
+  typedef typename GT::halfedge_descriptor halfedge_descriptor;
+  typedef typename GT::vertex_descriptor vertex_descriptor;
+  typedef typename GT::face_descriptor face_descriptor;
+
+  BOOST_FOREACH(halfedge_descriptor h, halfedges(p))
+  {
+    assert(
+      hash_value( edge(h,p) ) ==
+      hash_value( edge(opposite(h,p),p) ) );
+  }
+  face_descriptor f1=GT::null_face(), f2=GT::null_face();
+  vertex_descriptor v1=GT::null_vertex(), v2=GT::null_vertex();
+  halfedge_descriptor h1=GT::null_halfedge(), h2=GT::null_halfedge();
+
+  assert(hash_value(f1)==hash_value(f2));
+  assert(hash_value(v1)==hash_value(v2));
+  assert(hash_value(h1)==hash_value(h2));
+}
+
 template <typename P>
 void
 fct4(const P& p)
@@ -88,6 +113,7 @@ fct4(const P& p)
   fct<P, typename boost::graph_traits<P>::halfedge_descriptor>(p);
   fct<P, typename boost::graph_traits<P>::edge_descriptor>(p);
   fct<P, typename boost::graph_traits<P>::face_descriptor>(p);
+  test_edge_hash_and_null(p);
 }
 
 int main()
@@ -96,17 +122,24 @@ int main()
   fct<Arrangement_2, boost::graph_traits<Arrangement_2>::vertex_descriptor>(A);
   fct<Arrangement_2, boost::graph_traits<Arrangement_2>::edge_descriptor>(A);
 
+  Kernel::Point_3 p3;
   Polyhedron P;
+  CGAL::make_triangle(p3,p3,p3,P);
   fct4(P);
 
   Surface_mesh S;
+  CGAL::make_triangle(p3,p3,p3,S);
   fct4(S);
 
   Triangulation_2 T;
+  T.insert(Kernel::Point_2(0,0));
+  T.insert(Kernel::Point_2(0,1));
+  T.insert(Kernel::Point_2(1,0));
+  T.insert(Kernel::Point_2(1,1));
   fct4(T);
 
   fct2();
-  
+
 #ifdef CGAL_LINKED_WITH_TBB
   Triangulation_3 T3;
 fct3(T3);