# HG changeset patch
# User Balazs Dezso <deba@inf.elte.hu>
# Date 2008-07-15 13:15:39
# Node ID a5d8c039f21898d8ab83727b426af73e100972d4
# Parent  b67149f0e6757cc1132d30f6ca7d4050e210b66c

Reorganize header files (Ticket #97)

In addition on some places the DefaultMap<G, K, V> is replaced with
ItemSetTraits<G, K>::template Map<V>::Type, to decrease the dependencies
of different tools. It is obviously better solution.

diff --git a/demo/graph_to_eps_demo.cc b/demo/graph_to_eps_demo.cc
--- a/demo/graph_to_eps_demo.cc
+++ b/demo/graph_to_eps_demo.cc
@@ -31,7 +31,6 @@
 /// \include graph_to_eps_demo.cc
 
 #include<lemon/list_graph.h>
-#include<lemon/graph_utils.h>
 #include<lemon/graph_to_eps.h>
 #include<lemon/math.h>
 
diff --git a/lemon/Makefile.am b/lemon/Makefile.am
--- a/lemon/Makefile.am
+++ b/lemon/Makefile.am
@@ -24,12 +24,12 @@
         lemon/color.h \
 	lemon/concept_check.h \
         lemon/counter.h \
+	lemon/core.h \
         lemon/dfs.h \
         lemon/dijkstra.h \
         lemon/dim2.h \
 	lemon/error.h \
         lemon/graph_to_eps.h \
-	lemon/graph_utils.h \
 	lemon/kruskal.h \
 	lemon/lgf_reader.h \
 	lemon/lgf_writer.h \
@@ -49,12 +49,11 @@
 	lemon/bits/base_extender.h \
         lemon/bits/bezier.h \
 	lemon/bits/default_map.h \
+        lemon/bits/enable_if.h \
 	lemon/bits/graph_extender.h \
-        lemon/bits/invalid.h \
 	lemon/bits/map_extender.h \
 	lemon/bits/path_dump.h \
 	lemon/bits/traits.h \
-        lemon/bits/utility.h \
 	lemon/bits/vector_map.h
 
 concept_HEADERS += \
diff --git a/lemon/base.cc b/lemon/base.cc
--- a/lemon/base.cc
+++ b/lemon/base.cc
@@ -20,7 +20,7 @@
 ///\brief Some basic non-inline functions and static global data.
 
 #include<lemon/tolerance.h>
-#include<lemon/bits/invalid.h>
+#include<lemon/core.h>
 namespace lemon {
 
   float Tolerance<float>::def_epsilon = 1e-4;
diff --git a/lemon/bfs.h b/lemon/bfs.h
--- a/lemon/bfs.h
+++ b/lemon/bfs.h
@@ -24,9 +24,8 @@
 ///\brief Bfs algorithm.
 
 #include <lemon/list_graph.h>
-#include <lemon/graph_utils.h>
 #include <lemon/bits/path_dump.h>
-#include <lemon/bits/invalid.h>
+#include <lemon/core.h>
 #include <lemon/error.h>
 #include <lemon/maps.h>
 
diff --git a/lemon/bits/alteration_notifier.h b/lemon/bits/alteration_notifier.h
--- a/lemon/bits/alteration_notifier.h
+++ b/lemon/bits/alteration_notifier.h
@@ -22,7 +22,7 @@
 #include <vector>
 #include <list>
 
-#include <lemon/bits/utility.h>
+#include <lemon/core.h>
 
 ///\ingroup graphbits
 ///\file
diff --git a/lemon/bits/base_extender.h b/lemon/bits/base_extender.h
--- a/lemon/bits/base_extender.h
+++ b/lemon/bits/base_extender.h
@@ -19,7 +19,7 @@
 #ifndef LEMON_BITS_BASE_EXTENDER_H
 #define LEMON_BITS_BASE_EXTENDER_H
 
-#include <lemon/bits/invalid.h>
+#include <lemon/core.h>
 #include <lemon/error.h>
 
 #include <lemon/bits/map_extender.h>
diff --git a/lemon/bits/enable_if.h b/lemon/bits/enable_if.h
new file mode 100644
--- /dev/null
+++ b/lemon/bits/enable_if.h
@@ -0,0 +1,131 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+// This file contains a modified version of the enable_if library from BOOST.
+// See the appropriate copyright notice below.
+
+// Boost enable_if library
+
+// Copyright 2003 (c) The Trustees of Indiana University.
+
+// Use, modification, and distribution is subject to the Boost Software
+// License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+
+//    Authors: Jaakko Jarvi (jajarvi at osl.iu.edu)
+//             Jeremiah Willcock (jewillco at osl.iu.edu)
+//             Andrew Lumsdaine (lums at osl.iu.edu)
+
+
+#ifndef LEMON_BITS_ENABLE_IF_H
+#define LEMON_BITS_ENABLE_IF_H
+
+///\file
+///\brief Miscellaneous basic utilities
+
+namespace lemon
+{
+
+  /// Basic type for defining "tags". A "YES" condition for \c enable_if.
+
+  /// Basic type for defining "tags". A "YES" condition for \c enable_if.
+  ///
+  ///\sa False
+  struct True {
+    ///\e
+    static const bool value = true;
+  };
+
+  /// Basic type for defining "tags". A "NO" condition for \c enable_if.
+
+  /// Basic type for defining "tags". A "NO" condition for \c enable_if.
+  ///
+  ///\sa True
+  struct False {
+    ///\e
+    static const bool value = false;
+  };
+
+
+
+  template <typename T>
+  struct Wrap {
+    const T &value;
+    Wrap(const T &t) : value(t) {}
+  };
+
+  /**************** dummy class to avoid ambiguity ****************/
+
+  template<int T> struct dummy { dummy(int) {} };
+
+  /**************** enable_if from BOOST ****************/
+
+  template <typename Type, typename T = void>
+  struct exists {
+    typedef T type;
+  };
+
+
+  template <bool B, class T = void>
+  struct enable_if_c {
+    typedef T type;
+  };
+
+  template <class T>
+  struct enable_if_c<false, T> {};
+
+  template <class Cond, class T = void>
+  struct enable_if : public enable_if_c<Cond::value, T> {};
+
+  template <bool B, class T>
+  struct lazy_enable_if_c {
+    typedef typename T::type type;
+  };
+
+  template <class T>
+  struct lazy_enable_if_c<false, T> {};
+
+  template <class Cond, class T>
+  struct lazy_enable_if : public lazy_enable_if_c<Cond::value, T> {};
+
+
+  template <bool B, class T = void>
+  struct disable_if_c {
+    typedef T type;
+  };
+
+  template <class T>
+  struct disable_if_c<true, T> {};
+
+  template <class Cond, class T = void>
+  struct disable_if : public disable_if_c<Cond::value, T> {};
+
+  template <bool B, class T>
+  struct lazy_disable_if_c {
+    typedef typename T::type type;
+  };
+
+  template <class T>
+  struct lazy_disable_if_c<true, T> {};
+
+  template <class Cond, class T>
+  struct lazy_disable_if : public lazy_disable_if_c<Cond::value, T> {};
+
+} // namespace lemon
+
+#endif
diff --git a/lemon/bits/graph_extender.h b/lemon/bits/graph_extender.h
--- a/lemon/bits/graph_extender.h
+++ b/lemon/bits/graph_extender.h
@@ -19,8 +19,7 @@
 #ifndef LEMON_BITS_GRAPH_EXTENDER_H
 #define LEMON_BITS_GRAPH_EXTENDER_H
 
-#include <lemon/bits/invalid.h>
-#include <lemon/bits/utility.h>
+#include <lemon/core.h>
 
 #include <lemon/bits/map_extender.h>
 #include <lemon/bits/default_map.h>
diff --git a/lemon/bits/invalid.h b/lemon/bits/invalid.h
deleted file mode 100644
--- a/lemon/bits/invalid.h
+++ /dev/null
@@ -1,55 +0,0 @@
-/* -*- mode: C++; indent-tabs-mode: nil; -*-
- *
- * This file is a part of LEMON, a generic C++ optimization library.
- *
- * Copyright (C) 2003-2008
- * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
- * (Egervary Research Group on Combinatorial Optimization, EGRES).
- *
- * Permission to use, modify and distribute this software is granted
- * provided that this copyright notice appears in all copies. For
- * precise terms see the accompanying LICENSE file.
- *
- * This software is provided "AS IS" with no warranty of any kind,
- * express or implied, and with no claim as to its suitability for any
- * purpose.
- *
- */
-
-#ifndef LEMON_BITS_INVALID_H
-#define LEMON_BITS_INVALID_H
-
-///\file
-///\brief Definition of INVALID.
-
-namespace lemon {
-
-  /// \brief Dummy type to make it easier to create invalid iterators.
-  ///
-  /// Dummy type to make it easier to create invalid iterators.
-  /// See \ref INVALID for the usage.
-  struct Invalid {
-  public:
-    bool operator==(Invalid) { return true;  }
-    bool operator!=(Invalid) { return false; }
-    bool operator< (Invalid) { return false; }
-  };
-
-  /// \brief Invalid iterators.
-  ///
-  /// \ref Invalid is a global type that converts to each iterator
-  /// in such a way that the value of the target iterator will be invalid.
-
-  //Some people didn't like this:
-  //const Invalid &INVALID = *(Invalid *)0;
-
-#ifdef LEMON_ONLY_TEMPLATES
-  const Invalid INVALID = Invalid();
-#else
-  extern const Invalid INVALID;
-#endif
-
-} //namespace lemon
-
-#endif
-
diff --git a/lemon/bits/traits.h b/lemon/bits/traits.h
--- a/lemon/bits/traits.h
+++ b/lemon/bits/traits.h
@@ -19,13 +19,16 @@
 #ifndef LEMON_BITS_TRAITS_H
 #define LEMON_BITS_TRAITS_H
 
-#include <lemon/bits/utility.h>
-
 ///\file
 ///\brief Traits for graphs and maps
 ///
 
+#include <lemon/bits/enable_if.h>
+
 namespace lemon {
+
+  struct InvalidType {};
+
   template <typename _Graph, typename _Item>
   class ItemSetTraits {};
 
diff --git a/lemon/bits/utility.h b/lemon/bits/utility.h
deleted file mode 100644
--- a/lemon/bits/utility.h
+++ /dev/null
@@ -1,140 +0,0 @@
-/* -*- mode: C++; indent-tabs-mode: nil; -*-
- *
- * This file is a part of LEMON, a generic C++ optimization library.
- *
- * Copyright (C) 2003-2008
- * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
- * (Egervary Research Group on Combinatorial Optimization, EGRES).
- *
- * Permission to use, modify and distribute this software is granted
- * provided that this copyright notice appears in all copies. For
- * precise terms see the accompanying LICENSE file.
- *
- * This software is provided "AS IS" with no warranty of any kind,
- * express or implied, and with no claim as to its suitability for any
- * purpose.
- *
- */
-
-// This file contains a modified version of the enable_if library from BOOST.
-// See the appropriate copyright notice below.
-
-// Boost enable_if library
-
-// Copyright 2003 (c) The Trustees of Indiana University.
-
-// Use, modification, and distribution is subject to the Boost Software
-// License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
-// http://www.boost.org/LICENSE_1_0.txt)
-
-//    Authors: Jaakko Jarvi (jajarvi at osl.iu.edu)
-//             Jeremiah Willcock (jewillco at osl.iu.edu)
-//             Andrew Lumsdaine (lums at osl.iu.edu)
-
-
-#ifndef LEMON_BITS_UTILITY_H
-#define LEMON_BITS_UTILITY_H
-
-///\file
-///\brief Miscellaneous basic utilities
-///
-///\todo Please rethink the organisation of the basic files like this.
-///E.g. this file might be merged with invalid.h.
-
-
-namespace lemon
-{
-
-  /// Basic type for defining "tags". A "YES" condition for \c enable_if.
-
-  /// Basic type for defining "tags". A "YES" condition for \c enable_if.
-  ///
-  ///\sa False
-  ///
-  /// \todo This should go to a separate "basic_types.h" (or something)
-  /// file.
-  struct True {
-    ///\e
-    static const bool value = true;
-  };
-
-  /// Basic type for defining "tags". A "NO" condition for \c enable_if.
-
-  /// Basic type for defining "tags". A "NO" condition for \c enable_if.
-  ///
-  ///\sa True
-  struct False {
-    ///\e
-    static const bool value = false;
-  };
-
-
-  struct InvalidType {
-  };
-
-  template <typename T>
-  struct Wrap {
-    const T &value;
-    Wrap(const T &t) : value(t) {}
-  };
-
-  /**************** dummy class to avoid ambiguity ****************/
-
-  template<int T> struct dummy { dummy(int) {} };
-
-  /**************** enable_if from BOOST ****************/
-
-  template <typename Type, typename T = void>
-  struct exists {
-    typedef T type;
-  };
-
-
-  template <bool B, class T = void>
-  struct enable_if_c {
-    typedef T type;
-  };
-
-  template <class T>
-  struct enable_if_c<false, T> {};
-
-  template <class Cond, class T = void>
-  struct enable_if : public enable_if_c<Cond::value, T> {};
-
-  template <bool B, class T>
-  struct lazy_enable_if_c {
-    typedef typename T::type type;
-  };
-
-  template <class T>
-  struct lazy_enable_if_c<false, T> {};
-
-  template <class Cond, class T>
-  struct lazy_enable_if : public lazy_enable_if_c<Cond::value, T> {};
-
-
-  template <bool B, class T = void>
-  struct disable_if_c {
-    typedef T type;
-  };
-
-  template <class T>
-  struct disable_if_c<true, T> {};
-
-  template <class Cond, class T = void>
-  struct disable_if : public disable_if_c<Cond::value, T> {};
-
-  template <bool B, class T>
-  struct lazy_disable_if_c {
-    typedef typename T::type type;
-  };
-
-  template <class T>
-  struct lazy_disable_if_c<true, T> {};
-
-  template <class Cond, class T>
-  struct lazy_disable_if : public lazy_disable_if_c<Cond::value, T> {};
-
-} // namespace lemon
-
-#endif
diff --git a/lemon/bits/vector_map.h b/lemon/bits/vector_map.h
--- a/lemon/bits/vector_map.h
+++ b/lemon/bits/vector_map.h
@@ -22,9 +22,7 @@
 #include <vector>
 #include <algorithm>
 
-#include <lemon/bits/traits.h>
-#include <lemon/bits/utility.h>
-
+#include <lemon/core.h>
 #include <lemon/bits/alteration_notifier.h>
 
 #include <lemon/concept_check.h>
diff --git a/lemon/concepts/digraph.h b/lemon/concepts/digraph.h
--- a/lemon/concepts/digraph.h
+++ b/lemon/concepts/digraph.h
@@ -23,8 +23,7 @@
 ///\file
 ///\brief The concept of directed graphs.
 
-#include <lemon/bits/invalid.h>
-#include <lemon/bits/utility.h>
+#include <lemon/core.h>
 #include <lemon/concepts/maps.h>
 #include <lemon/concept_check.h>
 #include <lemon/concepts/graph_components.h>
diff --git a/lemon/concepts/graph.h b/lemon/concepts/graph.h
--- a/lemon/concepts/graph.h
+++ b/lemon/concepts/graph.h
@@ -25,7 +25,7 @@
 
 #include <lemon/concepts/graph_components.h>
 #include <lemon/concepts/graph.h>
-#include <lemon/bits/utility.h>
+#include <lemon/core.h>
 
 namespace lemon {
   namespace concepts {
diff --git a/lemon/concepts/graph_components.h b/lemon/concepts/graph_components.h
--- a/lemon/concepts/graph_components.h
+++ b/lemon/concepts/graph_components.h
@@ -24,7 +24,7 @@
 #ifndef LEMON_CONCEPT_GRAPH_COMPONENTS_H
 #define LEMON_CONCEPT_GRAPH_COMPONENTS_H
 
-#include <lemon/bits/invalid.h>
+#include <lemon/core.h>
 #include <lemon/concepts/maps.h>
 
 #include <lemon/bits/alteration_notifier.h>
diff --git a/lemon/concepts/heap.h b/lemon/concepts/heap.h
--- a/lemon/concepts/heap.h
+++ b/lemon/concepts/heap.h
@@ -23,7 +23,7 @@
 #ifndef LEMON_CONCEPT_HEAP_H
 #define LEMON_CONCEPT_HEAP_H
 
-#include <lemon/bits/invalid.h>
+#include <lemon/core.h>
 
 namespace lemon {
 
diff --git a/lemon/concepts/maps.h b/lemon/concepts/maps.h
--- a/lemon/concepts/maps.h
+++ b/lemon/concepts/maps.h
@@ -19,7 +19,7 @@
 #ifndef LEMON_CONCEPT_MAPS_H
 #define LEMON_CONCEPT_MAPS_H
 
-#include <lemon/bits/utility.h>
+#include <lemon/core.h>
 #include <lemon/concept_check.h>
 
 ///\ingroup concept
diff --git a/lemon/concepts/path.h b/lemon/concepts/path.h
--- a/lemon/concepts/path.h
+++ b/lemon/concepts/path.h
@@ -25,8 +25,7 @@
 #ifndef LEMON_CONCEPT_PATH_H
 #define LEMON_CONCEPT_PATH_H
 
-#include <lemon/bits/invalid.h>
-#include <lemon/bits/utility.h>
+#include <lemon/core.h>
 #include <lemon/concept_check.h>
 
 namespace lemon {
diff --git a/lemon/core.h b/lemon/core.h
new file mode 100644
--- /dev/null
+++ b/lemon/core.h
@@ -0,0 +1,1851 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef LEMON_CORE_H
+#define LEMON_CORE_H
+
+#include <vector>
+#include <algorithm>
+
+#include <lemon/bits/enable_if.h>
+#include <lemon/bits/traits.h>
+
+///\file
+///\brief LEMON core utilities.
+
+namespace lemon {
+
+  /// \brief Dummy type to make it easier to create invalid iterators.
+  ///
+  /// Dummy type to make it easier to create invalid iterators.
+  /// See \ref INVALID for the usage.
+  struct Invalid {
+  public:
+    bool operator==(Invalid) { return true;  }
+    bool operator!=(Invalid) { return false; }
+    bool operator< (Invalid) { return false; }
+  };
+
+  /// \brief Invalid iterators.
+  ///
+  /// \ref Invalid is a global type that converts to each iterator
+  /// in such a way that the value of the target iterator will be invalid.
+#ifdef LEMON_ONLY_TEMPLATES
+  const Invalid INVALID = Invalid();
+#else
+  extern const Invalid INVALID;
+#endif
+
+  /// \addtogroup gutils
+  /// @{
+
+  ///Creates convenience typedefs for the digraph types and iterators
+
+  ///This \c \#define creates convenience typedefs for the following types
+  ///of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
+  ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
+  ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
+  ///
+  ///\note If the graph type is a dependent type, ie. the graph type depend
+  ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
+  ///macro.
+#define DIGRAPH_TYPEDEFS(Digraph)                                       \
+  typedef Digraph::Node Node;                                           \
+  typedef Digraph::NodeIt NodeIt;                                       \
+  typedef Digraph::Arc Arc;                                             \
+  typedef Digraph::ArcIt ArcIt;                                         \
+  typedef Digraph::InArcIt InArcIt;                                     \
+  typedef Digraph::OutArcIt OutArcIt;                                   \
+  typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
+  typedef Digraph::NodeMap<int> IntNodeMap;                             \
+  typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
+  typedef Digraph::ArcMap<bool> BoolArcMap;                             \
+  typedef Digraph::ArcMap<int> IntArcMap;                               \
+  typedef Digraph::ArcMap<double> DoubleArcMap
+
+  ///Creates convenience typedefs for the digraph types and iterators
+
+  ///\see DIGRAPH_TYPEDEFS
+  ///
+  ///\note Use this macro, if the graph type is a dependent type,
+  ///ie. the graph type depend on a template parameter.
+#define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
+  typedef typename Digraph::Node Node;                                  \
+  typedef typename Digraph::NodeIt NodeIt;                              \
+  typedef typename Digraph::Arc Arc;                                    \
+  typedef typename Digraph::ArcIt ArcIt;                                \
+  typedef typename Digraph::InArcIt InArcIt;                            \
+  typedef typename Digraph::OutArcIt OutArcIt;                          \
+  typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
+  typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
+  typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
+  typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
+  typedef typename Digraph::template ArcMap<int> IntArcMap;             \
+  typedef typename Digraph::template ArcMap<double> DoubleArcMap
+
+  ///Creates convenience typedefs for the graph types and iterators
+
+  ///This \c \#define creates the same convenience typedefs as defined
+  ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
+  ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
+  ///\c DoubleEdgeMap.
+  ///
+  ///\note If the graph type is a dependent type, ie. the graph type depend
+  ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
+  ///macro.
+#define GRAPH_TYPEDEFS(Graph)                                           \
+  DIGRAPH_TYPEDEFS(Graph);                                              \
+  typedef Graph::Edge Edge;                                             \
+  typedef Graph::EdgeIt EdgeIt;                                         \
+  typedef Graph::IncEdgeIt IncEdgeIt;                                   \
+  typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
+  typedef Graph::EdgeMap<int> IntEdgeMap;                               \
+  typedef Graph::EdgeMap<double> DoubleEdgeMap
+
+  ///Creates convenience typedefs for the graph types and iterators
+
+  ///\see GRAPH_TYPEDEFS
+  ///
+  ///\note Use this macro, if the graph type is a dependent type,
+  ///ie. the graph type depend on a template parameter.
+#define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
+  TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
+  typedef typename Graph::Edge Edge;                                    \
+  typedef typename Graph::EdgeIt EdgeIt;                                \
+  typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
+  typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
+  typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
+  typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
+
+  /// \brief Function to count the items in the graph.
+  ///
+  /// This function counts the items (nodes, arcs etc) in the graph.
+  /// The complexity of the function is O(n) because
+  /// it iterates on all of the items.
+  template <typename Graph, typename Item>
+  inline int countItems(const Graph& g) {
+    typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
+    int num = 0;
+    for (ItemIt it(g); it != INVALID; ++it) {
+      ++num;
+    }
+    return num;
+  }
+
+  // Node counting:
+
+  namespace _core_bits {
+
+    template <typename Graph, typename Enable = void>
+    struct CountNodesSelector {
+      static int count(const Graph &g) {
+        return countItems<Graph, typename Graph::Node>(g);
+      }
+    };
+
+    template <typename Graph>
+    struct CountNodesSelector<
+      Graph, typename
+      enable_if<typename Graph::NodeNumTag, void>::type>
+    {
+      static int count(const Graph &g) {
+        return g.nodeNum();
+      }
+    };
+  }
+
+  /// \brief Function to count the nodes in the graph.
+  ///
+  /// This function counts the nodes in the graph.
+  /// The complexity of the function is O(n) but for some
+  /// graph structures it is specialized to run in O(1).
+  ///
+  /// If the graph contains a \e nodeNum() member function and a
+  /// \e NodeNumTag tag then this function calls directly the member
+  /// function to query the cardinality of the node set.
+  template <typename Graph>
+  inline int countNodes(const Graph& g) {
+    return _core_bits::CountNodesSelector<Graph>::count(g);
+  }
+
+  // Arc counting:
+
+  namespace _core_bits {
+
+    template <typename Graph, typename Enable = void>
+    struct CountArcsSelector {
+      static int count(const Graph &g) {
+        return countItems<Graph, typename Graph::Arc>(g);
+      }
+    };
+
+    template <typename Graph>
+    struct CountArcsSelector<
+      Graph,
+      typename enable_if<typename Graph::ArcNumTag, void>::type>
+    {
+      static int count(const Graph &g) {
+        return g.arcNum();
+      }
+    };
+  }
+
+  /// \brief Function to count the arcs in the graph.
+  ///
+  /// This function counts the arcs in the graph.
+  /// The complexity of the function is O(e) but for some
+  /// graph structures it is specialized to run in O(1).
+  ///
+  /// If the graph contains a \e arcNum() member function and a
+  /// \e EdgeNumTag tag then this function calls directly the member
+  /// function to query the cardinality of the arc set.
+  template <typename Graph>
+  inline int countArcs(const Graph& g) {
+    return _core_bits::CountArcsSelector<Graph>::count(g);
+  }
+
+  // Edge counting:
+  namespace _core_bits {
+
+    template <typename Graph, typename Enable = void>
+    struct CountEdgesSelector {
+      static int count(const Graph &g) {
+        return countItems<Graph, typename Graph::Edge>(g);
+      }
+    };
+
+    template <typename Graph>
+    struct CountEdgesSelector<
+      Graph,
+      typename enable_if<typename Graph::EdgeNumTag, void>::type>
+    {
+      static int count(const Graph &g) {
+        return g.edgeNum();
+      }
+    };
+  }
+
+  /// \brief Function to count the edges in the graph.
+  ///
+  /// This function counts the edges in the graph.
+  /// The complexity of the function is O(m) but for some
+  /// graph structures it is specialized to run in O(1).
+  ///
+  /// If the graph contains a \e edgeNum() member function and a
+  /// \e EdgeNumTag tag then this function calls directly the member
+  /// function to query the cardinality of the edge set.
+  template <typename Graph>
+  inline int countEdges(const Graph& g) {
+    return _core_bits::CountEdgesSelector<Graph>::count(g);
+
+  }
+
+
+  template <typename Graph, typename DegIt>
+  inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
+    int num = 0;
+    for (DegIt it(_g, _n); it != INVALID; ++it) {
+      ++num;
+    }
+    return num;
+  }
+
+  /// \brief Function to count the number of the out-arcs from node \c n.
+  ///
+  /// This function counts the number of the out-arcs from node \c n
+  /// in the graph.
+  template <typename Graph>
+  inline int countOutArcs(const Graph& _g,  const typename Graph::Node& _n) {
+    return countNodeDegree<Graph, typename Graph::OutArcIt>(_g, _n);
+  }
+
+  /// \brief Function to count the number of the in-arcs to node \c n.
+  ///
+  /// This function counts the number of the in-arcs to node \c n
+  /// in the graph.
+  template <typename Graph>
+  inline int countInArcs(const Graph& _g,  const typename Graph::Node& _n) {
+    return countNodeDegree<Graph, typename Graph::InArcIt>(_g, _n);
+  }
+
+  /// \brief Function to count the number of the inc-edges to node \c n.
+  ///
+  /// This function counts the number of the inc-edges to node \c n
+  /// in the graph.
+  template <typename Graph>
+  inline int countIncEdges(const Graph& _g,  const typename Graph::Node& _n) {
+    return countNodeDegree<Graph, typename Graph::IncEdgeIt>(_g, _n);
+  }
+
+  namespace _core_bits {
+
+    template <typename Digraph, typename Item, typename RefMap>
+    class MapCopyBase {
+    public:
+      virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
+
+      virtual ~MapCopyBase() {}
+    };
+
+    template <typename Digraph, typename Item, typename RefMap,
+              typename ToMap, typename FromMap>
+    class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
+    public:
+
+      MapCopy(ToMap& tmap, const FromMap& map)
+        : _tmap(tmap), _map(map) {}
+
+      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
+        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+        for (ItemIt it(digraph); it != INVALID; ++it) {
+          _tmap.set(refMap[it], _map[it]);
+        }
+      }
+
+    private:
+      ToMap& _tmap;
+      const FromMap& _map;
+    };
+
+    template <typename Digraph, typename Item, typename RefMap, typename It>
+    class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
+    public:
+
+      ItemCopy(It& it, const Item& item) : _it(it), _item(item) {}
+
+      virtual void copy(const Digraph&, const RefMap& refMap) {
+        _it = refMap[_item];
+      }
+
+    private:
+      It& _it;
+      Item _item;
+    };
+
+    template <typename Digraph, typename Item, typename RefMap, typename Ref>
+    class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
+    public:
+
+      RefCopy(Ref& map) : _map(map) {}
+
+      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
+        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+        for (ItemIt it(digraph); it != INVALID; ++it) {
+          _map.set(it, refMap[it]);
+        }
+      }
+
+    private:
+      Ref& _map;
+    };
+
+    template <typename Digraph, typename Item, typename RefMap,
+              typename CrossRef>
+    class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
+    public:
+
+      CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
+
+      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
+        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+        for (ItemIt it(digraph); it != INVALID; ++it) {
+          _cmap.set(refMap[it], it);
+        }
+      }
+
+    private:
+      CrossRef& _cmap;
+    };
+
+    template <typename Digraph, typename Enable = void>
+    struct DigraphCopySelector {
+      template <typename From, typename NodeRefMap, typename ArcRefMap>
+      static void copy(Digraph &to, const From& from,
+                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
+        for (typename From::NodeIt it(from); it != INVALID; ++it) {
+          nodeRefMap[it] = to.addNode();
+        }
+        for (typename From::ArcIt it(from); it != INVALID; ++it) {
+          arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
+                                    nodeRefMap[from.target(it)]);
+        }
+      }
+    };
+
+    template <typename Digraph>
+    struct DigraphCopySelector<
+      Digraph,
+      typename enable_if<typename Digraph::BuildTag, void>::type>
+    {
+      template <typename From, typename NodeRefMap, typename ArcRefMap>
+      static void copy(Digraph &to, const From& from,
+                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
+        to.build(from, nodeRefMap, arcRefMap);
+      }
+    };
+
+    template <typename Graph, typename Enable = void>
+    struct GraphCopySelector {
+      template <typename From, typename NodeRefMap, typename EdgeRefMap>
+      static void copy(Graph &to, const From& from,
+                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
+        for (typename From::NodeIt it(from); it != INVALID; ++it) {
+          nodeRefMap[it] = to.addNode();
+        }
+        for (typename From::EdgeIt it(from); it != INVALID; ++it) {
+          edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
+                                      nodeRefMap[from.v(it)]);
+        }
+      }
+    };
+
+    template <typename Graph>
+    struct GraphCopySelector<
+      Graph,
+      typename enable_if<typename Graph::BuildTag, void>::type>
+    {
+      template <typename From, typename NodeRefMap, typename EdgeRefMap>
+      static void copy(Graph &to, const From& from,
+                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
+        to.build(from, nodeRefMap, edgeRefMap);
+      }
+    };
+
+  }
+
+  /// \brief Class to copy a digraph.
+  ///
+  /// Class to copy a digraph to another digraph (duplicate a digraph). The
+  /// simplest way of using it is through the \c copyDigraph() function.
+  ///
+  /// This class not just make a copy of a graph, but it can create
+  /// references and cross references between the nodes and arcs of
+  /// the two graphs, it can copy maps for use with the newly created
+  /// graph and copy nodes and arcs.
+  ///
+  /// To make a copy from a graph, first an instance of DigraphCopy
+  /// should be created, then the data belongs to the graph should
+  /// assigned to copy. In the end, the \c run() member should be
+  /// called.
+  ///
+  /// The next code copies a graph with several data:
+  ///\code
+  ///  DigraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
+  ///  // create a reference for the nodes
+  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
+  ///  dc.nodeRef(nr);
+  ///  // create a cross reference (inverse) for the arcs
+  ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
+  ///  dc.arcCrossRef(acr);
+  ///  // copy an arc map
+  ///  OrigGraph::ArcMap<double> oamap(orig_graph);
+  ///  NewGraph::ArcMap<double> namap(new_graph);
+  ///  dc.arcMap(namap, oamap);
+  ///  // copy a node
+  ///  OrigGraph::Node on;
+  ///  NewGraph::Node nn;
+  ///  dc.node(nn, on);
+  ///  // Executions of copy
+  ///  dc.run();
+  ///\endcode
+  template <typename To, typename From>
+  class DigraphCopy {
+  private:
+
+    typedef typename From::Node Node;
+    typedef typename From::NodeIt NodeIt;
+    typedef typename From::Arc Arc;
+    typedef typename From::ArcIt ArcIt;
+
+    typedef typename To::Node TNode;
+    typedef typename To::Arc TArc;
+
+    typedef typename From::template NodeMap<TNode> NodeRefMap;
+    typedef typename From::template ArcMap<TArc> ArcRefMap;
+
+
+  public:
+
+
+    /// \brief Constructor for the DigraphCopy.
+    ///
+    /// It copies the content of the \c _from digraph into the
+    /// \c _to digraph.
+    DigraphCopy(To& to, const From& from)
+      : _from(from), _to(to) {}
+
+    /// \brief Destructor of the DigraphCopy
+    ///
+    /// Destructor of the DigraphCopy
+    ~DigraphCopy() {
+      for (int i = 0; i < int(_node_maps.size()); ++i) {
+        delete _node_maps[i];
+      }
+      for (int i = 0; i < int(_arc_maps.size()); ++i) {
+        delete _arc_maps[i];
+      }
+
+    }
+
+    /// \brief Copies the node references into the given map.
+    ///
+    /// Copies the node references into the given map. The parameter
+    /// should be a map, which key type is the Node type of the source
+    /// graph, while the value type is the Node type of the
+    /// destination graph.
+    template <typename NodeRef>
+    DigraphCopy& nodeRef(NodeRef& map) {
+      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
+                           NodeRefMap, NodeRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the node cross references into the given map.
+    ///
+    ///  Copies the node cross references (reverse references) into
+    ///  the given map. The parameter should be a map, which key type
+    ///  is the Node type of the destination graph, while the value type is
+    ///  the Node type of the source graph.
+    template <typename NodeCrossRef>
+    DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
+      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
+                           NodeRefMap, NodeCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created digraph.
+    /// The new map's key type is the destination graph's node type,
+    /// and the copied map's key type is the source graph's node type.
+    template <typename ToMap, typename FromMap>
+    DigraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
+      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
+                           NodeRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given node.
+    ///
+    /// Make a copy of the given node.
+    DigraphCopy& node(TNode& tnode, const Node& snode) {
+      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
+                           NodeRefMap, TNode>(tnode, snode));
+      return *this;
+    }
+
+    /// \brief Copies the arc references into the given map.
+    ///
+    /// Copies the arc references into the given map.
+    template <typename ArcRef>
+    DigraphCopy& arcRef(ArcRef& map) {
+      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
+                          ArcRefMap, ArcRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the arc cross references into the given map.
+    ///
+    ///  Copies the arc cross references (reverse references) into
+    ///  the given map.
+    template <typename ArcCrossRef>
+    DigraphCopy& arcCrossRef(ArcCrossRef& map) {
+      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
+                          ArcRefMap, ArcCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created digraph.
+    /// The new map's key type is the to digraph's arc type,
+    /// and the copied map's key type is the from digraph's arc
+    /// type.
+    template <typename ToMap, typename FromMap>
+    DigraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
+      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
+                          ArcRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given arc.
+    ///
+    /// Make a copy of the given arc.
+    DigraphCopy& arc(TArc& tarc, const Arc& sarc) {
+      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
+                          ArcRefMap, TArc>(tarc, sarc));
+      return *this;
+    }
+
+    /// \brief Executes the copies.
+    ///
+    /// Executes the copies.
+    void run() {
+      NodeRefMap nodeRefMap(_from);
+      ArcRefMap arcRefMap(_from);
+      _core_bits::DigraphCopySelector<To>::
+        copy(_to, _from, nodeRefMap, arcRefMap);
+      for (int i = 0; i < int(_node_maps.size()); ++i) {
+        _node_maps[i]->copy(_from, nodeRefMap);
+      }
+      for (int i = 0; i < int(_arc_maps.size()); ++i) {
+        _arc_maps[i]->copy(_from, arcRefMap);
+      }
+    }
+
+  protected:
+
+
+    const From& _from;
+    To& _to;
+
+    std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
+    _node_maps;
+
+    std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
+    _arc_maps;
+
+  };
+
+  /// \brief Copy a digraph to another digraph.
+  ///
+  /// Copy a digraph to another digraph. The complete usage of the
+  /// function is detailed in the DigraphCopy class, but a short
+  /// example shows a basic work:
+  ///\code
+  /// copyDigraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
+  ///\endcode
+  ///
+  /// After the copy the \c nr map will contain the mapping from the
+  /// nodes of the \c from digraph to the nodes of the \c to digraph and
+  /// \c ecr will contain the mapping from the arcs of the \c to digraph
+  /// to the arcs of the \c from digraph.
+  ///
+  /// \see DigraphCopy
+  template <typename To, typename From>
+  DigraphCopy<To, From> copyDigraph(To& to, const From& from) {
+    return DigraphCopy<To, From>(to, from);
+  }
+
+  /// \brief Class to copy a graph.
+  ///
+  /// Class to copy a graph to another graph (duplicate a graph). The
+  /// simplest way of using it is through the \c copyGraph() function.
+  ///
+  /// This class not just make a copy of a graph, but it can create
+  /// references and cross references between the nodes, edges and arcs of
+  /// the two graphs, it can copy maps for use with the newly created
+  /// graph and copy nodes, edges and arcs.
+  ///
+  /// To make a copy from a graph, first an instance of GraphCopy
+  /// should be created, then the data belongs to the graph should
+  /// assigned to copy. In the end, the \c run() member should be
+  /// called.
+  ///
+  /// The next code copies a graph with several data:
+  ///\code
+  ///  GraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
+  ///  // create a reference for the nodes
+  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
+  ///  dc.nodeRef(nr);
+  ///  // create a cross reference (inverse) for the edges
+  ///  NewGraph::EdgeMap<OrigGraph::Arc> ecr(new_graph);
+  ///  dc.edgeCrossRef(ecr);
+  ///  // copy an arc map
+  ///  OrigGraph::ArcMap<double> oamap(orig_graph);
+  ///  NewGraph::ArcMap<double> namap(new_graph);
+  ///  dc.arcMap(namap, oamap);
+  ///  // copy a node
+  ///  OrigGraph::Node on;
+  ///  NewGraph::Node nn;
+  ///  dc.node(nn, on);
+  ///  // Executions of copy
+  ///  dc.run();
+  ///\endcode
+  template <typename To, typename From>
+  class GraphCopy {
+  private:
+
+    typedef typename From::Node Node;
+    typedef typename From::NodeIt NodeIt;
+    typedef typename From::Arc Arc;
+    typedef typename From::ArcIt ArcIt;
+    typedef typename From::Edge Edge;
+    typedef typename From::EdgeIt EdgeIt;
+
+    typedef typename To::Node TNode;
+    typedef typename To::Arc TArc;
+    typedef typename To::Edge TEdge;
+
+    typedef typename From::template NodeMap<TNode> NodeRefMap;
+    typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
+
+    struct ArcRefMap {
+      ArcRefMap(const To& to, const From& from,
+                const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
+        : _to(to), _from(from),
+          _edge_ref(edge_ref), _node_ref(node_ref) {}
+
+      typedef typename From::Arc Key;
+      typedef typename To::Arc Value;
+
+      Value operator[](const Key& key) const {
+        bool forward = _from.u(key) != _from.v(key) ?
+          _node_ref[_from.source(key)] ==
+          _to.source(_to.direct(_edge_ref[key], true)) :
+          _from.direction(key);
+        return _to.direct(_edge_ref[key], forward);
+      }
+
+      const To& _to;
+      const From& _from;
+      const EdgeRefMap& _edge_ref;
+      const NodeRefMap& _node_ref;
+    };
+
+
+  public:
+
+
+    /// \brief Constructor for the GraphCopy.
+    ///
+    /// It copies the content of the \c _from graph into the
+    /// \c _to graph.
+    GraphCopy(To& to, const From& from)
+      : _from(from), _to(to) {}
+
+    /// \brief Destructor of the GraphCopy
+    ///
+    /// Destructor of the GraphCopy
+    ~GraphCopy() {
+      for (int i = 0; i < int(_node_maps.size()); ++i) {
+        delete _node_maps[i];
+      }
+      for (int i = 0; i < int(_arc_maps.size()); ++i) {
+        delete _arc_maps[i];
+      }
+      for (int i = 0; i < int(_edge_maps.size()); ++i) {
+        delete _edge_maps[i];
+      }
+
+    }
+
+    /// \brief Copies the node references into the given map.
+    ///
+    /// Copies the node references into the given map.
+    template <typename NodeRef>
+    GraphCopy& nodeRef(NodeRef& map) {
+      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
+                           NodeRefMap, NodeRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the node cross references into the given map.
+    ///
+    ///  Copies the node cross references (reverse references) into
+    ///  the given map.
+    template <typename NodeCrossRef>
+    GraphCopy& nodeCrossRef(NodeCrossRef& map) {
+      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
+                           NodeRefMap, NodeCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created graph.
+    /// The new map's key type is the to graph's node type,
+    /// and the copied map's key type is the from graph's node
+    /// type.
+    template <typename ToMap, typename FromMap>
+    GraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
+      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
+                           NodeRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given node.
+    ///
+    /// Make a copy of the given node.
+    GraphCopy& node(TNode& tnode, const Node& snode) {
+      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
+                           NodeRefMap, TNode>(tnode, snode));
+      return *this;
+    }
+
+    /// \brief Copies the arc references into the given map.
+    ///
+    /// Copies the arc references into the given map.
+    template <typename ArcRef>
+    GraphCopy& arcRef(ArcRef& map) {
+      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
+                          ArcRefMap, ArcRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the arc cross references into the given map.
+    ///
+    ///  Copies the arc cross references (reverse references) into
+    ///  the given map.
+    template <typename ArcCrossRef>
+    GraphCopy& arcCrossRef(ArcCrossRef& map) {
+      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
+                          ArcRefMap, ArcCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created graph.
+    /// The new map's key type is the to graph's arc type,
+    /// and the copied map's key type is the from graph's arc
+    /// type.
+    template <typename ToMap, typename FromMap>
+    GraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
+      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
+                          ArcRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given arc.
+    ///
+    /// Make a copy of the given arc.
+    GraphCopy& arc(TArc& tarc, const Arc& sarc) {
+      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
+                          ArcRefMap, TArc>(tarc, sarc));
+      return *this;
+    }
+
+    /// \brief Copies the edge references into the given map.
+    ///
+    /// Copies the edge references into the given map.
+    template <typename EdgeRef>
+    GraphCopy& edgeRef(EdgeRef& map) {
+      _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
+                           EdgeRefMap, EdgeRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the edge cross references into the given map.
+    ///
+    /// Copies the edge cross references (reverse
+    /// references) into the given map.
+    template <typename EdgeCrossRef>
+    GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
+      _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
+                           Edge, EdgeRefMap, EdgeCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created graph.
+    /// The new map's key type is the to graph's edge type,
+    /// and the copied map's key type is the from graph's edge
+    /// type.
+    template <typename ToMap, typename FromMap>
+    GraphCopy& edgeMap(ToMap& tmap, const FromMap& map) {
+      _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
+                           EdgeRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given edge.
+    ///
+    /// Make a copy of the given edge.
+    GraphCopy& edge(TEdge& tedge, const Edge& sedge) {
+      _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
+                           EdgeRefMap, TEdge>(tedge, sedge));
+      return *this;
+    }
+
+    /// \brief Executes the copies.
+    ///
+    /// Executes the copies.
+    void run() {
+      NodeRefMap nodeRefMap(_from);
+      EdgeRefMap edgeRefMap(_from);
+      ArcRefMap arcRefMap(_to, _from, edgeRefMap, nodeRefMap);
+      _core_bits::GraphCopySelector<To>::
+        copy(_to, _from, nodeRefMap, edgeRefMap);
+      for (int i = 0; i < int(_node_maps.size()); ++i) {
+        _node_maps[i]->copy(_from, nodeRefMap);
+      }
+      for (int i = 0; i < int(_edge_maps.size()); ++i) {
+        _edge_maps[i]->copy(_from, edgeRefMap);
+      }
+      for (int i = 0; i < int(_arc_maps.size()); ++i) {
+        _arc_maps[i]->copy(_from, arcRefMap);
+      }
+    }
+
+  private:
+
+    const From& _from;
+    To& _to;
+
+    std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
+    _node_maps;
+
+    std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
+    _arc_maps;
+
+    std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
+    _edge_maps;
+
+  };
+
+  /// \brief Copy a graph to another graph.
+  ///
+  /// Copy a graph to another graph. The complete usage of the
+  /// function is detailed in the GraphCopy class, but a short
+  /// example shows a basic work:
+  ///\code
+  /// copyGraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
+  ///\endcode
+  ///
+  /// After the copy the \c nr map will contain the mapping from the
+  /// nodes of the \c from graph to the nodes of the \c to graph and
+  /// \c ecr will contain the mapping from the arcs of the \c to graph
+  /// to the arcs of the \c from graph.
+  ///
+  /// \see GraphCopy
+  template <typename To, typename From>
+  GraphCopy<To, From>
+  copyGraph(To& to, const From& from) {
+    return GraphCopy<To, From>(to, from);
+  }
+
+  namespace _core_bits {
+
+    template <typename Graph, typename Enable = void>
+    struct FindArcSelector {
+      typedef typename Graph::Node Node;
+      typedef typename Graph::Arc Arc;
+      static Arc find(const Graph &g, Node u, Node v, Arc e) {
+        if (e == INVALID) {
+          g.firstOut(e, u);
+        } else {
+          g.nextOut(e);
+        }
+        while (e != INVALID && g.target(e) != v) {
+          g.nextOut(e);
+        }
+        return e;
+      }
+    };
+
+    template <typename Graph>
+    struct FindArcSelector<
+      Graph,
+      typename enable_if<typename Graph::FindEdgeTag, void>::type>
+    {
+      typedef typename Graph::Node Node;
+      typedef typename Graph::Arc Arc;
+      static Arc find(const Graph &g, Node u, Node v, Arc prev) {
+        return g.findArc(u, v, prev);
+      }
+    };
+  }
+
+  /// \brief Finds an arc between two nodes of a graph.
+  ///
+  /// Finds an arc from node \c u to node \c v in graph \c g.
+  ///
+  /// If \c prev is \ref INVALID (this is the default value), then
+  /// it finds the first arc from \c u to \c v. Otherwise it looks for
+  /// the next arc from \c u to \c v after \c prev.
+  /// \return The found arc or \ref INVALID if there is no such an arc.
+  ///
+  /// Thus you can iterate through each arc from \c u to \c v as it follows.
+  ///\code
+  /// for(Arc e=findArc(g,u,v);e!=INVALID;e=findArc(g,u,v,e)) {
+  ///   ...
+  /// }
+  ///\endcode
+  ///
+  ///\sa ArcLookUp
+  ///\sa AllArcLookUp
+  ///\sa DynArcLookUp
+  ///\sa ConArcIt
+  template <typename Graph>
+  inline typename Graph::Arc
+  findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
+          typename Graph::Arc prev = INVALID) {
+    return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
+  }
+
+  /// \brief Iterator for iterating on arcs connected the same nodes.
+  ///
+  /// Iterator for iterating on arcs connected the same nodes. It is
+  /// higher level interface for the findArc() function. You can
+  /// use it the following way:
+  ///\code
+  /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
+  ///   ...
+  /// }
+  ///\endcode
+  ///
+  ///\sa findArc()
+  ///\sa ArcLookUp
+  ///\sa AllArcLookUp
+  ///\sa DynArcLookUp
+  template <typename _Graph>
+  class ConArcIt : public _Graph::Arc {
+  public:
+
+    typedef _Graph Graph;
+    typedef typename Graph::Arc Parent;
+
+    typedef typename Graph::Arc Arc;
+    typedef typename Graph::Node Node;
+
+    /// \brief Constructor.
+    ///
+    /// Construct a new ConArcIt iterating on the arcs which
+    /// connects the \c u and \c v node.
+    ConArcIt(const Graph& g, Node u, Node v) : _graph(g) {
+      Parent::operator=(findArc(_graph, u, v));
+    }
+
+    /// \brief Constructor.
+    ///
+    /// Construct a new ConArcIt which continues the iterating from
+    /// the \c e arc.
+    ConArcIt(const Graph& g, Arc a) : Parent(a), _graph(g) {}
+
+    /// \brief Increment operator.
+    ///
+    /// It increments the iterator and gives back the next arc.
+    ConArcIt& operator++() {
+      Parent::operator=(findArc(_graph, _graph.source(*this),
+                                _graph.target(*this), *this));
+      return *this;
+    }
+  private:
+    const Graph& _graph;
+  };
+
+  namespace _core_bits {
+
+    template <typename Graph, typename Enable = void>
+    struct FindEdgeSelector {
+      typedef typename Graph::Node Node;
+      typedef typename Graph::Edge Edge;
+      static Edge find(const Graph &g, Node u, Node v, Edge e) {
+        bool b;
+        if (u != v) {
+          if (e == INVALID) {
+            g.firstInc(e, b, u);
+          } else {
+            b = g.u(e) == u;
+            g.nextInc(e, b);
+          }
+          while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
+            g.nextInc(e, b);
+          }
+        } else {
+          if (e == INVALID) {
+            g.firstInc(e, b, u);
+          } else {
+            b = true;
+            g.nextInc(e, b);
+          }
+          while (e != INVALID && (!b || g.v(e) != v)) {
+            g.nextInc(e, b);
+          }
+        }
+        return e;
+      }
+    };
+
+    template <typename Graph>
+    struct FindEdgeSelector<
+      Graph,
+      typename enable_if<typename Graph::FindEdgeTag, void>::type>
+    {
+      typedef typename Graph::Node Node;
+      typedef typename Graph::Edge Edge;
+      static Edge find(const Graph &g, Node u, Node v, Edge prev) {
+        return g.findEdge(u, v, prev);
+      }
+    };
+  }
+
+  /// \brief Finds an edge between two nodes of a graph.
+  ///
+  /// Finds an edge from node \c u to node \c v in graph \c g.
+  /// If the node \c u and node \c v is equal then each loop edge
+  /// will be enumerated once.
+  ///
+  /// If \c prev is \ref INVALID (this is the default value), then
+  /// it finds the first arc from \c u to \c v. Otherwise it looks for
+  /// the next arc from \c u to \c v after \c prev.
+  /// \return The found arc or \ref INVALID if there is no such an arc.
+  ///
+  /// Thus you can iterate through each arc from \c u to \c v as it follows.
+  ///\code
+  /// for(Edge e = findEdge(g,u,v); e != INVALID;
+  ///     e = findEdge(g,u,v,e)) {
+  ///   ...
+  /// }
+  ///\endcode
+  ///
+  ///\sa ConEdgeIt
+
+  template <typename Graph>
+  inline typename Graph::Edge
+  findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
+            typename Graph::Edge p = INVALID) {
+    return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
+  }
+
+  /// \brief Iterator for iterating on edges connected the same nodes.
+  ///
+  /// Iterator for iterating on edges connected the same nodes. It is
+  /// higher level interface for the findEdge() function. You can
+  /// use it the following way:
+  ///\code
+  /// for (ConEdgeIt<Graph> it(g, src, trg); it != INVALID; ++it) {
+  ///   ...
+  /// }
+  ///\endcode
+  ///
+  ///\sa findEdge()
+  template <typename _Graph>
+  class ConEdgeIt : public _Graph::Edge {
+  public:
+
+    typedef _Graph Graph;
+    typedef typename Graph::Edge Parent;
+
+    typedef typename Graph::Edge Edge;
+    typedef typename Graph::Node Node;
+
+    /// \brief Constructor.
+    ///
+    /// Construct a new ConEdgeIt iterating on the edges which
+    /// connects the \c u and \c v node.
+    ConEdgeIt(const Graph& g, Node u, Node v) : _graph(g) {
+      Parent::operator=(findEdge(_graph, u, v));
+    }
+
+    /// \brief Constructor.
+    ///
+    /// Construct a new ConEdgeIt which continues the iterating from
+    /// the \c e edge.
+    ConEdgeIt(const Graph& g, Edge e) : Parent(e), _graph(g) {}
+
+    /// \brief Increment operator.
+    ///
+    /// It increments the iterator and gives back the next edge.
+    ConEdgeIt& operator++() {
+      Parent::operator=(findEdge(_graph, _graph.u(*this),
+                                 _graph.v(*this), *this));
+      return *this;
+    }
+  private:
+    const Graph& _graph;
+  };
+
+
+  ///Dynamic arc look up between given endpoints.
+
+  ///Using this class, you can find an arc in a digraph from a given
+  ///source to a given target in amortized time <em>O(log d)</em>,
+  ///where <em>d</em> is the out-degree of the source node.
+  ///
+  ///It is possible to find \e all parallel arcs between two nodes with
+  ///the \c findFirst() and \c findNext() members.
+  ///
+  ///See the \ref ArcLookUp and \ref AllArcLookUp classes if your
+  ///digraph is not changed so frequently.
+  ///
+  ///This class uses a self-adjusting binary search tree, Sleator's
+  ///and Tarjan's Splay tree for guarantee the logarithmic amortized
+  ///time bound for arc lookups. This class also guarantees the
+  ///optimal time bound in a constant factor for any distribution of
+  ///queries.
+  ///
+  ///\tparam G The type of the underlying digraph.
+  ///
+  ///\sa ArcLookUp
+  ///\sa AllArcLookUp
+  template<class G>
+  class DynArcLookUp
+    : protected ItemSetTraits<G, typename G::Arc>::ItemNotifier::ObserverBase
+  {
+  public:
+    typedef typename ItemSetTraits<G, typename G::Arc>
+    ::ItemNotifier::ObserverBase Parent;
+
+    TEMPLATE_DIGRAPH_TYPEDEFS(G);
+    typedef G Digraph;
+
+  protected:
+
+    class AutoNodeMap : public ItemSetTraits<G, Node>::template Map<Arc>::Type {
+    public:
+
+      typedef typename ItemSetTraits<G, Node>::template Map<Arc>::Type Parent;
+
+      AutoNodeMap(const G& digraph) : Parent(digraph, INVALID) {}
+
+      virtual void add(const Node& node) {
+        Parent::add(node);
+        Parent::set(node, INVALID);
+      }
+
+      virtual void add(const std::vector<Node>& nodes) {
+        Parent::add(nodes);
+        for (int i = 0; i < int(nodes.size()); ++i) {
+          Parent::set(nodes[i], INVALID);
+        }
+      }
+
+      virtual void build() {
+        Parent::build();
+        Node it;
+        typename Parent::Notifier* nf = Parent::notifier();
+        for (nf->first(it); it != INVALID; nf->next(it)) {
+          Parent::set(it, INVALID);
+        }
+      }
+    };
+
+    const Digraph &_g;
+    AutoNodeMap _head;
+    typename Digraph::template ArcMap<Arc> _parent;
+    typename Digraph::template ArcMap<Arc> _left;
+    typename Digraph::template ArcMap<Arc> _right;
+
+    class ArcLess {
+      const Digraph &g;
+    public:
+      ArcLess(const Digraph &_g) : g(_g) {}
+      bool operator()(Arc a,Arc b) const
+      {
+        return g.target(a)<g.target(b);
+      }
+    };
+
+  public:
+
+    ///Constructor
+
+    ///Constructor.
+    ///
+    ///It builds up the search database.
+    DynArcLookUp(const Digraph &g)
+      : _g(g),_head(g),_parent(g),_left(g),_right(g)
+    {
+      Parent::attach(_g.notifier(typename Digraph::Arc()));
+      refresh();
+    }
+
+  protected:
+
+    virtual void add(const Arc& arc) {
+      insert(arc);
+    }
+
+    virtual void add(const std::vector<Arc>& arcs) {
+      for (int i = 0; i < int(arcs.size()); ++i) {
+        insert(arcs[i]);
+      }
+    }
+
+    virtual void erase(const Arc& arc) {
+      remove(arc);
+    }
+
+    virtual void erase(const std::vector<Arc>& arcs) {
+      for (int i = 0; i < int(arcs.size()); ++i) {
+        remove(arcs[i]);
+      }
+    }
+
+    virtual void build() {
+      refresh();
+    }
+
+    virtual void clear() {
+      for(NodeIt n(_g);n!=INVALID;++n) {
+        _head.set(n, INVALID);
+      }
+    }
+
+    void insert(Arc arc) {
+      Node s = _g.source(arc);
+      Node t = _g.target(arc);
+      _left.set(arc, INVALID);
+      _right.set(arc, INVALID);
+
+      Arc e = _head[s];
+      if (e == INVALID) {
+        _head.set(s, arc);
+        _parent.set(arc, INVALID);
+        return;
+      }
+      while (true) {
+        if (t < _g.target(e)) {
+          if (_left[e] == INVALID) {
+            _left.set(e, arc);
+            _parent.set(arc, e);
+            splay(arc);
+            return;
+          } else {
+            e = _left[e];
+          }
+        } else {
+          if (_right[e] == INVALID) {
+            _right.set(e, arc);
+            _parent.set(arc, e);
+            splay(arc);
+            return;
+          } else {
+            e = _right[e];
+          }
+        }
+      }
+    }
+
+    void remove(Arc arc) {
+      if (_left[arc] == INVALID) {
+        if (_right[arc] != INVALID) {
+          _parent.set(_right[arc], _parent[arc]);
+        }
+        if (_parent[arc] != INVALID) {
+          if (_left[_parent[arc]] == arc) {
+            _left.set(_parent[arc], _right[arc]);
+          } else {
+            _right.set(_parent[arc], _right[arc]);
+          }
+        } else {
+          _head.set(_g.source(arc), _right[arc]);
+        }
+      } else if (_right[arc] == INVALID) {
+        _parent.set(_left[arc], _parent[arc]);
+        if (_parent[arc] != INVALID) {
+          if (_left[_parent[arc]] == arc) {
+            _left.set(_parent[arc], _left[arc]);
+          } else {
+            _right.set(_parent[arc], _left[arc]);
+          }
+        } else {
+          _head.set(_g.source(arc), _left[arc]);
+        }
+      } else {
+        Arc e = _left[arc];
+        if (_right[e] != INVALID) {
+          e = _right[e];
+          while (_right[e] != INVALID) {
+            e = _right[e];
+          }
+          Arc s = _parent[e];
+          _right.set(_parent[e], _left[e]);
+          if (_left[e] != INVALID) {
+            _parent.set(_left[e], _parent[e]);
+          }
+
+          _left.set(e, _left[arc]);
+          _parent.set(_left[arc], e);
+          _right.set(e, _right[arc]);
+          _parent.set(_right[arc], e);
+
+          _parent.set(e, _parent[arc]);
+          if (_parent[arc] != INVALID) {
+            if (_left[_parent[arc]] == arc) {
+              _left.set(_parent[arc], e);
+            } else {
+              _right.set(_parent[arc], e);
+            }
+          }
+          splay(s);
+        } else {
+          _right.set(e, _right[arc]);
+          _parent.set(_right[arc], e);
+
+          if (_parent[arc] != INVALID) {
+            if (_left[_parent[arc]] == arc) {
+              _left.set(_parent[arc], e);
+            } else {
+              _right.set(_parent[arc], e);
+            }
+          } else {
+            _head.set(_g.source(arc), e);
+          }
+        }
+      }
+    }
+
+    Arc refreshRec(std::vector<Arc> &v,int a,int b)
+    {
+      int m=(a+b)/2;
+      Arc me=v[m];
+      if (a < m) {
+        Arc left = refreshRec(v,a,m-1);
+        _left.set(me, left);
+        _parent.set(left, me);
+      } else {
+        _left.set(me, INVALID);
+      }
+      if (m < b) {
+        Arc right = refreshRec(v,m+1,b);
+        _right.set(me, right);
+        _parent.set(right, me);
+      } else {
+        _right.set(me, INVALID);
+      }
+      return me;
+    }
+
+    void refresh() {
+      for(NodeIt n(_g);n!=INVALID;++n) {
+        std::vector<Arc> v;
+        for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
+        if(v.size()) {
+          std::sort(v.begin(),v.end(),ArcLess(_g));
+          Arc head = refreshRec(v,0,v.size()-1);
+          _head.set(n, head);
+          _parent.set(head, INVALID);
+        }
+        else _head.set(n, INVALID);
+      }
+    }
+
+    void zig(Arc v) {
+      Arc w = _parent[v];
+      _parent.set(v, _parent[w]);
+      _parent.set(w, v);
+      _left.set(w, _right[v]);
+      _right.set(v, w);
+      if (_parent[v] != INVALID) {
+        if (_right[_parent[v]] == w) {
+          _right.set(_parent[v], v);
+        } else {
+          _left.set(_parent[v], v);
+        }
+      }
+      if (_left[w] != INVALID){
+        _parent.set(_left[w], w);
+      }
+    }
+
+    void zag(Arc v) {
+      Arc w = _parent[v];
+      _parent.set(v, _parent[w]);
+      _parent.set(w, v);
+      _right.set(w, _left[v]);
+      _left.set(v, w);
+      if (_parent[v] != INVALID){
+        if (_left[_parent[v]] == w) {
+          _left.set(_parent[v], v);
+        } else {
+          _right.set(_parent[v], v);
+        }
+      }
+      if (_right[w] != INVALID){
+        _parent.set(_right[w], w);
+      }
+    }
+
+    void splay(Arc v) {
+      while (_parent[v] != INVALID) {
+        if (v == _left[_parent[v]]) {
+          if (_parent[_parent[v]] == INVALID) {
+            zig(v);
+          } else {
+            if (_parent[v] == _left[_parent[_parent[v]]]) {
+              zig(_parent[v]);
+              zig(v);
+            } else {
+              zig(v);
+              zag(v);
+            }
+          }
+        } else {
+          if (_parent[_parent[v]] == INVALID) {
+            zag(v);
+          } else {
+            if (_parent[v] == _left[_parent[_parent[v]]]) {
+              zag(v);
+              zig(v);
+            } else {
+              zag(_parent[v]);
+              zag(v);
+            }
+          }
+        }
+      }
+      _head[_g.source(v)] = v;
+    }
+
+
+  public:
+
+    ///Find an arc between two nodes.
+
+    ///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
+    /// <em>d</em> is the number of outgoing arcs of \c s.
+    ///\param s The source node
+    ///\param t The target node
+    ///\return An arc from \c s to \c t if there exists,
+    ///\ref INVALID otherwise.
+    Arc operator()(Node s, Node t) const
+    {
+      Arc a = _head[s];
+      while (true) {
+        if (_g.target(a) == t) {
+          const_cast<DynArcLookUp&>(*this).splay(a);
+          return a;
+        } else if (t < _g.target(a)) {
+          if (_left[a] == INVALID) {
+            const_cast<DynArcLookUp&>(*this).splay(a);
+            return INVALID;
+          } else {
+            a = _left[a];
+          }
+        } else  {
+          if (_right[a] == INVALID) {
+            const_cast<DynArcLookUp&>(*this).splay(a);
+            return INVALID;
+          } else {
+            a = _right[a];
+          }
+        }
+      }
+    }
+
+    ///Find the first arc between two nodes.
+
+    ///Find the first arc between two nodes in time
+    /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
+    /// outgoing arcs of \c s.
+    ///\param s The source node
+    ///\param t The target node
+    ///\return An arc from \c s to \c t if there exists, \ref INVALID
+    /// otherwise.
+    Arc findFirst(Node s, Node t) const
+    {
+      Arc a = _head[s];
+      Arc r = INVALID;
+      while (true) {
+        if (_g.target(a) < t) {
+          if (_right[a] == INVALID) {
+            const_cast<DynArcLookUp&>(*this).splay(a);
+            return r;
+          } else {
+            a = _right[a];
+          }
+        } else {
+          if (_g.target(a) == t) {
+            r = a;
+          }
+          if (_left[a] == INVALID) {
+            const_cast<DynArcLookUp&>(*this).splay(a);
+            return r;
+          } else {
+            a = _left[a];
+          }
+        }
+      }
+    }
+
+    ///Find the next arc between two nodes.
+
+    ///Find the next arc between two nodes in time
+    /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
+    /// outgoing arcs of \c s.
+    ///\param s The source node
+    ///\param t The target node
+    ///\return An arc from \c s to \c t if there exists, \ref INVALID
+    /// otherwise.
+
+    ///\note If \c e is not the result of the previous \c findFirst()
+    ///operation then the amorized time bound can not be guaranteed.
+#ifdef DOXYGEN
+    Arc findNext(Node s, Node t, Arc a) const
+#else
+    Arc findNext(Node, Node t, Arc a) const
+#endif
+    {
+      if (_right[a] != INVALID) {
+        a = _right[a];
+        while (_left[a] != INVALID) {
+          a = _left[a];
+        }
+        const_cast<DynArcLookUp&>(*this).splay(a);
+      } else {
+        while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
+          a = _parent[a];
+        }
+        if (_parent[a] == INVALID) {
+          return INVALID;
+        } else {
+          a = _parent[a];
+          const_cast<DynArcLookUp&>(*this).splay(a);
+        }
+      }
+      if (_g.target(a) == t) return a;
+      else return INVALID;
+    }
+
+  };
+
+  ///Fast arc look up between given endpoints.
+
+  ///Using this class, you can find an arc in a digraph from a given
+  ///source to a given target in time <em>O(log d)</em>,
+  ///where <em>d</em> is the out-degree of the source node.
+  ///
+  ///It is not possible to find \e all parallel arcs between two nodes.
+  ///Use \ref AllArcLookUp for this purpose.
+  ///
+  ///\warning This class is static, so you should refresh() (or at least
+  ///refresh(Node)) this data structure
+  ///whenever the digraph changes. This is a time consuming (superlinearly
+  ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
+  ///
+  ///\tparam G The type of the underlying digraph.
+  ///
+  ///\sa DynArcLookUp
+  ///\sa AllArcLookUp
+  template<class G>
+  class ArcLookUp
+  {
+  public:
+    TEMPLATE_DIGRAPH_TYPEDEFS(G);
+    typedef G Digraph;
+
+  protected:
+    const Digraph &_g;
+    typename Digraph::template NodeMap<Arc> _head;
+    typename Digraph::template ArcMap<Arc> _left;
+    typename Digraph::template ArcMap<Arc> _right;
+
+    class ArcLess {
+      const Digraph &g;
+    public:
+      ArcLess(const Digraph &_g) : g(_g) {}
+      bool operator()(Arc a,Arc b) const
+      {
+        return g.target(a)<g.target(b);
+      }
+    };
+
+  public:
+
+    ///Constructor
+
+    ///Constructor.
+    ///
+    ///It builds up the search database, which remains valid until the digraph
+    ///changes.
+    ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
+
+  private:
+    Arc refreshRec(std::vector<Arc> &v,int a,int b)
+    {
+      int m=(a+b)/2;
+      Arc me=v[m];
+      _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
+      _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
+      return me;
+    }
+  public:
+    ///Refresh the data structure at a node.
+
+    ///Build up the search database of node \c n.
+    ///
+    ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
+    ///the number of the outgoing arcs of \c n.
+    void refresh(Node n)
+    {
+      std::vector<Arc> v;
+      for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
+      if(v.size()) {
+        std::sort(v.begin(),v.end(),ArcLess(_g));
+        _head[n]=refreshRec(v,0,v.size()-1);
+      }
+      else _head[n]=INVALID;
+    }
+    ///Refresh the full data structure.
+
+    ///Build up the full search database. In fact, it simply calls
+    ///\ref refresh(Node) "refresh(n)" for each node \c n.
+    ///
+    ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
+    ///the number of the arcs of \c n and <em>D</em> is the maximum
+    ///out-degree of the digraph.
+
+    void refresh()
+    {
+      for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
+    }
+
+    ///Find an arc between two nodes.
+
+    ///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
+    /// <em>d</em> is the number of outgoing arcs of \c s.
+    ///\param s The source node
+    ///\param t The target node
+    ///\return An arc from \c s to \c t if there exists,
+    ///\ref INVALID otherwise.
+    ///
+    ///\warning If you change the digraph, refresh() must be called before using
+    ///this operator. If you change the outgoing arcs of
+    ///a single node \c n, then
+    ///\ref refresh(Node) "refresh(n)" is enough.
+    ///
+    Arc operator()(Node s, Node t) const
+    {
+      Arc e;
+      for(e=_head[s];
+          e!=INVALID&&_g.target(e)!=t;
+          e = t < _g.target(e)?_left[e]:_right[e]) ;
+      return e;
+    }
+
+  };
+
+  ///Fast look up of all arcs between given endpoints.
+
+  ///This class is the same as \ref ArcLookUp, with the addition
+  ///that it makes it possible to find all arcs between given endpoints.
+  ///
+  ///\warning This class is static, so you should refresh() (or at least
+  ///refresh(Node)) this data structure
+  ///whenever the digraph changes. This is a time consuming (superlinearly
+  ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
+  ///
+  ///\tparam G The type of the underlying digraph.
+  ///
+  ///\sa DynArcLookUp
+  ///\sa ArcLookUp
+  template<class G>
+  class AllArcLookUp : public ArcLookUp<G>
+  {
+    using ArcLookUp<G>::_g;
+    using ArcLookUp<G>::_right;
+    using ArcLookUp<G>::_left;
+    using ArcLookUp<G>::_head;
+
+    TEMPLATE_DIGRAPH_TYPEDEFS(G);
+    typedef G Digraph;
+
+    typename Digraph::template ArcMap<Arc> _next;
+
+    Arc refreshNext(Arc head,Arc next=INVALID)
+    {
+      if(head==INVALID) return next;
+      else {
+        next=refreshNext(_right[head],next);
+//         _next[head]=next;
+        _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
+          ? next : INVALID;
+        return refreshNext(_left[head],head);
+      }
+    }
+
+    void refreshNext()
+    {
+      for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
+    }
+
+  public:
+    ///Constructor
+
+    ///Constructor.
+    ///
+    ///It builds up the search database, which remains valid until the digraph
+    ///changes.
+    AllArcLookUp(const Digraph &g) : ArcLookUp<G>(g), _next(g) {refreshNext();}
+
+    ///Refresh the data structure at a node.
+
+    ///Build up the search database of node \c n.
+    ///
+    ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
+    ///the number of the outgoing arcs of \c n.
+
+    void refresh(Node n)
+    {
+      ArcLookUp<G>::refresh(n);
+      refreshNext(_head[n]);
+    }
+
+    ///Refresh the full data structure.
+
+    ///Build up the full search database. In fact, it simply calls
+    ///\ref refresh(Node) "refresh(n)" for each node \c n.
+    ///
+    ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
+    ///the number of the arcs of \c n and <em>D</em> is the maximum
+    ///out-degree of the digraph.
+
+    void refresh()
+    {
+      for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
+    }
+
+    ///Find an arc between two nodes.
+
+    ///Find an arc between two nodes.
+    ///\param s The source node
+    ///\param t The target node
+    ///\param prev The previous arc between \c s and \c t. It it is INVALID or
+    ///not given, the operator finds the first appropriate arc.
+    ///\return An arc from \c s to \c t after \c prev or
+    ///\ref INVALID if there is no more.
+    ///
+    ///For example, you can count the number of arcs from \c u to \c v in the
+    ///following way.
+    ///\code
+    ///AllArcLookUp<ListDigraph> ae(g);
+    ///...
+    ///int n=0;
+    ///for(Arc e=ae(u,v);e!=INVALID;e=ae(u,v,e)) n++;
+    ///\endcode
+    ///
+    ///Finding the first arc take <em>O(</em>log<em>d)</em> time, where
+    /// <em>d</em> is the number of outgoing arcs of \c s. Then, the
+    ///consecutive arcs are found in constant time.
+    ///
+    ///\warning If you change the digraph, refresh() must be called before using
+    ///this operator. If you change the outgoing arcs of
+    ///a single node \c n, then
+    ///\ref refresh(Node) "refresh(n)" is enough.
+    ///
+#ifdef DOXYGEN
+    Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
+#else
+    using ArcLookUp<G>::operator() ;
+    Arc operator()(Node s, Node t, Arc prev) const
+    {
+      return prev==INVALID?(*this)(s,t):_next[prev];
+    }
+#endif
+
+  };
+
+  /// @}
+
+} //namespace lemon
+
+#endif
diff --git a/lemon/dfs.h b/lemon/dfs.h
--- a/lemon/dfs.h
+++ b/lemon/dfs.h
@@ -24,9 +24,8 @@
 ///\brief Dfs algorithm.
 
 #include <lemon/list_graph.h>
-#include <lemon/graph_utils.h>
 #include <lemon/bits/path_dump.h>
-#include <lemon/bits/invalid.h>
+#include <lemon/core.h>
 #include <lemon/error.h>
 #include <lemon/maps.h>
 
diff --git a/lemon/dijkstra.h b/lemon/dijkstra.h
--- a/lemon/dijkstra.h
+++ b/lemon/dijkstra.h
@@ -27,7 +27,7 @@
 #include <lemon/list_graph.h>
 #include <lemon/bin_heap.h>
 #include <lemon/bits/path_dump.h>
-#include <lemon/bits/invalid.h>
+#include <lemon/core.h>
 #include <lemon/error.h>
 #include <lemon/maps.h>
 
diff --git a/lemon/dim2.h b/lemon/dim2.h
--- a/lemon/dim2.h
+++ b/lemon/dim2.h
@@ -20,7 +20,7 @@
 #define LEMON_DIM2_H
 
 #include <iostream>
-#include <lemon/bits/utility.h>
+#include <lemon/core.h>
 
 ///\ingroup misc
 ///\file
diff --git a/lemon/graph_to_eps.h b/lemon/graph_to_eps.h
--- a/lemon/graph_to_eps.h
+++ b/lemon/graph_to_eps.h
@@ -35,7 +35,7 @@
 #endif
 
 #include<lemon/math.h>
-#include<lemon/bits/invalid.h>
+#include<lemon/core.h>
 #include<lemon/dim2.h>
 #include<lemon/maps.h>
 #include<lemon/color.h>
diff --git a/lemon/graph_utils.h b/lemon/graph_utils.h
deleted file mode 100644
--- a/lemon/graph_utils.h
+++ /dev/null
@@ -1,2760 +0,0 @@
-/* -*- mode: C++; indent-tabs-mode: nil; -*-
- *
- * This file is a part of LEMON, a generic C++ optimization library.
- *
- * Copyright (C) 2003-2008
- * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
- * (Egervary Research Group on Combinatorial Optimization, EGRES).
- *
- * Permission to use, modify and distribute this software is granted
- * provided that this copyright notice appears in all copies. For
- * precise terms see the accompanying LICENSE file.
- *
- * This software is provided "AS IS" with no warranty of any kind,
- * express or implied, and with no claim as to its suitability for any
- * purpose.
- *
- */
-
-#ifndef LEMON_GRAPH_UTILS_H
-#define LEMON_GRAPH_UTILS_H
-
-#include <iterator>
-#include <vector>
-#include <map>
-#include <cmath>
-#include <algorithm>
-
-#include <lemon/bits/invalid.h>
-#include <lemon/bits/utility.h>
-#include <lemon/maps.h>
-#include <lemon/bits/traits.h>
-
-#include <lemon/bits/alteration_notifier.h>
-#include <lemon/bits/default_map.h>
-
-///\ingroup gutils
-///\file
-///\brief Graph utilities.
-
-namespace lemon {
-
-  /// \addtogroup gutils
-  /// @{
-
-  ///Creates convenience typedefs for the digraph types and iterators
-
-  ///This \c \#define creates convenience typedefs for the following types
-  ///of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
-  ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
-  ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
-  ///
-  ///\note If the graph type is a dependent type, ie. the graph type depend
-  ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
-  ///macro.
-#define DIGRAPH_TYPEDEFS(Digraph)                                       \
-  typedef Digraph::Node Node;                                           \
-  typedef Digraph::NodeIt NodeIt;                                       \
-  typedef Digraph::Arc Arc;                                             \
-  typedef Digraph::ArcIt ArcIt;                                         \
-  typedef Digraph::InArcIt InArcIt;                                     \
-  typedef Digraph::OutArcIt OutArcIt;                                   \
-  typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
-  typedef Digraph::NodeMap<int> IntNodeMap;                             \
-  typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
-  typedef Digraph::ArcMap<bool> BoolArcMap;                             \
-  typedef Digraph::ArcMap<int> IntArcMap;                               \
-  typedef Digraph::ArcMap<double> DoubleArcMap
-
-  ///Creates convenience typedefs for the digraph types and iterators
-
-  ///\see DIGRAPH_TYPEDEFS
-  ///
-  ///\note Use this macro, if the graph type is a dependent type,
-  ///ie. the graph type depend on a template parameter.
-#define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
-  typedef typename Digraph::Node Node;                                  \
-  typedef typename Digraph::NodeIt NodeIt;                              \
-  typedef typename Digraph::Arc Arc;                                    \
-  typedef typename Digraph::ArcIt ArcIt;                                \
-  typedef typename Digraph::InArcIt InArcIt;                            \
-  typedef typename Digraph::OutArcIt OutArcIt;                          \
-  typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
-  typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
-  typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
-  typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
-  typedef typename Digraph::template ArcMap<int> IntArcMap;             \
-  typedef typename Digraph::template ArcMap<double> DoubleArcMap
-
-  ///Creates convenience typedefs for the graph types and iterators
-
-  ///This \c \#define creates the same convenience typedefs as defined
-  ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
-  ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
-  ///\c DoubleEdgeMap.
-  ///
-  ///\note If the graph type is a dependent type, ie. the graph type depend
-  ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
-  ///macro.
-#define GRAPH_TYPEDEFS(Graph)                                           \
-  DIGRAPH_TYPEDEFS(Graph);                                              \
-  typedef Graph::Edge Edge;                                             \
-  typedef Graph::EdgeIt EdgeIt;                                         \
-  typedef Graph::IncEdgeIt IncEdgeIt;                                   \
-  typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
-  typedef Graph::EdgeMap<int> IntEdgeMap;                               \
-  typedef Graph::EdgeMap<double> DoubleEdgeMap
-
-  ///Creates convenience typedefs for the graph types and iterators
-
-  ///\see GRAPH_TYPEDEFS
-  ///
-  ///\note Use this macro, if the graph type is a dependent type,
-  ///ie. the graph type depend on a template parameter.
-#define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
-  TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
-  typedef typename Graph::Edge Edge;                                    \
-  typedef typename Graph::EdgeIt EdgeIt;                                \
-  typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
-  typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
-  typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
-  typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
-
-  /// \brief Function to count the items in the graph.
-  ///
-  /// This function counts the items (nodes, arcs etc) in the graph.
-  /// The complexity of the function is O(n) because
-  /// it iterates on all of the items.
-  template <typename Graph, typename Item>
-  inline int countItems(const Graph& g) {
-    typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
-    int num = 0;
-    for (ItemIt it(g); it != INVALID; ++it) {
-      ++num;
-    }
-    return num;
-  }
-
-  // Node counting:
-
-  namespace _graph_utils_bits {
-
-    template <typename Graph, typename Enable = void>
-    struct CountNodesSelector {
-      static int count(const Graph &g) {
-        return countItems<Graph, typename Graph::Node>(g);
-      }
-    };
-
-    template <typename Graph>
-    struct CountNodesSelector<
-      Graph, typename
-      enable_if<typename Graph::NodeNumTag, void>::type>
-    {
-      static int count(const Graph &g) {
-        return g.nodeNum();
-      }
-    };
-  }
-
-  /// \brief Function to count the nodes in the graph.
-  ///
-  /// This function counts the nodes in the graph.
-  /// The complexity of the function is O(n) but for some
-  /// graph structures it is specialized to run in O(1).
-  ///
-  /// If the graph contains a \e nodeNum() member function and a
-  /// \e NodeNumTag tag then this function calls directly the member
-  /// function to query the cardinality of the node set.
-  template <typename Graph>
-  inline int countNodes(const Graph& g) {
-    return _graph_utils_bits::CountNodesSelector<Graph>::count(g);
-  }
-
-  // Arc counting:
-
-  namespace _graph_utils_bits {
-
-    template <typename Graph, typename Enable = void>
-    struct CountArcsSelector {
-      static int count(const Graph &g) {
-        return countItems<Graph, typename Graph::Arc>(g);
-      }
-    };
-
-    template <typename Graph>
-    struct CountArcsSelector<
-      Graph,
-      typename enable_if<typename Graph::ArcNumTag, void>::type>
-    {
-      static int count(const Graph &g) {
-        return g.arcNum();
-      }
-    };
-  }
-
-  /// \brief Function to count the arcs in the graph.
-  ///
-  /// This function counts the arcs in the graph.
-  /// The complexity of the function is O(e) but for some
-  /// graph structures it is specialized to run in O(1).
-  ///
-  /// If the graph contains a \e arcNum() member function and a
-  /// \e EdgeNumTag tag then this function calls directly the member
-  /// function to query the cardinality of the arc set.
-  template <typename Graph>
-  inline int countArcs(const Graph& g) {
-    return _graph_utils_bits::CountArcsSelector<Graph>::count(g);
-  }
-
-  // Edge counting:
-  namespace _graph_utils_bits {
-
-    template <typename Graph, typename Enable = void>
-    struct CountEdgesSelector {
-      static int count(const Graph &g) {
-        return countItems<Graph, typename Graph::Edge>(g);
-      }
-    };
-
-    template <typename Graph>
-    struct CountEdgesSelector<
-      Graph,
-      typename enable_if<typename Graph::EdgeNumTag, void>::type>
-    {
-      static int count(const Graph &g) {
-        return g.edgeNum();
-      }
-    };
-  }
-
-  /// \brief Function to count the edges in the graph.
-  ///
-  /// This function counts the edges in the graph.
-  /// The complexity of the function is O(m) but for some
-  /// graph structures it is specialized to run in O(1).
-  ///
-  /// If the graph contains a \e edgeNum() member function and a
-  /// \e EdgeNumTag tag then this function calls directly the member
-  /// function to query the cardinality of the edge set.
-  template <typename Graph>
-  inline int countEdges(const Graph& g) {
-    return _graph_utils_bits::CountEdgesSelector<Graph>::count(g);
-
-  }
-
-
-  template <typename Graph, typename DegIt>
-  inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
-    int num = 0;
-    for (DegIt it(_g, _n); it != INVALID; ++it) {
-      ++num;
-    }
-    return num;
-  }
-
-  /// \brief Function to count the number of the out-arcs from node \c n.
-  ///
-  /// This function counts the number of the out-arcs from node \c n
-  /// in the graph.
-  template <typename Graph>
-  inline int countOutArcs(const Graph& _g,  const typename Graph::Node& _n) {
-    return countNodeDegree<Graph, typename Graph::OutArcIt>(_g, _n);
-  }
-
-  /// \brief Function to count the number of the in-arcs to node \c n.
-  ///
-  /// This function counts the number of the in-arcs to node \c n
-  /// in the graph.
-  template <typename Graph>
-  inline int countInArcs(const Graph& _g,  const typename Graph::Node& _n) {
-    return countNodeDegree<Graph, typename Graph::InArcIt>(_g, _n);
-  }
-
-  /// \brief Function to count the number of the inc-edges to node \c n.
-  ///
-  /// This function counts the number of the inc-edges to node \c n
-  /// in the graph.
-  template <typename Graph>
-  inline int countIncEdges(const Graph& _g,  const typename Graph::Node& _n) {
-    return countNodeDegree<Graph, typename Graph::IncEdgeIt>(_g, _n);
-  }
-
-  namespace _graph_utils_bits {
-
-    template <typename Graph, typename Enable = void>
-    struct FindArcSelector {
-      typedef typename Graph::Node Node;
-      typedef typename Graph::Arc Arc;
-      static Arc find(const Graph &g, Node u, Node v, Arc e) {
-        if (e == INVALID) {
-          g.firstOut(e, u);
-        } else {
-          g.nextOut(e);
-        }
-        while (e != INVALID && g.target(e) != v) {
-          g.nextOut(e);
-        }
-        return e;
-      }
-    };
-
-    template <typename Graph>
-    struct FindArcSelector<
-      Graph,
-      typename enable_if<typename Graph::FindEdgeTag, void>::type>
-    {
-      typedef typename Graph::Node Node;
-      typedef typename Graph::Arc Arc;
-      static Arc find(const Graph &g, Node u, Node v, Arc prev) {
-        return g.findArc(u, v, prev);
-      }
-    };
-  }
-
-  /// \brief Finds an arc between two nodes of a graph.
-  ///
-  /// Finds an arc from node \c u to node \c v in graph \c g.
-  ///
-  /// If \c prev is \ref INVALID (this is the default value), then
-  /// it finds the first arc from \c u to \c v. Otherwise it looks for
-  /// the next arc from \c u to \c v after \c prev.
-  /// \return The found arc or \ref INVALID if there is no such an arc.
-  ///
-  /// Thus you can iterate through each arc from \c u to \c v as it follows.
-  ///\code
-  /// for(Arc e=findArc(g,u,v);e!=INVALID;e=findArc(g,u,v,e)) {
-  ///   ...
-  /// }
-  ///\endcode
-  ///
-  ///\sa ArcLookUp
-  ///\sa AllArcLookUp
-  ///\sa DynArcLookUp
-  ///\sa ConArcIt
-  template <typename Graph>
-  inline typename Graph::Arc
-  findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
-           typename Graph::Arc prev = INVALID) {
-    return _graph_utils_bits::FindArcSelector<Graph>::find(g, u, v, prev);
-  }
-
-  /// \brief Iterator for iterating on arcs connected the same nodes.
-  ///
-  /// Iterator for iterating on arcs connected the same nodes. It is
-  /// higher level interface for the findArc() function. You can
-  /// use it the following way:
-  ///\code
-  /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
-  ///   ...
-  /// }
-  ///\endcode
-  ///
-  ///\sa findArc()
-  ///\sa ArcLookUp
-  ///\sa AllArcLookUp
-  ///\sa DynArcLookUp
-  template <typename _Graph>
-  class ConArcIt : public _Graph::Arc {
-  public:
-
-    typedef _Graph Graph;
-    typedef typename Graph::Arc Parent;
-
-    typedef typename Graph::Arc Arc;
-    typedef typename Graph::Node Node;
-
-    /// \brief Constructor.
-    ///
-    /// Construct a new ConArcIt iterating on the arcs which
-    /// connects the \c u and \c v node.
-    ConArcIt(const Graph& g, Node u, Node v) : _graph(g) {
-      Parent::operator=(findArc(_graph, u, v));
-    }
-
-    /// \brief Constructor.
-    ///
-    /// Construct a new ConArcIt which continues the iterating from
-    /// the \c e arc.
-    ConArcIt(const Graph& g, Arc a) : Parent(a), _graph(g) {}
-
-    /// \brief Increment operator.
-    ///
-    /// It increments the iterator and gives back the next arc.
-    ConArcIt& operator++() {
-      Parent::operator=(findArc(_graph, _graph.source(*this),
-                                _graph.target(*this), *this));
-      return *this;
-    }
-  private:
-    const Graph& _graph;
-  };
-
-  namespace _graph_utils_bits {
-
-    template <typename Graph, typename Enable = void>
-    struct FindEdgeSelector {
-      typedef typename Graph::Node Node;
-      typedef typename Graph::Edge Edge;
-      static Edge find(const Graph &g, Node u, Node v, Edge e) {
-        bool b;
-        if (u != v) {
-          if (e == INVALID) {
-            g.firstInc(e, b, u);
-          } else {
-            b = g.u(e) == u;
-            g.nextInc(e, b);
-          }
-          while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
-            g.nextInc(e, b);
-          }
-        } else {
-          if (e == INVALID) {
-            g.firstInc(e, b, u);
-          } else {
-            b = true;
-            g.nextInc(e, b);
-          }
-          while (e != INVALID && (!b || g.v(e) != v)) {
-            g.nextInc(e, b);
-          }
-        }
-        return e;
-      }
-    };
-
-    template <typename Graph>
-    struct FindEdgeSelector<
-      Graph,
-      typename enable_if<typename Graph::FindEdgeTag, void>::type>
-    {
-      typedef typename Graph::Node Node;
-      typedef typename Graph::Edge Edge;
-      static Edge find(const Graph &g, Node u, Node v, Edge prev) {
-        return g.findEdge(u, v, prev);
-      }
-    };
-  }
-
-  /// \brief Finds an edge between two nodes of a graph.
-  ///
-  /// Finds an edge from node \c u to node \c v in graph \c g.
-  /// If the node \c u and node \c v is equal then each loop edge
-  /// will be enumerated once.
-  ///
-  /// If \c prev is \ref INVALID (this is the default value), then
-  /// it finds the first arc from \c u to \c v. Otherwise it looks for
-  /// the next arc from \c u to \c v after \c prev.
-  /// \return The found arc or \ref INVALID if there is no such an arc.
-  ///
-  /// Thus you can iterate through each arc from \c u to \c v as it follows.
-  ///\code
-  /// for(Edge e = findEdge(g,u,v); e != INVALID;
-  ///     e = findEdge(g,u,v,e)) {
-  ///   ...
-  /// }
-  ///\endcode
-  ///
-  ///\sa ConEdgeIt
-
-  template <typename Graph>
-  inline typename Graph::Edge
-  findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
-            typename Graph::Edge p = INVALID) {
-    return _graph_utils_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
-  }
-
-  /// \brief Iterator for iterating on edges connected the same nodes.
-  ///
-  /// Iterator for iterating on edges connected the same nodes. It is
-  /// higher level interface for the findEdge() function. You can
-  /// use it the following way:
-  ///\code
-  /// for (ConEdgeIt<Graph> it(g, src, trg); it != INVALID; ++it) {
-  ///   ...
-  /// }
-  ///\endcode
-  ///
-  ///\sa findEdge()
-  template <typename _Graph>
-  class ConEdgeIt : public _Graph::Edge {
-  public:
-
-    typedef _Graph Graph;
-    typedef typename Graph::Edge Parent;
-
-    typedef typename Graph::Edge Edge;
-    typedef typename Graph::Node Node;
-
-    /// \brief Constructor.
-    ///
-    /// Construct a new ConEdgeIt iterating on the edges which
-    /// connects the \c u and \c v node.
-    ConEdgeIt(const Graph& g, Node u, Node v) : _graph(g) {
-      Parent::operator=(findEdge(_graph, u, v));
-    }
-
-    /// \brief Constructor.
-    ///
-    /// Construct a new ConEdgeIt which continues the iterating from
-    /// the \c e edge.
-    ConEdgeIt(const Graph& g, Edge e) : Parent(e), _graph(g) {}
-
-    /// \brief Increment operator.
-    ///
-    /// It increments the iterator and gives back the next edge.
-    ConEdgeIt& operator++() {
-      Parent::operator=(findEdge(_graph, _graph.u(*this),
-                                 _graph.v(*this), *this));
-      return *this;
-    }
-  private:
-    const Graph& _graph;
-  };
-
-  namespace _graph_utils_bits {
-
-    template <typename Digraph, typename Item, typename RefMap>
-    class MapCopyBase {
-    public:
-      virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
-
-      virtual ~MapCopyBase() {}
-    };
-
-    template <typename Digraph, typename Item, typename RefMap,
-              typename ToMap, typename FromMap>
-    class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
-    public:
-
-      MapCopy(ToMap& tmap, const FromMap& map)
-        : _tmap(tmap), _map(map) {}
-
-      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
-        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
-        for (ItemIt it(digraph); it != INVALID; ++it) {
-          _tmap.set(refMap[it], _map[it]);
-        }
-      }
-
-    private:
-      ToMap& _tmap;
-      const FromMap& _map;
-    };
-
-    template <typename Digraph, typename Item, typename RefMap, typename It>
-    class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
-    public:
-
-      ItemCopy(It& it, const Item& item) : _it(it), _item(item) {}
-
-      virtual void copy(const Digraph&, const RefMap& refMap) {
-        _it = refMap[_item];
-      }
-
-    private:
-      It& _it;
-      Item _item;
-    };
-
-    template <typename Digraph, typename Item, typename RefMap, typename Ref>
-    class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
-    public:
-
-      RefCopy(Ref& map) : _map(map) {}
-
-      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
-        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
-        for (ItemIt it(digraph); it != INVALID; ++it) {
-          _map.set(it, refMap[it]);
-        }
-      }
-
-    private:
-      Ref& _map;
-    };
-
-    template <typename Digraph, typename Item, typename RefMap,
-              typename CrossRef>
-    class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
-    public:
-
-      CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
-
-      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
-        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
-        for (ItemIt it(digraph); it != INVALID; ++it) {
-          _cmap.set(refMap[it], it);
-        }
-      }
-
-    private:
-      CrossRef& _cmap;
-    };
-
-    template <typename Digraph, typename Enable = void>
-    struct DigraphCopySelector {
-      template <typename From, typename NodeRefMap, typename ArcRefMap>
-      static void copy(Digraph &to, const From& from,
-                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
-        for (typename From::NodeIt it(from); it != INVALID; ++it) {
-          nodeRefMap[it] = to.addNode();
-        }
-        for (typename From::ArcIt it(from); it != INVALID; ++it) {
-          arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
-                                    nodeRefMap[from.target(it)]);
-        }
-      }
-    };
-
-    template <typename Digraph>
-    struct DigraphCopySelector<
-      Digraph,
-      typename enable_if<typename Digraph::BuildTag, void>::type>
-    {
-      template <typename From, typename NodeRefMap, typename ArcRefMap>
-      static void copy(Digraph &to, const From& from,
-                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
-        to.build(from, nodeRefMap, arcRefMap);
-      }
-    };
-
-    template <typename Graph, typename Enable = void>
-    struct GraphCopySelector {
-      template <typename From, typename NodeRefMap, typename EdgeRefMap>
-      static void copy(Graph &to, const From& from,
-                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
-        for (typename From::NodeIt it(from); it != INVALID; ++it) {
-          nodeRefMap[it] = to.addNode();
-        }
-        for (typename From::EdgeIt it(from); it != INVALID; ++it) {
-          edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
-                                      nodeRefMap[from.v(it)]);
-        }
-      }
-    };
-
-    template <typename Graph>
-    struct GraphCopySelector<
-      Graph,
-      typename enable_if<typename Graph::BuildTag, void>::type>
-    {
-      template <typename From, typename NodeRefMap, typename EdgeRefMap>
-      static void copy(Graph &to, const From& from,
-                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
-        to.build(from, nodeRefMap, edgeRefMap);
-      }
-    };
-
-  }
-
-  /// \brief Class to copy a digraph.
-  ///
-  /// Class to copy a digraph to another digraph (duplicate a digraph). The
-  /// simplest way of using it is through the \c copyDigraph() function.
-  ///
-  /// This class not just make a copy of a graph, but it can create
-  /// references and cross references between the nodes and arcs of
-  /// the two graphs, it can copy maps for use with the newly created
-  /// graph and copy nodes and arcs.
-  ///
-  /// To make a copy from a graph, first an instance of DigraphCopy
-  /// should be created, then the data belongs to the graph should
-  /// assigned to copy. In the end, the \c run() member should be
-  /// called.
-  ///
-  /// The next code copies a graph with several data:
-  ///\code
-  ///  DigraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
-  ///  // create a reference for the nodes
-  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
-  ///  dc.nodeRef(nr);
-  ///  // create a cross reference (inverse) for the arcs
-  ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
-  ///  dc.arcCrossRef(acr);
-  ///  // copy an arc map
-  ///  OrigGraph::ArcMap<double> oamap(orig_graph);
-  ///  NewGraph::ArcMap<double> namap(new_graph);
-  ///  dc.arcMap(namap, oamap);
-  ///  // copy a node
-  ///  OrigGraph::Node on;
-  ///  NewGraph::Node nn;
-  ///  dc.node(nn, on);
-  ///  // Executions of copy
-  ///  dc.run();
-  ///\endcode
-  template <typename To, typename From>
-  class DigraphCopy {
-  private:
-
-    typedef typename From::Node Node;
-    typedef typename From::NodeIt NodeIt;
-    typedef typename From::Arc Arc;
-    typedef typename From::ArcIt ArcIt;
-
-    typedef typename To::Node TNode;
-    typedef typename To::Arc TArc;
-
-    typedef typename From::template NodeMap<TNode> NodeRefMap;
-    typedef typename From::template ArcMap<TArc> ArcRefMap;
-
-
-  public:
-
-
-    /// \brief Constructor for the DigraphCopy.
-    ///
-    /// It copies the content of the \c _from digraph into the
-    /// \c _to digraph.
-    DigraphCopy(To& to, const From& from)
-      : _from(from), _to(to) {}
-
-    /// \brief Destructor of the DigraphCopy
-    ///
-    /// Destructor of the DigraphCopy
-    ~DigraphCopy() {
-      for (int i = 0; i < int(_node_maps.size()); ++i) {
-        delete _node_maps[i];
-      }
-      for (int i = 0; i < int(_arc_maps.size()); ++i) {
-        delete _arc_maps[i];
-      }
-
-    }
-
-    /// \brief Copies the node references into the given map.
-    ///
-    /// Copies the node references into the given map. The parameter
-    /// should be a map, which key type is the Node type of the source
-    /// graph, while the value type is the Node type of the
-    /// destination graph.
-    template <typename NodeRef>
-    DigraphCopy& nodeRef(NodeRef& map) {
-      _node_maps.push_back(new _graph_utils_bits::RefCopy<From, Node,
-                           NodeRefMap, NodeRef>(map));
-      return *this;
-    }
-
-    /// \brief Copies the node cross references into the given map.
-    ///
-    ///  Copies the node cross references (reverse references) into
-    ///  the given map. The parameter should be a map, which key type
-    ///  is the Node type of the destination graph, while the value type is
-    ///  the Node type of the source graph.
-    template <typename NodeCrossRef>
-    DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
-      _node_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Node,
-                           NodeRefMap, NodeCrossRef>(map));
-      return *this;
-    }
-
-    /// \brief Make copy of the given map.
-    ///
-    /// Makes copy of the given map for the newly created digraph.
-    /// The new map's key type is the destination graph's node type,
-    /// and the copied map's key type is the source graph's node type.
-    template <typename ToMap, typename FromMap>
-    DigraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
-      _node_maps.push_back(new _graph_utils_bits::MapCopy<From, Node,
-                           NodeRefMap, ToMap, FromMap>(tmap, map));
-      return *this;
-    }
-
-    /// \brief Make a copy of the given node.
-    ///
-    /// Make a copy of the given node.
-    DigraphCopy& node(TNode& tnode, const Node& snode) {
-      _node_maps.push_back(new _graph_utils_bits::ItemCopy<From, Node,
-                           NodeRefMap, TNode>(tnode, snode));
-      return *this;
-    }
-
-    /// \brief Copies the arc references into the given map.
-    ///
-    /// Copies the arc references into the given map.
-    template <typename ArcRef>
-    DigraphCopy& arcRef(ArcRef& map) {
-      _arc_maps.push_back(new _graph_utils_bits::RefCopy<From, Arc,
-                          ArcRefMap, ArcRef>(map));
-      return *this;
-    }
-
-    /// \brief Copies the arc cross references into the given map.
-    ///
-    ///  Copies the arc cross references (reverse references) into
-    ///  the given map.
-    template <typename ArcCrossRef>
-    DigraphCopy& arcCrossRef(ArcCrossRef& map) {
-      _arc_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Arc,
-                          ArcRefMap, ArcCrossRef>(map));
-      return *this;
-    }
-
-    /// \brief Make copy of the given map.
-    ///
-    /// Makes copy of the given map for the newly created digraph.
-    /// The new map's key type is the to digraph's arc type,
-    /// and the copied map's key type is the from digraph's arc
-    /// type.
-    template <typename ToMap, typename FromMap>
-    DigraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
-      _arc_maps.push_back(new _graph_utils_bits::MapCopy<From, Arc,
-                          ArcRefMap, ToMap, FromMap>(tmap, map));
-      return *this;
-    }
-
-    /// \brief Make a copy of the given arc.
-    ///
-    /// Make a copy of the given arc.
-    DigraphCopy& arc(TArc& tarc, const Arc& sarc) {
-      _arc_maps.push_back(new _graph_utils_bits::ItemCopy<From, Arc,
-                          ArcRefMap, TArc>(tarc, sarc));
-      return *this;
-    }
-
-    /// \brief Executes the copies.
-    ///
-    /// Executes the copies.
-    void run() {
-      NodeRefMap nodeRefMap(_from);
-      ArcRefMap arcRefMap(_from);
-      _graph_utils_bits::DigraphCopySelector<To>::
-        copy(_to, _from, nodeRefMap, arcRefMap);
-      for (int i = 0; i < int(_node_maps.size()); ++i) {
-        _node_maps[i]->copy(_from, nodeRefMap);
-      }
-      for (int i = 0; i < int(_arc_maps.size()); ++i) {
-        _arc_maps[i]->copy(_from, arcRefMap);
-      }
-    }
-
-  protected:
-
-
-    const From& _from;
-    To& _to;
-
-    std::vector<_graph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* >
-    _node_maps;
-
-    std::vector<_graph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* >
-    _arc_maps;
-
-  };
-
-  /// \brief Copy a digraph to another digraph.
-  ///
-  /// Copy a digraph to another digraph. The complete usage of the
-  /// function is detailed in the DigraphCopy class, but a short
-  /// example shows a basic work:
-  ///\code
-  /// copyDigraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
-  ///\endcode
-  ///
-  /// After the copy the \c nr map will contain the mapping from the
-  /// nodes of the \c from digraph to the nodes of the \c to digraph and
-  /// \c ecr will contain the mapping from the arcs of the \c to digraph
-  /// to the arcs of the \c from digraph.
-  ///
-  /// \see DigraphCopy
-  template <typename To, typename From>
-  DigraphCopy<To, From> copyDigraph(To& to, const From& from) {
-    return DigraphCopy<To, From>(to, from);
-  }
-
-  /// \brief Class to copy a graph.
-  ///
-  /// Class to copy a graph to another graph (duplicate a graph). The
-  /// simplest way of using it is through the \c copyGraph() function.
-  ///
-  /// This class not just make a copy of a graph, but it can create
-  /// references and cross references between the nodes, edges and arcs of
-  /// the two graphs, it can copy maps for use with the newly created
-  /// graph and copy nodes, edges and arcs.
-  ///
-  /// To make a copy from a graph, first an instance of GraphCopy
-  /// should be created, then the data belongs to the graph should
-  /// assigned to copy. In the end, the \c run() member should be
-  /// called.
-  ///
-  /// The next code copies a graph with several data:
-  ///\code
-  ///  GraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
-  ///  // create a reference for the nodes
-  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
-  ///  dc.nodeRef(nr);
-  ///  // create a cross reference (inverse) for the edges
-  ///  NewGraph::EdgeMap<OrigGraph::Arc> ecr(new_graph);
-  ///  dc.edgeCrossRef(ecr);
-  ///  // copy an arc map
-  ///  OrigGraph::ArcMap<double> oamap(orig_graph);
-  ///  NewGraph::ArcMap<double> namap(new_graph);
-  ///  dc.arcMap(namap, oamap);
-  ///  // copy a node
-  ///  OrigGraph::Node on;
-  ///  NewGraph::Node nn;
-  ///  dc.node(nn, on);
-  ///  // Executions of copy
-  ///  dc.run();
-  ///\endcode
-  template <typename To, typename From>
-  class GraphCopy {
-  private:
-
-    typedef typename From::Node Node;
-    typedef typename From::NodeIt NodeIt;
-    typedef typename From::Arc Arc;
-    typedef typename From::ArcIt ArcIt;
-    typedef typename From::Edge Edge;
-    typedef typename From::EdgeIt EdgeIt;
-
-    typedef typename To::Node TNode;
-    typedef typename To::Arc TArc;
-    typedef typename To::Edge TEdge;
-
-    typedef typename From::template NodeMap<TNode> NodeRefMap;
-    typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
-
-    struct ArcRefMap {
-      ArcRefMap(const To& to, const From& from,
-                const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
-        : _to(to), _from(from),
-          _edge_ref(edge_ref), _node_ref(node_ref) {}
-
-      typedef typename From::Arc Key;
-      typedef typename To::Arc Value;
-
-      Value operator[](const Key& key) const {
-        bool forward = _from.u(key) != _from.v(key) ?
-          _node_ref[_from.source(key)] ==
-          _to.source(_to.direct(_edge_ref[key], true)) :
-          _from.direction(key);
-        return _to.direct(_edge_ref[key], forward);
-      }
-
-      const To& _to;
-      const From& _from;
-      const EdgeRefMap& _edge_ref;
-      const NodeRefMap& _node_ref;
-    };
-
-
-  public:
-
-
-    /// \brief Constructor for the GraphCopy.
-    ///
-    /// It copies the content of the \c _from graph into the
-    /// \c _to graph.
-    GraphCopy(To& to, const From& from)
-      : _from(from), _to(to) {}
-
-    /// \brief Destructor of the GraphCopy
-    ///
-    /// Destructor of the GraphCopy
-    ~GraphCopy() {
-      for (int i = 0; i < int(_node_maps.size()); ++i) {
-        delete _node_maps[i];
-      }
-      for (int i = 0; i < int(_arc_maps.size()); ++i) {
-        delete _arc_maps[i];
-      }
-      for (int i = 0; i < int(_edge_maps.size()); ++i) {
-        delete _edge_maps[i];
-      }
-
-    }
-
-    /// \brief Copies the node references into the given map.
-    ///
-    /// Copies the node references into the given map.
-    template <typename NodeRef>
-    GraphCopy& nodeRef(NodeRef& map) {
-      _node_maps.push_back(new _graph_utils_bits::RefCopy<From, Node,
-                           NodeRefMap, NodeRef>(map));
-      return *this;
-    }
-
-    /// \brief Copies the node cross references into the given map.
-    ///
-    ///  Copies the node cross references (reverse references) into
-    ///  the given map.
-    template <typename NodeCrossRef>
-    GraphCopy& nodeCrossRef(NodeCrossRef& map) {
-      _node_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Node,
-                           NodeRefMap, NodeCrossRef>(map));
-      return *this;
-    }
-
-    /// \brief Make copy of the given map.
-    ///
-    /// Makes copy of the given map for the newly created graph.
-    /// The new map's key type is the to graph's node type,
-    /// and the copied map's key type is the from graph's node
-    /// type.
-    template <typename ToMap, typename FromMap>
-    GraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
-      _node_maps.push_back(new _graph_utils_bits::MapCopy<From, Node,
-                           NodeRefMap, ToMap, FromMap>(tmap, map));
-      return *this;
-    }
-
-    /// \brief Make a copy of the given node.
-    ///
-    /// Make a copy of the given node.
-    GraphCopy& node(TNode& tnode, const Node& snode) {
-      _node_maps.push_back(new _graph_utils_bits::ItemCopy<From, Node,
-                           NodeRefMap, TNode>(tnode, snode));
-      return *this;
-    }
-
-    /// \brief Copies the arc references into the given map.
-    ///
-    /// Copies the arc references into the given map.
-    template <typename ArcRef>
-    GraphCopy& arcRef(ArcRef& map) {
-      _arc_maps.push_back(new _graph_utils_bits::RefCopy<From, Arc,
-                          ArcRefMap, ArcRef>(map));
-      return *this;
-    }
-
-    /// \brief Copies the arc cross references into the given map.
-    ///
-    ///  Copies the arc cross references (reverse references) into
-    ///  the given map.
-    template <typename ArcCrossRef>
-    GraphCopy& arcCrossRef(ArcCrossRef& map) {
-      _arc_maps.push_back(new _graph_utils_bits::CrossRefCopy<From, Arc,
-                          ArcRefMap, ArcCrossRef>(map));
-      return *this;
-    }
-
-    /// \brief Make copy of the given map.
-    ///
-    /// Makes copy of the given map for the newly created graph.
-    /// The new map's key type is the to graph's arc type,
-    /// and the copied map's key type is the from graph's arc
-    /// type.
-    template <typename ToMap, typename FromMap>
-    GraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
-      _arc_maps.push_back(new _graph_utils_bits::MapCopy<From, Arc,
-                          ArcRefMap, ToMap, FromMap>(tmap, map));
-      return *this;
-    }
-
-    /// \brief Make a copy of the given arc.
-    ///
-    /// Make a copy of the given arc.
-    GraphCopy& arc(TArc& tarc, const Arc& sarc) {
-      _arc_maps.push_back(new _graph_utils_bits::ItemCopy<From, Arc,
-                          ArcRefMap, TArc>(tarc, sarc));
-      return *this;
-    }
-
-    /// \brief Copies the edge references into the given map.
-    ///
-    /// Copies the edge references into the given map.
-    template <typename EdgeRef>
-    GraphCopy& edgeRef(EdgeRef& map) {
-      _edge_maps.push_back(new _graph_utils_bits::RefCopy<From, Edge,
-                           EdgeRefMap, EdgeRef>(map));
-      return *this;
-    }
-
-    /// \brief Copies the edge cross references into the given map.
-    ///
-    /// Copies the edge cross references (reverse
-    /// references) into the given map.
-    template <typename EdgeCrossRef>
-    GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
-      _edge_maps.push_back(new _graph_utils_bits::CrossRefCopy<From,
-                           Edge, EdgeRefMap, EdgeCrossRef>(map));
-      return *this;
-    }
-
-    /// \brief Make copy of the given map.
-    ///
-    /// Makes copy of the given map for the newly created graph.
-    /// The new map's key type is the to graph's edge type,
-    /// and the copied map's key type is the from graph's edge
-    /// type.
-    template <typename ToMap, typename FromMap>
-    GraphCopy& edgeMap(ToMap& tmap, const FromMap& map) {
-      _edge_maps.push_back(new _graph_utils_bits::MapCopy<From, Edge,
-                           EdgeRefMap, ToMap, FromMap>(tmap, map));
-      return *this;
-    }
-
-    /// \brief Make a copy of the given edge.
-    ///
-    /// Make a copy of the given edge.
-    GraphCopy& edge(TEdge& tedge, const Edge& sedge) {
-      _edge_maps.push_back(new _graph_utils_bits::ItemCopy<From, Edge,
-                           EdgeRefMap, TEdge>(tedge, sedge));
-      return *this;
-    }
-
-    /// \brief Executes the copies.
-    ///
-    /// Executes the copies.
-    void run() {
-      NodeRefMap nodeRefMap(_from);
-      EdgeRefMap edgeRefMap(_from);
-      ArcRefMap arcRefMap(_to, _from, edgeRefMap, nodeRefMap);
-      _graph_utils_bits::GraphCopySelector<To>::
-        copy(_to, _from, nodeRefMap, edgeRefMap);
-      for (int i = 0; i < int(_node_maps.size()); ++i) {
-        _node_maps[i]->copy(_from, nodeRefMap);
-      }
-      for (int i = 0; i < int(_edge_maps.size()); ++i) {
-        _edge_maps[i]->copy(_from, edgeRefMap);
-      }
-      for (int i = 0; i < int(_arc_maps.size()); ++i) {
-        _arc_maps[i]->copy(_from, arcRefMap);
-      }
-    }
-
-  private:
-
-    const From& _from;
-    To& _to;
-
-    std::vector<_graph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* >
-    _node_maps;
-
-    std::vector<_graph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* >
-    _arc_maps;
-
-    std::vector<_graph_utils_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
-    _edge_maps;
-
-  };
-
-  /// \brief Copy a graph to another graph.
-  ///
-  /// Copy a graph to another graph. The complete usage of the
-  /// function is detailed in the GraphCopy class, but a short
-  /// example shows a basic work:
-  ///\code
-  /// copyGraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
-  ///\endcode
-  ///
-  /// After the copy the \c nr map will contain the mapping from the
-  /// nodes of the \c from graph to the nodes of the \c to graph and
-  /// \c ecr will contain the mapping from the arcs of the \c to graph
-  /// to the arcs of the \c from graph.
-  ///
-  /// \see GraphCopy
-  template <typename To, typename From>
-  GraphCopy<To, From>
-  copyGraph(To& to, const From& from) {
-    return GraphCopy<To, From>(to, from);
-  }
-
-  /// @}
-
-  /// \addtogroup graph_maps
-  /// @{
-
-  /// Provides an immutable and unique id for each item in the graph.
-
-  /// The IdMap class provides a unique and immutable id for each item of the
-  /// same type (e.g. node) in the graph. This id is <ul><li>\b unique:
-  /// different items (nodes) get different ids <li>\b immutable: the id of an
-  /// item (node) does not change (even if you delete other nodes).  </ul>
-  /// Through this map you get access (i.e. can read) the inner id values of
-  /// the items stored in the graph. This map can be inverted with its member
-  /// class \c InverseMap or with the \c operator() member.
-  ///
-  template <typename _Graph, typename _Item>
-  class IdMap {
-  public:
-    typedef _Graph Graph;
-    typedef int Value;
-    typedef _Item Item;
-    typedef _Item Key;
-
-    /// \brief Constructor.
-    ///
-    /// Constructor of the map.
-    explicit IdMap(const Graph& graph) : _graph(&graph) {}
-
-    /// \brief Gives back the \e id of the item.
-    ///
-    /// Gives back the immutable and unique \e id of the item.
-    int operator[](const Item& item) const { return _graph->id(item);}
-
-    /// \brief Gives back the item by its id.
-    ///
-    /// Gives back the item by its id.
-    Item operator()(int id) { return _graph->fromId(id, Item()); }
-
-  private:
-    const Graph* _graph;
-
-  public:
-
-    /// \brief The class represents the inverse of its owner (IdMap).
-    ///
-    /// The class represents the inverse of its owner (IdMap).
-    /// \see inverse()
-    class InverseMap {
-    public:
-
-      /// \brief Constructor.
-      ///
-      /// Constructor for creating an id-to-item map.
-      explicit InverseMap(const Graph& graph) : _graph(&graph) {}
-
-      /// \brief Constructor.
-      ///
-      /// Constructor for creating an id-to-item map.
-      explicit InverseMap(const IdMap& map) : _graph(map._graph) {}
-
-      /// \brief Gives back the given item from its id.
-      ///
-      /// Gives back the given item from its id.
-      ///
-      Item operator[](int id) const { return _graph->fromId(id, Item());}
-
-    private:
-      const Graph* _graph;
-    };
-
-    /// \brief Gives back the inverse of the map.
-    ///
-    /// Gives back the inverse of the IdMap.
-    InverseMap inverse() const { return InverseMap(*_graph);}
-
-  };
-
-
-  /// \brief General invertable graph-map type.
-
-  /// This type provides simple invertable graph-maps.
-  /// The InvertableMap wraps an arbitrary ReadWriteMap
-  /// and if a key is set to a new value then store it
-  /// in the inverse map.
-  ///
-  /// The values of the map can be accessed
-  /// with stl compatible forward iterator.
-  ///
-  /// \tparam _Graph The graph type.
-  /// \tparam _Item The item type of the graph.
-  /// \tparam _Value The value type of the map.
-  ///
-  /// \see IterableValueMap
-  template <typename _Graph, typename _Item, typename _Value>
-  class InvertableMap : protected DefaultMap<_Graph, _Item, _Value> {
-  private:
-
-    typedef DefaultMap<_Graph, _Item, _Value> Map;
-    typedef _Graph Graph;
-
-    typedef std::map<_Value, _Item> Container;
-    Container _inv_map;
-
-  public:
-
-    /// The key type of InvertableMap (Node, Arc, Edge).
-    typedef typename Map::Key Key;
-    /// The value type of the InvertableMap.
-    typedef typename Map::Value Value;
-
-
-
-    /// \brief Constructor.
-    ///
-    /// Construct a new InvertableMap for the graph.
-    ///
-    explicit InvertableMap(const Graph& graph) : Map(graph) {}
-
-    /// \brief Forward iterator for values.
-    ///
-    /// This iterator is an stl compatible forward
-    /// iterator on the values of the map. The values can
-    /// be accessed in the [beginValue, endValue) range.
-    ///
-    class ValueIterator
-      : public std::iterator<std::forward_iterator_tag, Value> {
-      friend class InvertableMap;
-    private:
-      ValueIterator(typename Container::const_iterator _it)
-        : it(_it) {}
-    public:
-
-      ValueIterator() {}
-
-      ValueIterator& operator++() { ++it; return *this; }
-      ValueIterator operator++(int) {
-        ValueIterator tmp(*this);
-        operator++();
-        return tmp;
-      }
-
-      const Value& operator*() const { return it->first; }
-      const Value* operator->() const { return &(it->first); }
-
-      bool operator==(ValueIterator jt) const { return it == jt.it; }
-      bool operator!=(ValueIterator jt) const { return it != jt.it; }
-
-    private:
-      typename Container::const_iterator it;
-    };
-
-    /// \brief Returns an iterator to the first value.
-    ///
-    /// Returns an stl compatible iterator to the
-    /// first value of the map. The values of the
-    /// map can be accessed in the [beginValue, endValue)
-    /// range.
-    ValueIterator beginValue() const {
-      return ValueIterator(_inv_map.begin());
-    }
-
-    /// \brief Returns an iterator after the last value.
-    ///
-    /// Returns an stl compatible iterator after the
-    /// last value of the map. The values of the
-    /// map can be accessed in the [beginValue, endValue)
-    /// range.
-    ValueIterator endValue() const {
-      return ValueIterator(_inv_map.end());
-    }
-
-    /// \brief The setter function of the map.
-    ///
-    /// Sets the mapped value.
-    void set(const Key& key, const Value& val) {
-      Value oldval = Map::operator[](key);
-      typename Container::iterator it = _inv_map.find(oldval);
-      if (it != _inv_map.end() && it->second == key) {
-        _inv_map.erase(it);
-      }
-      _inv_map.insert(make_pair(val, key));
-      Map::set(key, val);
-    }
-
-    /// \brief The getter function of the map.
-    ///
-    /// It gives back the value associated with the key.
-    typename MapTraits<Map>::ConstReturnValue
-    operator[](const Key& key) const {
-      return Map::operator[](key);
-    }
-
-    /// \brief Gives back the item by its value.
-    ///
-    /// Gives back the item by its value.
-    Key operator()(const Value& key) const {
-      typename Container::const_iterator it = _inv_map.find(key);
-      return it != _inv_map.end() ? it->second : INVALID;
-    }
-
-  protected:
-
-    /// \brief Erase the key from the map.
-    ///
-    /// Erase the key to the map. It is called by the
-    /// \c AlterationNotifier.
-    virtual void erase(const Key& key) {
-      Value val = Map::operator[](key);
-      typename Container::iterator it = _inv_map.find(val);
-      if (it != _inv_map.end() && it->second == key) {
-        _inv_map.erase(it);
-      }
-      Map::erase(key);
-    }
-
-    /// \brief Erase more keys from the map.
-    ///
-    /// Erase more keys from the map. It is called by the
-    /// \c AlterationNotifier.
-    virtual void erase(const std::vector<Key>& keys) {
-      for (int i = 0; i < int(keys.size()); ++i) {
-        Value val = Map::operator[](keys[i]);
-        typename Container::iterator it = _inv_map.find(val);
-        if (it != _inv_map.end() && it->second == keys[i]) {
-          _inv_map.erase(it);
-        }
-      }
-      Map::erase(keys);
-    }
-
-    /// \brief Clear the keys from the map and inverse map.
-    ///
-    /// Clear the keys from the map and inverse map. It is called by the
-    /// \c AlterationNotifier.
-    virtual void clear() {
-      _inv_map.clear();
-      Map::clear();
-    }
-
-  public:
-
-    /// \brief The inverse map type.
-    ///
-    /// The inverse of this map. The subscript operator of the map
-    /// gives back always the item what was last assigned to the value.
-    class InverseMap {
-    public:
-      /// \brief Constructor of the InverseMap.
-      ///
-      /// Constructor of the InverseMap.
-      explicit InverseMap(const InvertableMap& inverted)
-        : _inverted(inverted) {}
-
-      /// The value type of the InverseMap.
-      typedef typename InvertableMap::Key Value;
-      /// The key type of the InverseMap.
-      typedef typename InvertableMap::Value Key;
-
-      /// \brief Subscript operator.
-      ///
-      /// Subscript operator. It gives back always the item
-      /// what was last assigned to the value.
-      Value operator[](const Key& key) const {
-        return _inverted(key);
-      }
-
-    private:
-      const InvertableMap& _inverted;
-    };
-
-    /// \brief It gives back the just readable inverse map.
-    ///
-    /// It gives back the just readable inverse map.
-    InverseMap inverse() const {
-      return InverseMap(*this);
-    }
-
-
-
-  };
-
-  /// \brief Provides a mutable, continuous and unique descriptor for each
-  /// item in the graph.
-  ///
-  /// The DescriptorMap class provides a unique and continuous (but mutable)
-  /// descriptor (id) for each item of the same type (e.g. node) in the
-  /// graph. This id is <ul><li>\b unique: different items (nodes) get
-  /// different ids <li>\b continuous: the range of the ids is the set of
-  /// integers between 0 and \c n-1, where \c n is the number of the items of
-  /// this type (e.g. nodes) (so the id of a node can change if you delete an
-  /// other node, i.e. this id is mutable).  </ul> This map can be inverted
-  /// with its member class \c InverseMap, or with the \c operator() member.
-  ///
-  /// \tparam _Graph The graph class the \c DescriptorMap belongs to.
-  /// \tparam _Item The Item is the Key of the Map. It may be Node, Arc or
-  /// Edge.
-  template <typename _Graph, typename _Item>
-  class DescriptorMap : protected DefaultMap<_Graph, _Item, int> {
-
-    typedef _Item Item;
-    typedef DefaultMap<_Graph, _Item, int> Map;
-
-  public:
-    /// The graph class of DescriptorMap.
-    typedef _Graph Graph;
-
-    /// The key type of DescriptorMap (Node, Arc, Edge).
-    typedef typename Map::Key Key;
-    /// The value type of DescriptorMap.
-    typedef typename Map::Value Value;
-
-    /// \brief Constructor.
-    ///
-    /// Constructor for descriptor map.
-    explicit DescriptorMap(const Graph& _graph) : Map(_graph) {
-      Item it;
-      const typename Map::Notifier* nf = Map::notifier();
-      for (nf->first(it); it != INVALID; nf->next(it)) {
-        Map::set(it, _inv_map.size());
-        _inv_map.push_back(it);
-      }
-    }
-
-  protected:
-
-    /// \brief Add a new key to the map.
-    ///
-    /// Add a new key to the map. It is called by the
-    /// \c AlterationNotifier.
-    virtual void add(const Item& item) {
-      Map::add(item);
-      Map::set(item, _inv_map.size());
-      _inv_map.push_back(item);
-    }
-
-    /// \brief Add more new keys to the map.
-    ///
-    /// Add more new keys to the map. It is called by the
-    /// \c AlterationNotifier.
-    virtual void add(const std::vector<Item>& items) {
-      Map::add(items);
-      for (int i = 0; i < int(items.size()); ++i) {
-        Map::set(items[i], _inv_map.size());
-        _inv_map.push_back(items[i]);
-      }
-    }
-
-    /// \brief Erase the key from the map.
-    ///
-    /// Erase the key from the map. It is called by the
-    /// \c AlterationNotifier.
-    virtual void erase(const Item& item) {
-      Map::set(_inv_map.back(), Map::operator[](item));
-      _inv_map[Map::operator[](item)] = _inv_map.back();
-      _inv_map.pop_back();
-      Map::erase(item);
-    }
-
-    /// \brief Erase more keys from the map.
-    ///
-    /// Erase more keys from the map. It is called by the
-    /// \c AlterationNotifier.
-    virtual void erase(const std::vector<Item>& items) {
-      for (int i = 0; i < int(items.size()); ++i) {
-        Map::set(_inv_map.back(), Map::operator[](items[i]));
-        _inv_map[Map::operator[](items[i])] = _inv_map.back();
-        _inv_map.pop_back();
-      }
-      Map::erase(items);
-    }
-
-    /// \brief Build the unique map.
-    ///
-    /// Build the unique map. It is called by the
-    /// \c AlterationNotifier.
-    virtual void build() {
-      Map::build();
-      Item it;
-      const typename Map::Notifier* nf = Map::notifier();
-      for (nf->first(it); it != INVALID; nf->next(it)) {
-        Map::set(it, _inv_map.size());
-        _inv_map.push_back(it);
-      }
-    }
-
-    /// \brief Clear the keys from the map.
-    ///
-    /// Clear the keys from the map. It is called by the
-    /// \c AlterationNotifier.
-    virtual void clear() {
-      _inv_map.clear();
-      Map::clear();
-    }
-
-  public:
-
-    /// \brief Returns the maximal value plus one.
-    ///
-    /// Returns the maximal value plus one in the map.
-    unsigned int size() const {
-      return _inv_map.size();
-    }
-
-    /// \brief Swaps the position of the two items in the map.
-    ///
-    /// Swaps the position of the two items in the map.
-    void swap(const Item& p, const Item& q) {
-      int pi = Map::operator[](p);
-      int qi = Map::operator[](q);
-      Map::set(p, qi);
-      _inv_map[qi] = p;
-      Map::set(q, pi);
-      _inv_map[pi] = q;
-    }
-
-    /// \brief Gives back the \e descriptor of the item.
-    ///
-    /// Gives back the mutable and unique \e descriptor of the map.
-    int operator[](const Item& item) const {
-      return Map::operator[](item);
-    }
-
-    /// \brief Gives back the item by its descriptor.
-    ///
-    /// Gives back th item by its descriptor.
-    Item operator()(int id) const {
-      return _inv_map[id];
-    }
-
-  private:
-
-    typedef std::vector<Item> Container;
-    Container _inv_map;
-
-  public:
-    /// \brief The inverse map type of DescriptorMap.
-    ///
-    /// The inverse map type of DescriptorMap.
-    class InverseMap {
-    public:
-      /// \brief Constructor of the InverseMap.
-      ///
-      /// Constructor of the InverseMap.
-      explicit InverseMap(const DescriptorMap& inverted)
-        : _inverted(inverted) {}
-
-
-      /// The value type of the InverseMap.
-      typedef typename DescriptorMap::Key Value;
-      /// The key type of the InverseMap.
-      typedef typename DescriptorMap::Value Key;
-
-      /// \brief Subscript operator.
-      ///
-      /// Subscript operator. It gives back the item
-      /// that the descriptor belongs to currently.
-      Value operator[](const Key& key) const {
-        return _inverted(key);
-      }
-
-      /// \brief Size of the map.
-      ///
-      /// Returns the size of the map.
-      unsigned int size() const {
-        return _inverted.size();
-      }
-
-    private:
-      const DescriptorMap& _inverted;
-    };
-
-    /// \brief Gives back the inverse of the map.
-    ///
-    /// Gives back the inverse of the map.
-    const InverseMap inverse() const {
-      return InverseMap(*this);
-    }
-  };
-
-  /// \brief Returns the source of the given arc.
-  ///
-  /// The SourceMap gives back the source Node of the given arc.
-  /// \see TargetMap
-  template <typename Digraph>
-  class SourceMap {
-  public:
-
-    typedef typename Digraph::Node Value;
-    typedef typename Digraph::Arc Key;
-
-    /// \brief Constructor
-    ///
-    /// Constructor
-    /// \param _digraph The digraph that the map belongs to.
-    explicit SourceMap(const Digraph& digraph) : _digraph(digraph) {}
-
-    /// \brief The subscript operator.
-    ///
-    /// The subscript operator.
-    /// \param arc The arc
-    /// \return The source of the arc
-    Value operator[](const Key& arc) const {
-      return _digraph.source(arc);
-    }
-
-  private:
-    const Digraph& _digraph;
-  };
-
-  /// \brief Returns a \ref SourceMap class.
-  ///
-  /// This function just returns an \ref SourceMap class.
-  /// \relates SourceMap
-  template <typename Digraph>
-  inline SourceMap<Digraph> sourceMap(const Digraph& digraph) {
-    return SourceMap<Digraph>(digraph);
-  }
-
-  /// \brief Returns the target of the given arc.
-  ///
-  /// The TargetMap gives back the target Node of the given arc.
-  /// \see SourceMap
-  template <typename Digraph>
-  class TargetMap {
-  public:
-
-    typedef typename Digraph::Node Value;
-    typedef typename Digraph::Arc Key;
-
-    /// \brief Constructor
-    ///
-    /// Constructor
-    /// \param _digraph The digraph that the map belongs to.
-    explicit TargetMap(const Digraph& digraph) : _digraph(digraph) {}
-
-    /// \brief The subscript operator.
-    ///
-    /// The subscript operator.
-    /// \param e The arc
-    /// \return The target of the arc
-    Value operator[](const Key& e) const {
-      return _digraph.target(e);
-    }
-
-  private:
-    const Digraph& _digraph;
-  };
-
-  /// \brief Returns a \ref TargetMap class.
-  ///
-  /// This function just returns a \ref TargetMap class.
-  /// \relates TargetMap
-  template <typename Digraph>
-  inline TargetMap<Digraph> targetMap(const Digraph& digraph) {
-    return TargetMap<Digraph>(digraph);
-  }
-
-  /// \brief Returns the "forward" directed arc view of an edge.
-  ///
-  /// Returns the "forward" directed arc view of an edge.
-  /// \see BackwardMap
-  template <typename Graph>
-  class ForwardMap {
-  public:
-
-    typedef typename Graph::Arc Value;
-    typedef typename Graph::Edge Key;
-
-    /// \brief Constructor
-    ///
-    /// Constructor
-    /// \param _graph The graph that the map belongs to.
-    explicit ForwardMap(const Graph& graph) : _graph(graph) {}
-
-    /// \brief The subscript operator.
-    ///
-    /// The subscript operator.
-    /// \param key An edge
-    /// \return The "forward" directed arc view of edge
-    Value operator[](const Key& key) const {
-      return _graph.direct(key, true);
-    }
-
-  private:
-    const Graph& _graph;
-  };
-
-  /// \brief Returns a \ref ForwardMap class.
-  ///
-  /// This function just returns an \ref ForwardMap class.
-  /// \relates ForwardMap
-  template <typename Graph>
-  inline ForwardMap<Graph> forwardMap(const Graph& graph) {
-    return ForwardMap<Graph>(graph);
-  }
-
-  /// \brief Returns the "backward" directed arc view of an edge.
-  ///
-  /// Returns the "backward" directed arc view of an edge.
-  /// \see ForwardMap
-  template <typename Graph>
-  class BackwardMap {
-  public:
-
-    typedef typename Graph::Arc Value;
-    typedef typename Graph::Edge Key;
-
-    /// \brief Constructor
-    ///
-    /// Constructor
-    /// \param _graph The graph that the map belongs to.
-    explicit BackwardMap(const Graph& graph) : _graph(graph) {}
-
-    /// \brief The subscript operator.
-    ///
-    /// The subscript operator.
-    /// \param key An edge
-    /// \return The "backward" directed arc view of edge
-    Value operator[](const Key& key) const {
-      return _graph.direct(key, false);
-    }
-
-  private:
-    const Graph& _graph;
-  };
-
-  /// \brief Returns a \ref BackwardMap class
-
-  /// This function just returns a \ref BackwardMap class.
-  /// \relates BackwardMap
-  template <typename Graph>
-  inline BackwardMap<Graph> backwardMap(const Graph& graph) {
-    return BackwardMap<Graph>(graph);
-  }
-
-  /// \brief Potential difference map
-  ///
-  /// If there is an potential map on the nodes then we
-  /// can get an arc map as we get the substraction of the
-  /// values of the target and source.
-  template <typename Digraph, typename NodeMap>
-  class PotentialDifferenceMap {
-  public:
-    typedef typename Digraph::Arc Key;
-    typedef typename NodeMap::Value Value;
-
-    /// \brief Constructor
-    ///
-    /// Contructor of the map
-    explicit PotentialDifferenceMap(const Digraph& digraph,
-                                    const NodeMap& potential)
-      : _digraph(digraph), _potential(potential) {}
-
-    /// \brief Const subscription operator
-    ///
-    /// Const subscription operator
-    Value operator[](const Key& arc) const {
-      return _potential[_digraph.target(arc)] -
-        _potential[_digraph.source(arc)];
-    }
-
-  private:
-    const Digraph& _digraph;
-    const NodeMap& _potential;
-  };
-
-  /// \brief Returns a PotentialDifferenceMap.
-  ///
-  /// This function just returns a PotentialDifferenceMap.
-  /// \relates PotentialDifferenceMap
-  template <typename Digraph, typename NodeMap>
-  PotentialDifferenceMap<Digraph, NodeMap>
-  potentialDifferenceMap(const Digraph& digraph, const NodeMap& potential) {
-    return PotentialDifferenceMap<Digraph, NodeMap>(digraph, potential);
-  }
-
-  /// \brief Map of the node in-degrees.
-  ///
-  /// This map returns the in-degree of a node. Once it is constructed,
-  /// the degrees are stored in a standard NodeMap, so each query is done
-  /// in constant time. On the other hand, the values are updated automatically
-  /// whenever the digraph changes.
-  ///
-  /// \warning Besides addNode() and addArc(), a digraph structure may provide
-  /// alternative ways to modify the digraph. The correct behavior of InDegMap
-  /// is not guarantied if these additional features are used. For example
-  /// the functions \ref ListDigraph::changeSource() "changeSource()",
-  /// \ref ListDigraph::changeTarget() "changeTarget()" and
-  /// \ref ListDigraph::reverseArc() "reverseArc()"
-  /// of \ref ListDigraph will \e not update the degree values correctly.
-  ///
-  /// \sa OutDegMap
-
-  template <typename _Digraph>
-  class InDegMap
-    : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
-      ::ItemNotifier::ObserverBase {
-
-  public:
-
-    typedef _Digraph Digraph;
-    typedef int Value;
-    typedef typename Digraph::Node Key;
-
-    typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
-    ::ItemNotifier::ObserverBase Parent;
-
-  private:
-
-    class AutoNodeMap : public DefaultMap<Digraph, Key, int> {
-    public:
-
-      typedef DefaultMap<Digraph, Key, int> Parent;
-
-      AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
-
-      virtual void add(const Key& key) {
-        Parent::add(key);
-        Parent::set(key, 0);
-      }
-
-      virtual void add(const std::vector<Key>& keys) {
-        Parent::add(keys);
-        for (int i = 0; i < int(keys.size()); ++i) {
-          Parent::set(keys[i], 0);
-        }
-      }
-
-      virtual void build() {
-        Parent::build();
-        Key it;
-        typename Parent::Notifier* nf = Parent::notifier();
-        for (nf->first(it); it != INVALID; nf->next(it)) {
-          Parent::set(it, 0);
-        }
-      }
-    };
-
-  public:
-
-    /// \brief Constructor.
-    ///
-    /// Constructor for creating in-degree map.
-    explicit InDegMap(const Digraph& digraph)
-      : _digraph(digraph), _deg(digraph) {
-      Parent::attach(_digraph.notifier(typename Digraph::Arc()));
-
-      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
-        _deg[it] = countInArcs(_digraph, it);
-      }
-    }
-
-    /// Gives back the in-degree of a Node.
-    int operator[](const Key& key) const {
-      return _deg[key];
-    }
-
-  protected:
-
-    typedef typename Digraph::Arc Arc;
-
-    virtual void add(const Arc& arc) {
-      ++_deg[_digraph.target(arc)];
-    }
-
-    virtual void add(const std::vector<Arc>& arcs) {
-      for (int i = 0; i < int(arcs.size()); ++i) {
-        ++_deg[_digraph.target(arcs[i])];
-      }
-    }
-
-    virtual void erase(const Arc& arc) {
-      --_deg[_digraph.target(arc)];
-    }
-
-    virtual void erase(const std::vector<Arc>& arcs) {
-      for (int i = 0; i < int(arcs.size()); ++i) {
-        --_deg[_digraph.target(arcs[i])];
-      }
-    }
-
-    virtual void build() {
-      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
-        _deg[it] = countInArcs(_digraph, it);
-      }
-    }
-
-    virtual void clear() {
-      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
-        _deg[it] = 0;
-      }
-    }
-  private:
-
-    const Digraph& _digraph;
-    AutoNodeMap _deg;
-  };
-
-  /// \brief Map of the node out-degrees.
-  ///
-  /// This map returns the out-degree of a node. Once it is constructed,
-  /// the degrees are stored in a standard NodeMap, so each query is done
-  /// in constant time. On the other hand, the values are updated automatically
-  /// whenever the digraph changes.
-  ///
-  /// \warning Besides addNode() and addArc(), a digraph structure may provide
-  /// alternative ways to modify the digraph. The correct behavior of OutDegMap
-  /// is not guarantied if these additional features are used. For example
-  /// the functions \ref ListDigraph::changeSource() "changeSource()",
-  /// \ref ListDigraph::changeTarget() "changeTarget()" and
-  /// \ref ListDigraph::reverseArc() "reverseArc()"
-  /// of \ref ListDigraph will \e not update the degree values correctly.
-  ///
-  /// \sa InDegMap
-
-  template <typename _Digraph>
-  class OutDegMap
-    : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
-      ::ItemNotifier::ObserverBase {
-
-  public:
-
-    typedef _Digraph Digraph;
-    typedef int Value;
-    typedef typename Digraph::Node Key;
-
-    typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
-    ::ItemNotifier::ObserverBase Parent;
-
-  private:
-
-    class AutoNodeMap : public DefaultMap<Digraph, Key, int> {
-    public:
-
-      typedef DefaultMap<Digraph, Key, int> Parent;
-
-      AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
-
-      virtual void add(const Key& key) {
-        Parent::add(key);
-        Parent::set(key, 0);
-      }
-      virtual void add(const std::vector<Key>& keys) {
-        Parent::add(keys);
-        for (int i = 0; i < int(keys.size()); ++i) {
-          Parent::set(keys[i], 0);
-        }
-      }
-      virtual void build() {
-        Parent::build();
-        Key it;
-        typename Parent::Notifier* nf = Parent::notifier();
-        for (nf->first(it); it != INVALID; nf->next(it)) {
-          Parent::set(it, 0);
-        }
-      }
-    };
-
-  public:
-
-    /// \brief Constructor.
-    ///
-    /// Constructor for creating out-degree map.
-    explicit OutDegMap(const Digraph& digraph)
-      : _digraph(digraph), _deg(digraph) {
-      Parent::attach(_digraph.notifier(typename Digraph::Arc()));
-
-      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
-        _deg[it] = countOutArcs(_digraph, it);
-      }
-    }
-
-    /// Gives back the out-degree of a Node.
-    int operator[](const Key& key) const {
-      return _deg[key];
-    }
-
-  protected:
-
-    typedef typename Digraph::Arc Arc;
-
-    virtual void add(const Arc& arc) {
-      ++_deg[_digraph.source(arc)];
-    }
-
-    virtual void add(const std::vector<Arc>& arcs) {
-      for (int i = 0; i < int(arcs.size()); ++i) {
-        ++_deg[_digraph.source(arcs[i])];
-      }
-    }
-
-    virtual void erase(const Arc& arc) {
-      --_deg[_digraph.source(arc)];
-    }
-
-    virtual void erase(const std::vector<Arc>& arcs) {
-      for (int i = 0; i < int(arcs.size()); ++i) {
-        --_deg[_digraph.source(arcs[i])];
-      }
-    }
-
-    virtual void build() {
-      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
-        _deg[it] = countOutArcs(_digraph, it);
-      }
-    }
-
-    virtual void clear() {
-      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
-        _deg[it] = 0;
-      }
-    }
-  private:
-
-    const Digraph& _digraph;
-    AutoNodeMap _deg;
-  };
-
-
-  ///Dynamic arc look up between given endpoints.
-
-  ///\ingroup gutils
-  ///Using this class, you can find an arc in a digraph from a given
-  ///source to a given target in amortized time <em>O(log d)</em>,
-  ///where <em>d</em> is the out-degree of the source node.
-  ///
-  ///It is possible to find \e all parallel arcs between two nodes with
-  ///the \c findFirst() and \c findNext() members.
-  ///
-  ///See the \ref ArcLookUp and \ref AllArcLookUp classes if your
-  ///digraph is not changed so frequently.
-  ///
-  ///This class uses a self-adjusting binary search tree, Sleator's
-  ///and Tarjan's Splay tree for guarantee the logarithmic amortized
-  ///time bound for arc lookups. This class also guarantees the
-  ///optimal time bound in a constant factor for any distribution of
-  ///queries.
-  ///
-  ///\tparam G The type of the underlying digraph.
-  ///
-  ///\sa ArcLookUp
-  ///\sa AllArcLookUp
-  template<class G>
-  class DynArcLookUp
-    : protected ItemSetTraits<G, typename G::Arc>::ItemNotifier::ObserverBase
-  {
-  public:
-    typedef typename ItemSetTraits<G, typename G::Arc>
-    ::ItemNotifier::ObserverBase Parent;
-
-    TEMPLATE_DIGRAPH_TYPEDEFS(G);
-    typedef G Digraph;
-
-  protected:
-
-    class AutoNodeMap : public DefaultMap<G, Node, Arc> {
-    public:
-
-      typedef DefaultMap<G, Node, Arc> Parent;
-
-      AutoNodeMap(const G& digraph) : Parent(digraph, INVALID) {}
-
-      virtual void add(const Node& node) {
-        Parent::add(node);
-        Parent::set(node, INVALID);
-      }
-
-      virtual void add(const std::vector<Node>& nodes) {
-        Parent::add(nodes);
-        for (int i = 0; i < int(nodes.size()); ++i) {
-          Parent::set(nodes[i], INVALID);
-        }
-      }
-
-      virtual void build() {
-        Parent::build();
-        Node it;
-        typename Parent::Notifier* nf = Parent::notifier();
-        for (nf->first(it); it != INVALID; nf->next(it)) {
-          Parent::set(it, INVALID);
-        }
-      }
-    };
-
-    const Digraph &_g;
-    AutoNodeMap _head;
-    typename Digraph::template ArcMap<Arc> _parent;
-    typename Digraph::template ArcMap<Arc> _left;
-    typename Digraph::template ArcMap<Arc> _right;
-
-    class ArcLess {
-      const Digraph &g;
-    public:
-      ArcLess(const Digraph &_g) : g(_g) {}
-      bool operator()(Arc a,Arc b) const
-      {
-        return g.target(a)<g.target(b);
-      }
-    };
-
-  public:
-
-    ///Constructor
-
-    ///Constructor.
-    ///
-    ///It builds up the search database.
-    DynArcLookUp(const Digraph &g)
-      : _g(g),_head(g),_parent(g),_left(g),_right(g)
-    {
-      Parent::attach(_g.notifier(typename Digraph::Arc()));
-      refresh();
-    }
-
-  protected:
-
-    virtual void add(const Arc& arc) {
-      insert(arc);
-    }
-
-    virtual void add(const std::vector<Arc>& arcs) {
-      for (int i = 0; i < int(arcs.size()); ++i) {
-        insert(arcs[i]);
-      }
-    }
-
-    virtual void erase(const Arc& arc) {
-      remove(arc);
-    }
-
-    virtual void erase(const std::vector<Arc>& arcs) {
-      for (int i = 0; i < int(arcs.size()); ++i) {
-        remove(arcs[i]);
-      }
-    }
-
-    virtual void build() {
-      refresh();
-    }
-
-    virtual void clear() {
-      for(NodeIt n(_g);n!=INVALID;++n) {
-        _head.set(n, INVALID);
-      }
-    }
-
-    void insert(Arc arc) {
-      Node s = _g.source(arc);
-      Node t = _g.target(arc);
-      _left.set(arc, INVALID);
-      _right.set(arc, INVALID);
-
-      Arc e = _head[s];
-      if (e == INVALID) {
-        _head.set(s, arc);
-        _parent.set(arc, INVALID);
-        return;
-      }
-      while (true) {
-        if (t < _g.target(e)) {
-          if (_left[e] == INVALID) {
-            _left.set(e, arc);
-            _parent.set(arc, e);
-            splay(arc);
-            return;
-          } else {
-            e = _left[e];
-          }
-        } else {
-          if (_right[e] == INVALID) {
-            _right.set(e, arc);
-            _parent.set(arc, e);
-            splay(arc);
-            return;
-          } else {
-            e = _right[e];
-          }
-        }
-      }
-    }
-
-    void remove(Arc arc) {
-      if (_left[arc] == INVALID) {
-        if (_right[arc] != INVALID) {
-          _parent.set(_right[arc], _parent[arc]);
-        }
-        if (_parent[arc] != INVALID) {
-          if (_left[_parent[arc]] == arc) {
-            _left.set(_parent[arc], _right[arc]);
-          } else {
-            _right.set(_parent[arc], _right[arc]);
-          }
-        } else {
-          _head.set(_g.source(arc), _right[arc]);
-        }
-      } else if (_right[arc] == INVALID) {
-        _parent.set(_left[arc], _parent[arc]);
-        if (_parent[arc] != INVALID) {
-          if (_left[_parent[arc]] == arc) {
-            _left.set(_parent[arc], _left[arc]);
-          } else {
-            _right.set(_parent[arc], _left[arc]);
-          }
-        } else {
-          _head.set(_g.source(arc), _left[arc]);
-        }
-      } else {
-        Arc e = _left[arc];
-        if (_right[e] != INVALID) {
-          e = _right[e];
-          while (_right[e] != INVALID) {
-            e = _right[e];
-          }
-          Arc s = _parent[e];
-          _right.set(_parent[e], _left[e]);
-          if (_left[e] != INVALID) {
-            _parent.set(_left[e], _parent[e]);
-          }
-
-          _left.set(e, _left[arc]);
-          _parent.set(_left[arc], e);
-          _right.set(e, _right[arc]);
-          _parent.set(_right[arc], e);
-
-          _parent.set(e, _parent[arc]);
-          if (_parent[arc] != INVALID) {
-            if (_left[_parent[arc]] == arc) {
-              _left.set(_parent[arc], e);
-            } else {
-              _right.set(_parent[arc], e);
-            }
-          }
-          splay(s);
-        } else {
-          _right.set(e, _right[arc]);
-          _parent.set(_right[arc], e);
-
-          if (_parent[arc] != INVALID) {
-            if (_left[_parent[arc]] == arc) {
-              _left.set(_parent[arc], e);
-            } else {
-              _right.set(_parent[arc], e);
-            }
-          } else {
-            _head.set(_g.source(arc), e);
-          }
-        }
-      }
-    }
-
-    Arc refreshRec(std::vector<Arc> &v,int a,int b)
-    {
-      int m=(a+b)/2;
-      Arc me=v[m];
-      if (a < m) {
-        Arc left = refreshRec(v,a,m-1);
-        _left.set(me, left);
-        _parent.set(left, me);
-      } else {
-        _left.set(me, INVALID);
-      }
-      if (m < b) {
-        Arc right = refreshRec(v,m+1,b);
-        _right.set(me, right);
-        _parent.set(right, me);
-      } else {
-        _right.set(me, INVALID);
-      }
-      return me;
-    }
-
-    void refresh() {
-      for(NodeIt n(_g);n!=INVALID;++n) {
-        std::vector<Arc> v;
-        for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
-        if(v.size()) {
-          std::sort(v.begin(),v.end(),ArcLess(_g));
-          Arc head = refreshRec(v,0,v.size()-1);
-          _head.set(n, head);
-          _parent.set(head, INVALID);
-        }
-        else _head.set(n, INVALID);
-      }
-    }
-
-    void zig(Arc v) {
-      Arc w = _parent[v];
-      _parent.set(v, _parent[w]);
-      _parent.set(w, v);
-      _left.set(w, _right[v]);
-      _right.set(v, w);
-      if (_parent[v] != INVALID) {
-        if (_right[_parent[v]] == w) {
-          _right.set(_parent[v], v);
-        } else {
-          _left.set(_parent[v], v);
-        }
-      }
-      if (_left[w] != INVALID){
-        _parent.set(_left[w], w);
-      }
-    }
-
-    void zag(Arc v) {
-      Arc w = _parent[v];
-      _parent.set(v, _parent[w]);
-      _parent.set(w, v);
-      _right.set(w, _left[v]);
-      _left.set(v, w);
-      if (_parent[v] != INVALID){
-        if (_left[_parent[v]] == w) {
-          _left.set(_parent[v], v);
-        } else {
-          _right.set(_parent[v], v);
-        }
-      }
-      if (_right[w] != INVALID){
-        _parent.set(_right[w], w);
-      }
-    }
-
-    void splay(Arc v) {
-      while (_parent[v] != INVALID) {
-        if (v == _left[_parent[v]]) {
-          if (_parent[_parent[v]] == INVALID) {
-            zig(v);
-          } else {
-            if (_parent[v] == _left[_parent[_parent[v]]]) {
-              zig(_parent[v]);
-              zig(v);
-            } else {
-              zig(v);
-              zag(v);
-            }
-          }
-        } else {
-          if (_parent[_parent[v]] == INVALID) {
-            zag(v);
-          } else {
-            if (_parent[v] == _left[_parent[_parent[v]]]) {
-              zag(v);
-              zig(v);
-            } else {
-              zag(_parent[v]);
-              zag(v);
-            }
-          }
-        }
-      }
-      _head[_g.source(v)] = v;
-    }
-
-
-  public:
-
-    ///Find an arc between two nodes.
-
-    ///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
-    /// <em>d</em> is the number of outgoing arcs of \c s.
-    ///\param s The source node
-    ///\param t The target node
-    ///\return An arc from \c s to \c t if there exists,
-    ///\ref INVALID otherwise.
-    Arc operator()(Node s, Node t) const
-    {
-      Arc a = _head[s];
-      while (true) {
-        if (_g.target(a) == t) {
-          const_cast<DynArcLookUp&>(*this).splay(a);
-          return a;
-        } else if (t < _g.target(a)) {
-          if (_left[a] == INVALID) {
-            const_cast<DynArcLookUp&>(*this).splay(a);
-            return INVALID;
-          } else {
-            a = _left[a];
-          }
-        } else  {
-          if (_right[a] == INVALID) {
-            const_cast<DynArcLookUp&>(*this).splay(a);
-            return INVALID;
-          } else {
-            a = _right[a];
-          }
-        }
-      }
-    }
-
-    ///Find the first arc between two nodes.
-
-    ///Find the first arc between two nodes in time
-    /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
-    /// outgoing arcs of \c s.
-    ///\param s The source node
-    ///\param t The target node
-    ///\return An arc from \c s to \c t if there exists, \ref INVALID
-    /// otherwise.
-    Arc findFirst(Node s, Node t) const
-    {
-      Arc a = _head[s];
-      Arc r = INVALID;
-      while (true) {
-        if (_g.target(a) < t) {
-          if (_right[a] == INVALID) {
-            const_cast<DynArcLookUp&>(*this).splay(a);
-            return r;
-          } else {
-            a = _right[a];
-          }
-        } else {
-          if (_g.target(a) == t) {
-            r = a;
-          }
-          if (_left[a] == INVALID) {
-            const_cast<DynArcLookUp&>(*this).splay(a);
-            return r;
-          } else {
-            a = _left[a];
-          }
-        }
-      }
-    }
-
-    ///Find the next arc between two nodes.
-
-    ///Find the next arc between two nodes in time
-    /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
-    /// outgoing arcs of \c s.
-    ///\param s The source node
-    ///\param t The target node
-    ///\return An arc from \c s to \c t if there exists, \ref INVALID
-    /// otherwise.
-
-    ///\note If \c e is not the result of the previous \c findFirst()
-    ///operation then the amorized time bound can not be guaranteed.
-#ifdef DOXYGEN
-    Arc findNext(Node s, Node t, Arc a) const
-#else
-    Arc findNext(Node, Node t, Arc a) const
-#endif
-    {
-      if (_right[a] != INVALID) {
-        a = _right[a];
-        while (_left[a] != INVALID) {
-          a = _left[a];
-        }
-        const_cast<DynArcLookUp&>(*this).splay(a);
-      } else {
-        while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
-          a = _parent[a];
-        }
-        if (_parent[a] == INVALID) {
-          return INVALID;
-        } else {
-          a = _parent[a];
-          const_cast<DynArcLookUp&>(*this).splay(a);
-        }
-      }
-      if (_g.target(a) == t) return a;
-      else return INVALID;
-    }
-
-  };
-
-  ///Fast arc look up between given endpoints.
-
-  ///\ingroup gutils
-  ///Using this class, you can find an arc in a digraph from a given
-  ///source to a given target in time <em>O(log d)</em>,
-  ///where <em>d</em> is the out-degree of the source node.
-  ///
-  ///It is not possible to find \e all parallel arcs between two nodes.
-  ///Use \ref AllArcLookUp for this purpose.
-  ///
-  ///\warning This class is static, so you should refresh() (or at least
-  ///refresh(Node)) this data structure
-  ///whenever the digraph changes. This is a time consuming (superlinearly
-  ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
-  ///
-  ///\tparam G The type of the underlying digraph.
-  ///
-  ///\sa DynArcLookUp
-  ///\sa AllArcLookUp
-  template<class G>
-  class ArcLookUp
-  {
-  public:
-    TEMPLATE_DIGRAPH_TYPEDEFS(G);
-    typedef G Digraph;
-
-  protected:
-    const Digraph &_g;
-    typename Digraph::template NodeMap<Arc> _head;
-    typename Digraph::template ArcMap<Arc> _left;
-    typename Digraph::template ArcMap<Arc> _right;
-
-    class ArcLess {
-      const Digraph &g;
-    public:
-      ArcLess(const Digraph &_g) : g(_g) {}
-      bool operator()(Arc a,Arc b) const
-      {
-        return g.target(a)<g.target(b);
-      }
-    };
-
-  public:
-
-    ///Constructor
-
-    ///Constructor.
-    ///
-    ///It builds up the search database, which remains valid until the digraph
-    ///changes.
-    ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
-
-  private:
-    Arc refreshRec(std::vector<Arc> &v,int a,int b)
-    {
-      int m=(a+b)/2;
-      Arc me=v[m];
-      _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
-      _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
-      return me;
-    }
-  public:
-    ///Refresh the data structure at a node.
-
-    ///Build up the search database of node \c n.
-    ///
-    ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
-    ///the number of the outgoing arcs of \c n.
-    void refresh(Node n)
-    {
-      std::vector<Arc> v;
-      for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
-      if(v.size()) {
-        std::sort(v.begin(),v.end(),ArcLess(_g));
-        _head[n]=refreshRec(v,0,v.size()-1);
-      }
-      else _head[n]=INVALID;
-    }
-    ///Refresh the full data structure.
-
-    ///Build up the full search database. In fact, it simply calls
-    ///\ref refresh(Node) "refresh(n)" for each node \c n.
-    ///
-    ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
-    ///the number of the arcs of \c n and <em>D</em> is the maximum
-    ///out-degree of the digraph.
-
-    void refresh()
-    {
-      for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
-    }
-
-    ///Find an arc between two nodes.
-
-    ///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
-    /// <em>d</em> is the number of outgoing arcs of \c s.
-    ///\param s The source node
-    ///\param t The target node
-    ///\return An arc from \c s to \c t if there exists,
-    ///\ref INVALID otherwise.
-    ///
-    ///\warning If you change the digraph, refresh() must be called before using
-    ///this operator. If you change the outgoing arcs of
-    ///a single node \c n, then
-    ///\ref refresh(Node) "refresh(n)" is enough.
-    ///
-    Arc operator()(Node s, Node t) const
-    {
-      Arc e;
-      for(e=_head[s];
-          e!=INVALID&&_g.target(e)!=t;
-          e = t < _g.target(e)?_left[e]:_right[e]) ;
-      return e;
-    }
-
-  };
-
-  ///Fast look up of all arcs between given endpoints.
-
-  ///\ingroup gutils
-  ///This class is the same as \ref ArcLookUp, with the addition
-  ///that it makes it possible to find all arcs between given endpoints.
-  ///
-  ///\warning This class is static, so you should refresh() (or at least
-  ///refresh(Node)) this data structure
-  ///whenever the digraph changes. This is a time consuming (superlinearly
-  ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
-  ///
-  ///\tparam G The type of the underlying digraph.
-  ///
-  ///\sa DynArcLookUp
-  ///\sa ArcLookUp
-  template<class G>
-  class AllArcLookUp : public ArcLookUp<G>
-  {
-    using ArcLookUp<G>::_g;
-    using ArcLookUp<G>::_right;
-    using ArcLookUp<G>::_left;
-    using ArcLookUp<G>::_head;
-
-    TEMPLATE_DIGRAPH_TYPEDEFS(G);
-    typedef G Digraph;
-
-    typename Digraph::template ArcMap<Arc> _next;
-
-    Arc refreshNext(Arc head,Arc next=INVALID)
-    {
-      if(head==INVALID) return next;
-      else {
-        next=refreshNext(_right[head],next);
-//         _next[head]=next;
-        _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
-          ? next : INVALID;
-        return refreshNext(_left[head],head);
-      }
-    }
-
-    void refreshNext()
-    {
-      for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
-    }
-
-  public:
-    ///Constructor
-
-    ///Constructor.
-    ///
-    ///It builds up the search database, which remains valid until the digraph
-    ///changes.
-    AllArcLookUp(const Digraph &g) : ArcLookUp<G>(g), _next(g) {refreshNext();}
-
-    ///Refresh the data structure at a node.
-
-    ///Build up the search database of node \c n.
-    ///
-    ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
-    ///the number of the outgoing arcs of \c n.
-
-    void refresh(Node n)
-    {
-      ArcLookUp<G>::refresh(n);
-      refreshNext(_head[n]);
-    }
-
-    ///Refresh the full data structure.
-
-    ///Build up the full search database. In fact, it simply calls
-    ///\ref refresh(Node) "refresh(n)" for each node \c n.
-    ///
-    ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
-    ///the number of the arcs of \c n and <em>D</em> is the maximum
-    ///out-degree of the digraph.
-
-    void refresh()
-    {
-      for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
-    }
-
-    ///Find an arc between two nodes.
-
-    ///Find an arc between two nodes.
-    ///\param s The source node
-    ///\param t The target node
-    ///\param prev The previous arc between \c s and \c t. It it is INVALID or
-    ///not given, the operator finds the first appropriate arc.
-    ///\return An arc from \c s to \c t after \c prev or
-    ///\ref INVALID if there is no more.
-    ///
-    ///For example, you can count the number of arcs from \c u to \c v in the
-    ///following way.
-    ///\code
-    ///AllArcLookUp<ListDigraph> ae(g);
-    ///...
-    ///int n=0;
-    ///for(Arc e=ae(u,v);e!=INVALID;e=ae(u,v,e)) n++;
-    ///\endcode
-    ///
-    ///Finding the first arc take <em>O(</em>log<em>d)</em> time, where
-    /// <em>d</em> is the number of outgoing arcs of \c s. Then, the
-    ///consecutive arcs are found in constant time.
-    ///
-    ///\warning If you change the digraph, refresh() must be called before using
-    ///this operator. If you change the outgoing arcs of
-    ///a single node \c n, then
-    ///\ref refresh(Node) "refresh(n)" is enough.
-    ///
-#ifdef DOXYGEN
-    Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
-#else
-    using ArcLookUp<G>::operator() ;
-    Arc operator()(Node s, Node t, Arc prev) const
-    {
-      return prev==INVALID?(*this)(s,t):_next[prev];
-    }
-#endif
-
-  };
-
-  /// @}
-
-} //END OF NAMESPACE LEMON
-
-#endif
diff --git a/lemon/kruskal.h b/lemon/kruskal.h
--- a/lemon/kruskal.h
+++ b/lemon/kruskal.h
@@ -22,12 +22,9 @@
 #include <algorithm>
 #include <vector>
 #include <lemon/unionfind.h>
-// #include <lemon/graph_utils.h>
 #include <lemon/maps.h>
 
-// #include <lemon/radix_sort.h>
-
-#include <lemon/bits/utility.h>
+#include <lemon/core.h>
 #include <lemon/bits/traits.h>
 
 ///\ingroup spantree
@@ -300,7 +297,7 @@
   ///
   /// \return The total cost of the found spanning tree.
   ///
-  /// \note If the input graph is not (weakly) connected, a spanning 
+  /// \note If the input graph is not (weakly) connected, a spanning
   /// forest is calculated instead of a spanning tree.
 
 #ifdef DOXYGEN
diff --git a/lemon/lgf_reader.h b/lemon/lgf_reader.h
--- a/lemon/lgf_reader.h
+++ b/lemon/lgf_reader.h
@@ -32,7 +32,7 @@
 #include <map>
 
 #include <lemon/assert.h>
-#include <lemon/graph_utils.h>
+#include <lemon/core.h>
 
 #include <lemon/lgf_writer.h>
 
diff --git a/lemon/lgf_writer.h b/lemon/lgf_writer.h
--- a/lemon/lgf_writer.h
+++ b/lemon/lgf_writer.h
@@ -34,7 +34,8 @@
 #include <functional>
 
 #include <lemon/assert.h>
-#include <lemon/graph_utils.h>
+#include <lemon/core.h>
+#include <lemon/maps.h>
 
 namespace lemon {
 
diff --git a/lemon/list_graph.h b/lemon/list_graph.h
--- a/lemon/list_graph.h
+++ b/lemon/list_graph.h
@@ -23,6 +23,8 @@
 ///\file
 ///\brief ListDigraph, ListGraph classes.
 
+#include <lemon/core.h>
+#include <lemon/error.h>
 #include <lemon/bits/graph_extender.h>
 
 #include <vector>
diff --git a/lemon/maps.h b/lemon/maps.h
--- a/lemon/maps.h
+++ b/lemon/maps.h
@@ -23,8 +23,7 @@
 #include <functional>
 #include <vector>
 
-#include <lemon/bits/utility.h>
-#include <lemon/bits/traits.h>
+#include <lemon/core.h>
 
 ///\file
 ///\ingroup maps
@@ -1780,6 +1779,926 @@
     return LoggerBoolMap<Iterator>(it);
   }
 
+  /// Provides an immutable and unique id for each item in the graph.
+
+  /// The IdMap class provides a unique and immutable id for each item of the
+  /// same type (e.g. node) in the graph. This id is <ul><li>\b unique:
+  /// different items (nodes) get different ids <li>\b immutable: the id of an
+  /// item (node) does not change (even if you delete other nodes).  </ul>
+  /// Through this map you get access (i.e. can read) the inner id values of
+  /// the items stored in the graph. This map can be inverted with its member
+  /// class \c InverseMap or with the \c operator() member.
+  ///
+  template <typename _Graph, typename _Item>
+  class IdMap {
+  public:
+    typedef _Graph Graph;
+    typedef int Value;
+    typedef _Item Item;
+    typedef _Item Key;
+
+    /// \brief Constructor.
+    ///
+    /// Constructor of the map.
+    explicit IdMap(const Graph& graph) : _graph(&graph) {}
+
+    /// \brief Gives back the \e id of the item.
+    ///
+    /// Gives back the immutable and unique \e id of the item.
+    int operator[](const Item& item) const { return _graph->id(item);}
+
+    /// \brief Gives back the item by its id.
+    ///
+    /// Gives back the item by its id.
+    Item operator()(int id) { return _graph->fromId(id, Item()); }
+
+  private:
+    const Graph* _graph;
+
+  public:
+
+    /// \brief The class represents the inverse of its owner (IdMap).
+    ///
+    /// The class represents the inverse of its owner (IdMap).
+    /// \see inverse()
+    class InverseMap {
+    public:
+
+      /// \brief Constructor.
+      ///
+      /// Constructor for creating an id-to-item map.
+      explicit InverseMap(const Graph& graph) : _graph(&graph) {}
+
+      /// \brief Constructor.
+      ///
+      /// Constructor for creating an id-to-item map.
+      explicit InverseMap(const IdMap& map) : _graph(map._graph) {}
+
+      /// \brief Gives back the given item from its id.
+      ///
+      /// Gives back the given item from its id.
+      ///
+      Item operator[](int id) const { return _graph->fromId(id, Item());}
+
+    private:
+      const Graph* _graph;
+    };
+
+    /// \brief Gives back the inverse of the map.
+    ///
+    /// Gives back the inverse of the IdMap.
+    InverseMap inverse() const { return InverseMap(*_graph);}
+
+  };
+
+
+  /// \brief General invertable graph-map type.
+
+  /// This type provides simple invertable graph-maps.
+  /// The InvertableMap wraps an arbitrary ReadWriteMap
+  /// and if a key is set to a new value then store it
+  /// in the inverse map.
+  ///
+  /// The values of the map can be accessed
+  /// with stl compatible forward iterator.
+  ///
+  /// \tparam _Graph The graph type.
+  /// \tparam _Item The item type of the graph.
+  /// \tparam _Value The value type of the map.
+  ///
+  /// \see IterableValueMap
+  template <typename _Graph, typename _Item, typename _Value>
+  class InvertableMap
+    : protected ItemSetTraits<_Graph, _Item>::template Map<_Value>::Type {
+  private:
+
+    typedef typename ItemSetTraits<_Graph, _Item>::
+    template Map<_Value>::Type Map;
+    typedef _Graph Graph;
+
+    typedef std::map<_Value, _Item> Container;
+    Container _inv_map;
+
+  public:
+
+    /// The key type of InvertableMap (Node, Arc, Edge).
+    typedef typename Map::Key Key;
+    /// The value type of the InvertableMap.
+    typedef typename Map::Value Value;
+
+
+
+    /// \brief Constructor.
+    ///
+    /// Construct a new InvertableMap for the graph.
+    ///
+    explicit InvertableMap(const Graph& graph) : Map(graph) {}
+
+    /// \brief Forward iterator for values.
+    ///
+    /// This iterator is an stl compatible forward
+    /// iterator on the values of the map. The values can
+    /// be accessed in the [beginValue, endValue) range.
+    ///
+    class ValueIterator
+      : public std::iterator<std::forward_iterator_tag, Value> {
+      friend class InvertableMap;
+    private:
+      ValueIterator(typename Container::const_iterator _it)
+        : it(_it) {}
+    public:
+
+      ValueIterator() {}
+
+      ValueIterator& operator++() { ++it; return *this; }
+      ValueIterator operator++(int) {
+        ValueIterator tmp(*this);
+        operator++();
+        return tmp;
+      }
+
+      const Value& operator*() const { return it->first; }
+      const Value* operator->() const { return &(it->first); }
+
+      bool operator==(ValueIterator jt) const { return it == jt.it; }
+      bool operator!=(ValueIterator jt) const { return it != jt.it; }
+
+    private:
+      typename Container::const_iterator it;
+    };
+
+    /// \brief Returns an iterator to the first value.
+    ///
+    /// Returns an stl compatible iterator to the
+    /// first value of the map. The values of the
+    /// map can be accessed in the [beginValue, endValue)
+    /// range.
+    ValueIterator beginValue() const {
+      return ValueIterator(_inv_map.begin());
+    }
+
+    /// \brief Returns an iterator after the last value.
+    ///
+    /// Returns an stl compatible iterator after the
+    /// last value of the map. The values of the
+    /// map can be accessed in the [beginValue, endValue)
+    /// range.
+    ValueIterator endValue() const {
+      return ValueIterator(_inv_map.end());
+    }
+
+    /// \brief The setter function of the map.
+    ///
+    /// Sets the mapped value.
+    void set(const Key& key, const Value& val) {
+      Value oldval = Map::operator[](key);
+      typename Container::iterator it = _inv_map.find(oldval);
+      if (it != _inv_map.end() && it->second == key) {
+        _inv_map.erase(it);
+      }
+      _inv_map.insert(make_pair(val, key));
+      Map::set(key, val);
+    }
+
+    /// \brief The getter function of the map.
+    ///
+    /// It gives back the value associated with the key.
+    typename MapTraits<Map>::ConstReturnValue
+    operator[](const Key& key) const {
+      return Map::operator[](key);
+    }
+
+    /// \brief Gives back the item by its value.
+    ///
+    /// Gives back the item by its value.
+    Key operator()(const Value& key) const {
+      typename Container::const_iterator it = _inv_map.find(key);
+      return it != _inv_map.end() ? it->second : INVALID;
+    }
+
+  protected:
+
+    /// \brief Erase the key from the map.
+    ///
+    /// Erase the key to the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void erase(const Key& key) {
+      Value val = Map::operator[](key);
+      typename Container::iterator it = _inv_map.find(val);
+      if (it != _inv_map.end() && it->second == key) {
+        _inv_map.erase(it);
+      }
+      Map::erase(key);
+    }
+
+    /// \brief Erase more keys from the map.
+    ///
+    /// Erase more keys from the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void erase(const std::vector<Key>& keys) {
+      for (int i = 0; i < int(keys.size()); ++i) {
+        Value val = Map::operator[](keys[i]);
+        typename Container::iterator it = _inv_map.find(val);
+        if (it != _inv_map.end() && it->second == keys[i]) {
+          _inv_map.erase(it);
+        }
+      }
+      Map::erase(keys);
+    }
+
+    /// \brief Clear the keys from the map and inverse map.
+    ///
+    /// Clear the keys from the map and inverse map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void clear() {
+      _inv_map.clear();
+      Map::clear();
+    }
+
+  public:
+
+    /// \brief The inverse map type.
+    ///
+    /// The inverse of this map. The subscript operator of the map
+    /// gives back always the item what was last assigned to the value.
+    class InverseMap {
+    public:
+      /// \brief Constructor of the InverseMap.
+      ///
+      /// Constructor of the InverseMap.
+      explicit InverseMap(const InvertableMap& inverted)
+        : _inverted(inverted) {}
+
+      /// The value type of the InverseMap.
+      typedef typename InvertableMap::Key Value;
+      /// The key type of the InverseMap.
+      typedef typename InvertableMap::Value Key;
+
+      /// \brief Subscript operator.
+      ///
+      /// Subscript operator. It gives back always the item
+      /// what was last assigned to the value.
+      Value operator[](const Key& key) const {
+        return _inverted(key);
+      }
+
+    private:
+      const InvertableMap& _inverted;
+    };
+
+    /// \brief It gives back the just readable inverse map.
+    ///
+    /// It gives back the just readable inverse map.
+    InverseMap inverse() const {
+      return InverseMap(*this);
+    }
+
+
+
+  };
+
+  /// \brief Provides a mutable, continuous and unique descriptor for each
+  /// item in the graph.
+  ///
+  /// The DescriptorMap class provides a unique and continuous (but mutable)
+  /// descriptor (id) for each item of the same type (e.g. node) in the
+  /// graph. This id is <ul><li>\b unique: different items (nodes) get
+  /// different ids <li>\b continuous: the range of the ids is the set of
+  /// integers between 0 and \c n-1, where \c n is the number of the items of
+  /// this type (e.g. nodes) (so the id of a node can change if you delete an
+  /// other node, i.e. this id is mutable).  </ul> This map can be inverted
+  /// with its member class \c InverseMap, or with the \c operator() member.
+  ///
+  /// \tparam _Graph The graph class the \c DescriptorMap belongs to.
+  /// \tparam _Item The Item is the Key of the Map. It may be Node, Arc or
+  /// Edge.
+  template <typename _Graph, typename _Item>
+  class DescriptorMap
+    : protected ItemSetTraits<_Graph, _Item>::template Map<int>::Type {
+
+    typedef _Item Item;
+    typedef typename ItemSetTraits<_Graph, _Item>::template Map<int>::Type Map;
+
+  public:
+    /// The graph class of DescriptorMap.
+    typedef _Graph Graph;
+
+    /// The key type of DescriptorMap (Node, Arc, Edge).
+    typedef typename Map::Key Key;
+    /// The value type of DescriptorMap.
+    typedef typename Map::Value Value;
+
+    /// \brief Constructor.
+    ///
+    /// Constructor for descriptor map.
+    explicit DescriptorMap(const Graph& _graph) : Map(_graph) {
+      Item it;
+      const typename Map::Notifier* nf = Map::notifier();
+      for (nf->first(it); it != INVALID; nf->next(it)) {
+        Map::set(it, _inv_map.size());
+        _inv_map.push_back(it);
+      }
+    }
+
+  protected:
+
+    /// \brief Add a new key to the map.
+    ///
+    /// Add a new key to the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void add(const Item& item) {
+      Map::add(item);
+      Map::set(item, _inv_map.size());
+      _inv_map.push_back(item);
+    }
+
+    /// \brief Add more new keys to the map.
+    ///
+    /// Add more new keys to the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void add(const std::vector<Item>& items) {
+      Map::add(items);
+      for (int i = 0; i < int(items.size()); ++i) {
+        Map::set(items[i], _inv_map.size());
+        _inv_map.push_back(items[i]);
+      }
+    }
+
+    /// \brief Erase the key from the map.
+    ///
+    /// Erase the key from the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void erase(const Item& item) {
+      Map::set(_inv_map.back(), Map::operator[](item));
+      _inv_map[Map::operator[](item)] = _inv_map.back();
+      _inv_map.pop_back();
+      Map::erase(item);
+    }
+
+    /// \brief Erase more keys from the map.
+    ///
+    /// Erase more keys from the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void erase(const std::vector<Item>& items) {
+      for (int i = 0; i < int(items.size()); ++i) {
+        Map::set(_inv_map.back(), Map::operator[](items[i]));
+        _inv_map[Map::operator[](items[i])] = _inv_map.back();
+        _inv_map.pop_back();
+      }
+      Map::erase(items);
+    }
+
+    /// \brief Build the unique map.
+    ///
+    /// Build the unique map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void build() {
+      Map::build();
+      Item it;
+      const typename Map::Notifier* nf = Map::notifier();
+      for (nf->first(it); it != INVALID; nf->next(it)) {
+        Map::set(it, _inv_map.size());
+        _inv_map.push_back(it);
+      }
+    }
+
+    /// \brief Clear the keys from the map.
+    ///
+    /// Clear the keys from the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void clear() {
+      _inv_map.clear();
+      Map::clear();
+    }
+
+  public:
+
+    /// \brief Returns the maximal value plus one.
+    ///
+    /// Returns the maximal value plus one in the map.
+    unsigned int size() const {
+      return _inv_map.size();
+    }
+
+    /// \brief Swaps the position of the two items in the map.
+    ///
+    /// Swaps the position of the two items in the map.
+    void swap(const Item& p, const Item& q) {
+      int pi = Map::operator[](p);
+      int qi = Map::operator[](q);
+      Map::set(p, qi);
+      _inv_map[qi] = p;
+      Map::set(q, pi);
+      _inv_map[pi] = q;
+    }
+
+    /// \brief Gives back the \e descriptor of the item.
+    ///
+    /// Gives back the mutable and unique \e descriptor of the map.
+    int operator[](const Item& item) const {
+      return Map::operator[](item);
+    }
+
+    /// \brief Gives back the item by its descriptor.
+    ///
+    /// Gives back th item by its descriptor.
+    Item operator()(int id) const {
+      return _inv_map[id];
+    }
+
+  private:
+
+    typedef std::vector<Item> Container;
+    Container _inv_map;
+
+  public:
+    /// \brief The inverse map type of DescriptorMap.
+    ///
+    /// The inverse map type of DescriptorMap.
+    class InverseMap {
+    public:
+      /// \brief Constructor of the InverseMap.
+      ///
+      /// Constructor of the InverseMap.
+      explicit InverseMap(const DescriptorMap& inverted)
+        : _inverted(inverted) {}
+
+
+      /// The value type of the InverseMap.
+      typedef typename DescriptorMap::Key Value;
+      /// The key type of the InverseMap.
+      typedef typename DescriptorMap::Value Key;
+
+      /// \brief Subscript operator.
+      ///
+      /// Subscript operator. It gives back the item
+      /// that the descriptor belongs to currently.
+      Value operator[](const Key& key) const {
+        return _inverted(key);
+      }
+
+      /// \brief Size of the map.
+      ///
+      /// Returns the size of the map.
+      unsigned int size() const {
+        return _inverted.size();
+      }
+
+    private:
+      const DescriptorMap& _inverted;
+    };
+
+    /// \brief Gives back the inverse of the map.
+    ///
+    /// Gives back the inverse of the map.
+    const InverseMap inverse() const {
+      return InverseMap(*this);
+    }
+  };
+
+  /// \brief Returns the source of the given arc.
+  ///
+  /// The SourceMap gives back the source Node of the given arc.
+  /// \see TargetMap
+  template <typename Digraph>
+  class SourceMap {
+  public:
+
+    typedef typename Digraph::Node Value;
+    typedef typename Digraph::Arc Key;
+
+    /// \brief Constructor
+    ///
+    /// Constructor
+    /// \param _digraph The digraph that the map belongs to.
+    explicit SourceMap(const Digraph& digraph) : _digraph(digraph) {}
+
+    /// \brief The subscript operator.
+    ///
+    /// The subscript operator.
+    /// \param arc The arc
+    /// \return The source of the arc
+    Value operator[](const Key& arc) const {
+      return _digraph.source(arc);
+    }
+
+  private:
+    const Digraph& _digraph;
+  };
+
+  /// \brief Returns a \ref SourceMap class.
+  ///
+  /// This function just returns an \ref SourceMap class.
+  /// \relates SourceMap
+  template <typename Digraph>
+  inline SourceMap<Digraph> sourceMap(const Digraph& digraph) {
+    return SourceMap<Digraph>(digraph);
+  }
+
+  /// \brief Returns the target of the given arc.
+  ///
+  /// The TargetMap gives back the target Node of the given arc.
+  /// \see SourceMap
+  template <typename Digraph>
+  class TargetMap {
+  public:
+
+    typedef typename Digraph::Node Value;
+    typedef typename Digraph::Arc Key;
+
+    /// \brief Constructor
+    ///
+    /// Constructor
+    /// \param _digraph The digraph that the map belongs to.
+    explicit TargetMap(const Digraph& digraph) : _digraph(digraph) {}
+
+    /// \brief The subscript operator.
+    ///
+    /// The subscript operator.
+    /// \param e The arc
+    /// \return The target of the arc
+    Value operator[](const Key& e) const {
+      return _digraph.target(e);
+    }
+
+  private:
+    const Digraph& _digraph;
+  };
+
+  /// \brief Returns a \ref TargetMap class.
+  ///
+  /// This function just returns a \ref TargetMap class.
+  /// \relates TargetMap
+  template <typename Digraph>
+  inline TargetMap<Digraph> targetMap(const Digraph& digraph) {
+    return TargetMap<Digraph>(digraph);
+  }
+
+  /// \brief Returns the "forward" directed arc view of an edge.
+  ///
+  /// Returns the "forward" directed arc view of an edge.
+  /// \see BackwardMap
+  template <typename Graph>
+  class ForwardMap {
+  public:
+
+    typedef typename Graph::Arc Value;
+    typedef typename Graph::Edge Key;
+
+    /// \brief Constructor
+    ///
+    /// Constructor
+    /// \param _graph The graph that the map belongs to.
+    explicit ForwardMap(const Graph& graph) : _graph(graph) {}
+
+    /// \brief The subscript operator.
+    ///
+    /// The subscript operator.
+    /// \param key An edge
+    /// \return The "forward" directed arc view of edge
+    Value operator[](const Key& key) const {
+      return _graph.direct(key, true);
+    }
+
+  private:
+    const Graph& _graph;
+  };
+
+  /// \brief Returns a \ref ForwardMap class.
+  ///
+  /// This function just returns an \ref ForwardMap class.
+  /// \relates ForwardMap
+  template <typename Graph>
+  inline ForwardMap<Graph> forwardMap(const Graph& graph) {
+    return ForwardMap<Graph>(graph);
+  }
+
+  /// \brief Returns the "backward" directed arc view of an edge.
+  ///
+  /// Returns the "backward" directed arc view of an edge.
+  /// \see ForwardMap
+  template <typename Graph>
+  class BackwardMap {
+  public:
+
+    typedef typename Graph::Arc Value;
+    typedef typename Graph::Edge Key;
+
+    /// \brief Constructor
+    ///
+    /// Constructor
+    /// \param _graph The graph that the map belongs to.
+    explicit BackwardMap(const Graph& graph) : _graph(graph) {}
+
+    /// \brief The subscript operator.
+    ///
+    /// The subscript operator.
+    /// \param key An edge
+    /// \return The "backward" directed arc view of edge
+    Value operator[](const Key& key) const {
+      return _graph.direct(key, false);
+    }
+
+  private:
+    const Graph& _graph;
+  };
+
+  /// \brief Returns a \ref BackwardMap class
+
+  /// This function just returns a \ref BackwardMap class.
+  /// \relates BackwardMap
+  template <typename Graph>
+  inline BackwardMap<Graph> backwardMap(const Graph& graph) {
+    return BackwardMap<Graph>(graph);
+  }
+
+  /// \brief Potential difference map
+  ///
+  /// If there is an potential map on the nodes then we
+  /// can get an arc map as we get the substraction of the
+  /// values of the target and source.
+  template <typename Digraph, typename NodeMap>
+  class PotentialDifferenceMap {
+  public:
+    typedef typename Digraph::Arc Key;
+    typedef typename NodeMap::Value Value;
+
+    /// \brief Constructor
+    ///
+    /// Contructor of the map
+    explicit PotentialDifferenceMap(const Digraph& digraph,
+                                    const NodeMap& potential)
+      : _digraph(digraph), _potential(potential) {}
+
+    /// \brief Const subscription operator
+    ///
+    /// Const subscription operator
+    Value operator[](const Key& arc) const {
+      return _potential[_digraph.target(arc)] -
+        _potential[_digraph.source(arc)];
+    }
+
+  private:
+    const Digraph& _digraph;
+    const NodeMap& _potential;
+  };
+
+  /// \brief Returns a PotentialDifferenceMap.
+  ///
+  /// This function just returns a PotentialDifferenceMap.
+  /// \relates PotentialDifferenceMap
+  template <typename Digraph, typename NodeMap>
+  PotentialDifferenceMap<Digraph, NodeMap>
+  potentialDifferenceMap(const Digraph& digraph, const NodeMap& potential) {
+    return PotentialDifferenceMap<Digraph, NodeMap>(digraph, potential);
+  }
+
+  /// \brief Map of the node in-degrees.
+  ///
+  /// This map returns the in-degree of a node. Once it is constructed,
+  /// the degrees are stored in a standard NodeMap, so each query is done
+  /// in constant time. On the other hand, the values are updated automatically
+  /// whenever the digraph changes.
+  ///
+  /// \warning Besides addNode() and addArc(), a digraph structure may provide
+  /// alternative ways to modify the digraph. The correct behavior of InDegMap
+  /// is not guarantied if these additional features are used. For example
+  /// the functions \ref ListDigraph::changeSource() "changeSource()",
+  /// \ref ListDigraph::changeTarget() "changeTarget()" and
+  /// \ref ListDigraph::reverseArc() "reverseArc()"
+  /// of \ref ListDigraph will \e not update the degree values correctly.
+  ///
+  /// \sa OutDegMap
+
+  template <typename _Digraph>
+  class InDegMap
+    : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
+      ::ItemNotifier::ObserverBase {
+
+  public:
+
+    typedef _Digraph Digraph;
+    typedef int Value;
+    typedef typename Digraph::Node Key;
+
+    typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
+    ::ItemNotifier::ObserverBase Parent;
+
+  private:
+
+    class AutoNodeMap
+      : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
+    public:
+
+      typedef typename ItemSetTraits<Digraph, Key>::
+      template Map<int>::Type Parent;
+
+      AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
+
+      virtual void add(const Key& key) {
+        Parent::add(key);
+        Parent::set(key, 0);
+      }
+
+      virtual void add(const std::vector<Key>& keys) {
+        Parent::add(keys);
+        for (int i = 0; i < int(keys.size()); ++i) {
+          Parent::set(keys[i], 0);
+        }
+      }
+
+      virtual void build() {
+        Parent::build();
+        Key it;
+        typename Parent::Notifier* nf = Parent::notifier();
+        for (nf->first(it); it != INVALID; nf->next(it)) {
+          Parent::set(it, 0);
+        }
+      }
+    };
+
+  public:
+
+    /// \brief Constructor.
+    ///
+    /// Constructor for creating in-degree map.
+    explicit InDegMap(const Digraph& digraph)
+      : _digraph(digraph), _deg(digraph) {
+      Parent::attach(_digraph.notifier(typename Digraph::Arc()));
+
+      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
+        _deg[it] = countInArcs(_digraph, it);
+      }
+    }
+
+    /// Gives back the in-degree of a Node.
+    int operator[](const Key& key) const {
+      return _deg[key];
+    }
+
+  protected:
+
+    typedef typename Digraph::Arc Arc;
+
+    virtual void add(const Arc& arc) {
+      ++_deg[_digraph.target(arc)];
+    }
+
+    virtual void add(const std::vector<Arc>& arcs) {
+      for (int i = 0; i < int(arcs.size()); ++i) {
+        ++_deg[_digraph.target(arcs[i])];
+      }
+    }
+
+    virtual void erase(const Arc& arc) {
+      --_deg[_digraph.target(arc)];
+    }
+
+    virtual void erase(const std::vector<Arc>& arcs) {
+      for (int i = 0; i < int(arcs.size()); ++i) {
+        --_deg[_digraph.target(arcs[i])];
+      }
+    }
+
+    virtual void build() {
+      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
+        _deg[it] = countInArcs(_digraph, it);
+      }
+    }
+
+    virtual void clear() {
+      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
+        _deg[it] = 0;
+      }
+    }
+  private:
+
+    const Digraph& _digraph;
+    AutoNodeMap _deg;
+  };
+
+  /// \brief Map of the node out-degrees.
+  ///
+  /// This map returns the out-degree of a node. Once it is constructed,
+  /// the degrees are stored in a standard NodeMap, so each query is done
+  /// in constant time. On the other hand, the values are updated automatically
+  /// whenever the digraph changes.
+  ///
+  /// \warning Besides addNode() and addArc(), a digraph structure may provide
+  /// alternative ways to modify the digraph. The correct behavior of OutDegMap
+  /// is not guarantied if these additional features are used. For example
+  /// the functions \ref ListDigraph::changeSource() "changeSource()",
+  /// \ref ListDigraph::changeTarget() "changeTarget()" and
+  /// \ref ListDigraph::reverseArc() "reverseArc()"
+  /// of \ref ListDigraph will \e not update the degree values correctly.
+  ///
+  /// \sa InDegMap
+
+  template <typename _Digraph>
+  class OutDegMap
+    : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
+      ::ItemNotifier::ObserverBase {
+
+  public:
+
+    typedef _Digraph Digraph;
+    typedef int Value;
+    typedef typename Digraph::Node Key;
+
+    typedef typename ItemSetTraits<Digraph, typename Digraph::Arc>
+    ::ItemNotifier::ObserverBase Parent;
+
+  private:
+
+    class AutoNodeMap
+      : public ItemSetTraits<Digraph, Key>::template Map<int>::Type {
+    public:
+
+      typedef typename ItemSetTraits<Digraph, Key>::
+      template Map<int>::Type Parent;
+
+      AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
+
+      virtual void add(const Key& key) {
+        Parent::add(key);
+        Parent::set(key, 0);
+      }
+      virtual void add(const std::vector<Key>& keys) {
+        Parent::add(keys);
+        for (int i = 0; i < int(keys.size()); ++i) {
+          Parent::set(keys[i], 0);
+        }
+      }
+      virtual void build() {
+        Parent::build();
+        Key it;
+        typename Parent::Notifier* nf = Parent::notifier();
+        for (nf->first(it); it != INVALID; nf->next(it)) {
+          Parent::set(it, 0);
+        }
+      }
+    };
+
+  public:
+
+    /// \brief Constructor.
+    ///
+    /// Constructor for creating out-degree map.
+    explicit OutDegMap(const Digraph& digraph)
+      : _digraph(digraph), _deg(digraph) {
+      Parent::attach(_digraph.notifier(typename Digraph::Arc()));
+
+      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
+        _deg[it] = countOutArcs(_digraph, it);
+      }
+    }
+
+    /// Gives back the out-degree of a Node.
+    int operator[](const Key& key) const {
+      return _deg[key];
+    }
+
+  protected:
+
+    typedef typename Digraph::Arc Arc;
+
+    virtual void add(const Arc& arc) {
+      ++_deg[_digraph.source(arc)];
+    }
+
+    virtual void add(const std::vector<Arc>& arcs) {
+      for (int i = 0; i < int(arcs.size()); ++i) {
+        ++_deg[_digraph.source(arcs[i])];
+      }
+    }
+
+    virtual void erase(const Arc& arc) {
+      --_deg[_digraph.source(arc)];
+    }
+
+    virtual void erase(const std::vector<Arc>& arcs) {
+      for (int i = 0; i < int(arcs.size()); ++i) {
+        --_deg[_digraph.source(arcs[i])];
+      }
+    }
+
+    virtual void build() {
+      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
+        _deg[it] = countOutArcs(_digraph, it);
+      }
+    }
+
+    virtual void clear() {
+      for(typename Digraph::NodeIt it(_digraph); it != INVALID; ++it) {
+        _deg[it] = 0;
+      }
+    }
+  private:
+
+    const Digraph& _digraph;
+    AutoNodeMap _deg;
+  };
+
   /// @}
 }
 
diff --git a/lemon/path.h b/lemon/path.h
--- a/lemon/path.h
+++ b/lemon/path.h
@@ -28,7 +28,7 @@
 #include <algorithm>
 
 #include <lemon/error.h>
-#include <lemon/bits/invalid.h>
+#include <lemon/core.h>
 #include <lemon/concepts/path.h>
 
 namespace lemon {
diff --git a/lemon/smart_graph.h b/lemon/smart_graph.h
--- a/lemon/smart_graph.h
+++ b/lemon/smart_graph.h
@@ -25,14 +25,8 @@
 
 #include <vector>
 
-#include <lemon/bits/invalid.h>
-
-#include <lemon/bits/base_extender.h>
-#include <lemon/bits/graph_extender.h>
-
-#include <lemon/bits/utility.h>
+#include <lemon/core.h>
 #include <lemon/error.h>
-
 #include <lemon/bits/graph_extender.h>
 
 namespace lemon {
diff --git a/lemon/unionfind.h b/lemon/unionfind.h
--- a/lemon/unionfind.h
+++ b/lemon/unionfind.h
@@ -30,7 +30,7 @@
 #include <algorithm>
 #include <functional>
 
-#include <lemon/bits/invalid.h>
+#include <lemon/core.h>
 
 namespace lemon {
 
diff --git a/test/dijkstra_test.cc b/test/dijkstra_test.cc
--- a/test/dijkstra_test.cc
+++ b/test/dijkstra_test.cc
@@ -19,7 +19,6 @@
 #include <lemon/concepts/digraph.h>
 #include <lemon/smart_graph.h>
 #include <lemon/list_graph.h>
-#include <lemon/graph_utils.h>
 #include <lemon/dijkstra.h>
 #include <lemon/path.h>
 
diff --git a/test/graph_copy_test.cc b/test/graph_copy_test.cc
--- a/test/graph_copy_test.cc
+++ b/test/graph_copy_test.cc
@@ -19,7 +19,6 @@
 #include <lemon/smart_graph.h>
 #include <lemon/list_graph.h>
 #include <lemon/lgf_reader.h>
-#include <lemon/graph_utils.h>
 #include <lemon/error.h>
 
 #include "test_tools.h"
diff --git a/test/graph_test.h b/test/graph_test.h
--- a/test/graph_test.h
+++ b/test/graph_test.h
@@ -19,7 +19,7 @@
 #ifndef LEMON_TEST_GRAPH_TEST_H
 #define LEMON_TEST_GRAPH_TEST_H
 
-#include <lemon/graph_utils.h>
+#include <lemon/core.h>
 #include "test_tools.h"
 
 namespace lemon {
diff --git a/test/graph_utils_test.cc b/test/graph_utils_test.cc
--- a/test/graph_utils_test.cc
+++ b/test/graph_utils_test.cc
@@ -20,9 +20,9 @@
 #include <ctime>
 
 #include <lemon/random.h>
-#include <lemon/graph_utils.h>
 #include <lemon/list_graph.h>
 #include <lemon/smart_graph.h>
+#include <lemon/maps.h>
 
 #include "graph_test.h"
 #include "test_tools.h"