Index: lemon/Makefile.am
===================================================================
--- lemon/Makefile.am	(revision 32)
+++ lemon/Makefile.am	(revision 57)
@@ -22,6 +22,16 @@
 
 bits_HEADERS += \
+	lemon/bits/alteration_notifier.h \
+	lemon/bits/array_map.h \
+	lemon/bits/base_extender.h \
+	lemon/bits/default_map.h \
         lemon/bits/invalid.h \
-        lemon/bits/utility.h
+	lemon/bits/map_extender.h \
+        lemon/bits/utility.h \
+	lemon/bits/vector_map.h
 
 concept_HEADERS +=
+	lemon/concept_check.h \
+	lemon/concepts/digraph.h \
+	lemon/concepts/graph.h \
+	lemon/concepts/graph_components.h
Index: lemon/bits/alteration_notifier.h
===================================================================
--- lemon/bits/alteration_notifier.h	(revision 57)
+++ lemon/bits/alteration_notifier.h	(revision 57)
@@ -0,0 +1,485 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2007
+ * 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_ALTERATION_NOTIFIER_H
+#define LEMON_BITS_ALTERATION_NOTIFIER_H
+
+#include <vector>
+#include <list>
+
+#include <lemon/bits/utility.h>
+
+///\ingroup graphbits
+///\file
+///\brief Observer notifier for graph alteration observers.
+
+namespace lemon {
+
+  /// \ingroup graphbits
+  ///
+  /// \brief Notifier class to notify observes about alterations in 
+  /// a container.
+  ///
+  /// The simple graph's can be refered as two containers, one node container
+  /// and one edge container. But they are not standard containers they
+  /// does not store values directly they are just key continars for more
+  /// value containers which are the node and edge maps.
+  ///
+  /// The graph's node and edge sets can be changed as we add or erase
+  /// nodes and edges in the graph. Lemon would like to handle easily
+  /// that the node and edge maps should contain values for all nodes or
+  /// edges. If we want to check on every indicing if the map contains
+  /// the current indicing key that cause a drawback in the performance
+  /// in the library. We use another solution we notify all maps about
+  /// an alteration in the graph, which cause only drawback on the
+  /// alteration of the graph.
+  ///
+  /// This class provides an interface to the container. The \e first() and \e 
+  /// next() member functions make possible to iterate on the keys of the
+  /// container. The \e id() function returns an integer id for each key.
+  /// The \e maxId() function gives back an upper bound of the ids.
+  ///
+  /// For the proper functonality of this class, we should notify it
+  /// about each alteration in the container. The alterations have four type
+  /// as \e add(), \e erase(), \e build() and \e clear(). The \e add() and
+  /// \e erase() signals that only one or few items added or erased to or
+  /// from the graph. If all items are erased from the graph or from an empty
+  /// graph a new graph is builded then it can be signaled with the
+  /// clear() and build() members. Important rule that if we erase items 
+  /// from graph we should first signal the alteration and after that erase
+  /// them from the container, on the other way on item addition we should
+  /// first extend the container and just after that signal the alteration.
+  ///
+  /// The alteration can be observed with a class inherited from the
+  /// \e ObserverBase nested class. The signals can be handled with
+  /// overriding the virtual functions defined in the base class.  The
+  /// observer base can be attached to the notifier with the 
+  /// \e attach() member and can be detached with detach() function. The
+  /// alteration handlers should not call any function which signals
+  /// an other alteration in the same notifier and should not
+  /// detach any observer from the notifier.
+  ///
+  /// Alteration observers try to be exception safe. If an \e add() or
+  /// a \e clear() function throws an exception then the remaining
+  /// observeres will not be notified and the fulfilled additions will
+  /// be rolled back by calling the \e erase() or \e clear()
+  /// functions. Thence the \e erase() and \e clear() should not throw
+  /// exception. Actullay, it can be throw only 
+  /// \ref AlterationObserver::ImmediateDetach ImmediateDetach
+  /// exception which detach the observer from the notifier.
+  ///
+  /// There are some place when the alteration observing is not completly
+  /// reliable. If we want to carry out the node degree in the graph
+  /// as in the \ref InDegMap and we use the reverseEdge that cause 
+  /// unreliable functionality. Because the alteration observing signals
+  /// only erasing and adding but not the reversing it will stores bad
+  /// degrees. The sub graph adaptors cannot signal the alterations because
+  /// just a setting in the filter map can modify the graph and this cannot
+  /// be watched in any way.
+  ///
+  /// \param _Container The container which is observed.
+  /// \param _Item The item type which is obserbved.
+  ///
+  /// \author Balazs Dezso
+
+  template <typename _Container, typename _Item>
+  class AlterationNotifier {
+  public:
+
+    typedef True Notifier;
+
+    typedef _Container Container;
+    typedef _Item Item;
+
+    /// \brief Exception which can be called from \e clear() and 
+    /// \e erase().
+    ///
+    /// From the \e clear() and \e erase() function only this
+    /// exception is allowed to throw. The exception immediatly
+    /// detaches the current observer from the notifier. Because the
+    /// \e clear() and \e erase() should not throw other exceptions
+    /// it can be used to invalidate the observer.
+    struct ImmediateDetach {};
+
+    /// \brief ObserverBase is the base class for the observers.
+    ///
+    /// ObserverBase is the abstract base class for the observers.
+    /// It will be notified about an item was inserted into or
+    /// erased from the graph.
+    ///
+    /// The observer interface contains some pure virtual functions
+    /// to override. The add() and erase() functions are
+    /// to notify the oberver when one item is added or
+    /// erased.
+    ///
+    /// The build() and clear() members are to notify the observer
+    /// about the container is built from an empty container or
+    /// is cleared to an empty container. 
+    /// 
+    /// \author Balazs Dezso
+
+    class ObserverBase {
+    protected:
+      typedef AlterationNotifier Notifier;
+
+      friend class AlterationNotifier;
+
+      /// \brief Default constructor.
+      ///
+      /// Default constructor for ObserverBase.
+      /// 
+      ObserverBase() : _notifier(0) {}
+
+      /// \brief Constructor which attach the observer into notifier.
+      ///
+      /// Constructor which attach the observer into notifier.
+      ObserverBase(AlterationNotifier& nf) {
+        attach(nf);
+      }
+
+      /// \brief Constructor which attach the obserever to the same notifier.
+      ///
+      /// Constructor which attach the obserever to the same notifier as
+      /// the other observer is attached to. 
+      ObserverBase(const ObserverBase& copy) {
+	if (copy.attached()) {
+          attach(*copy.notifier());
+	}
+      }
+	
+      /// \brief Destructor
+      virtual ~ObserverBase() {
+        if (attached()) {
+          detach();
+        }
+      }
+
+      /// \brief Attaches the observer into an AlterationNotifier.
+      ///
+      /// This member attaches the observer into an AlterationNotifier.
+      ///
+      void attach(AlterationNotifier& nf) {
+	nf.attach(*this);
+      }
+      
+      /// \brief Detaches the observer into an AlterationNotifier.
+      ///
+      /// This member detaches the observer from an AlterationNotifier.
+      ///
+      void detach() {
+        _notifier->detach(*this);
+      }
+      
+      /// \brief Gives back a pointer to the notifier which the map 
+      /// attached into.
+      ///
+      /// This function gives back a pointer to the notifier which the map
+      /// attached into.
+      ///
+      Notifier* notifier() const { return const_cast<Notifier*>(_notifier); }
+      
+      /// Gives back true when the observer is attached into a notifier.
+      bool attached() const { return _notifier != 0; }
+
+    private:
+
+      ObserverBase& operator=(const ObserverBase& copy);
+
+    protected:
+      
+      Notifier* _notifier;
+      typename std::list<ObserverBase*>::iterator _index;
+
+      /// \brief The member function to notificate the observer about an
+      /// item is added to the container.
+      ///
+      /// The add() member function notificates the observer about an item
+      /// is added to the container. It have to be overrided in the
+      /// subclasses.
+      virtual void add(const Item&) = 0;
+
+      /// \brief The member function to notificate the observer about 
+      /// more item is added to the container.
+      ///
+      /// The add() member function notificates the observer about more item
+      /// is added to the container. It have to be overrided in the
+      /// subclasses.
+      virtual void add(const std::vector<Item>& items) = 0;
+
+      /// \brief The member function to notificate the observer about an
+      /// item is erased from the container.
+      ///
+      /// The erase() member function notificates the observer about an
+      /// item is erased from the container. It have to be overrided in
+      /// the subclasses.	
+      virtual void erase(const Item&) = 0;
+
+      /// \brief The member function to notificate the observer about 
+      /// more item is erased from the container.
+      ///
+      /// The erase() member function notificates the observer about more item
+      /// is erased from the container. It have to be overrided in the
+      /// subclasses.
+      virtual void erase(const std::vector<Item>& items) = 0;
+
+      /// \brief The member function to notificate the observer about the
+      /// container is built.
+      ///
+      /// The build() member function notificates the observer about the
+      /// container is built from an empty container. It have to be
+      /// overrided in the subclasses.
+
+      virtual void build() = 0;
+
+      /// \brief The member function to notificate the observer about all
+      /// items are erased from the container.
+      ///
+      /// The clear() member function notificates the observer about all
+      /// items are erased from the container. It have to be overrided in
+      /// the subclasses.      
+      virtual void clear() = 0;
+
+    };
+	
+  protected:
+
+    const Container* container;
+
+    typedef std::list<ObserverBase*> Observers; 
+    Observers _observers;
+
+		
+  public:
+
+    /// \brief Default constructor.
+    ///
+    /// The default constructor of the AlterationNotifier. 
+    /// It creates an empty notifier.
+    AlterationNotifier() 
+      : container(0) {}
+
+    /// \brief Constructor.
+    ///
+    /// Constructor with the observed container parameter.
+    AlterationNotifier(const Container& _container) 
+      : container(&_container) {}
+
+    /// \brief Copy Constructor of the AlterationNotifier. 
+    ///
+    /// Copy constructor of the AlterationNotifier. 
+    /// It creates only an empty notifier because the copiable
+    /// notifier's observers have to be registered still into that notifier.
+    AlterationNotifier(const AlterationNotifier& _notifier) 
+      : container(_notifier.container) {}
+
+    /// \brief Destructor.
+    ///		
+    /// Destructor of the AlterationNotifier.
+    ///
+    ~AlterationNotifier() {
+      typename Observers::iterator it;
+      for (it = _observers.begin(); it != _observers.end(); ++it) {
+	(*it)->_notifier = 0;
+      }
+    }
+
+    /// \brief Sets the container.
+    ///
+    /// Sets the container.
+    void setContainer(const Container& _container) {
+      container = &_container;
+    }
+
+  protected:
+
+    AlterationNotifier& operator=(const AlterationNotifier&);
+
+  public:
+
+
+
+    /// \brief First item in the container.
+    ///
+    /// Returns the first item in the container. It is
+    /// for start the iteration on the container.
+    void first(Item& item) const {
+      container->first(item);
+    }
+
+    /// \brief Next item in the container.
+    ///
+    /// Returns the next item in the container. It is
+    /// for iterate on the container.
+    void next(Item& item) const {
+      container->next(item);
+    }
+
+    /// \brief Returns the id of the item.
+    ///
+    /// Returns the id of the item provided by the container.
+    int id(const Item& item) const {
+      return container->id(item);
+    }
+
+    /// \brief Returns the maximum id of the container.
+    ///
+    /// Returns the maximum id of the container.
+    int maxId() const {
+      return container->maxId(Item());
+    }
+		
+  protected:
+
+    void attach(ObserverBase& observer) {
+      observer._index = _observers.insert(_observers.begin(), &observer);
+      observer._notifier = this;
+    } 
+
+    void detach(ObserverBase& observer) {
+      _observers.erase(observer._index);
+      observer._index = _observers.end();
+      observer._notifier = 0;
+    }
+
+  public:
+	
+    /// \brief Notifies all the registed observers about an item added to 
+    /// the container.
+    ///
+    /// It notifies all the registed observers about an item added to 
+    /// the container.
+    /// 
+    void add(const Item& item) {
+      typename Observers::reverse_iterator it;
+      try {
+        for (it = _observers.rbegin(); it != _observers.rend(); ++it) {
+          (*it)->add(item);
+        }
+      } catch (...) {
+        typename Observers::iterator jt;
+        for (jt = it.base(); jt != _observers.end(); ++jt) {
+          (*jt)->erase(item);
+        }
+        throw;
+      }
+    }	
+
+    /// \brief Notifies all the registed observers about more item added to 
+    /// the container.
+    ///
+    /// It notifies all the registed observers about more item added to 
+    /// the container.
+    /// 
+    void add(const std::vector<Item>& items) {
+      typename Observers::reverse_iterator it;
+      try {
+        for (it = _observers.rbegin(); it != _observers.rend(); ++it) {
+          (*it)->add(items);
+        }
+      } catch (...) {
+        typename Observers::iterator jt;
+        for (jt = it.base(); jt != _observers.end(); ++jt) {
+          (*jt)->erase(items);
+        }
+        throw;
+      }
+    }	
+
+    /// \brief Notifies all the registed observers about an item erased from 
+    /// the container.
+    ///	
+    /// It notifies all the registed observers about an item erased from 
+    /// the container.
+    /// 
+    void erase(const Item& item) throw() {
+      typename Observers::iterator it = _observers.begin();
+      while (it != _observers.end()) {
+        try {
+          (*it)->erase(item);
+          ++it;
+        } catch (const ImmediateDetach&) {
+          it = _observers.erase(it);
+          (*it)->_index = _observers.end();
+          (*it)->_notifier = 0;
+        }
+      }
+    }
+
+    /// \brief Notifies all the registed observers about more item erased  
+    /// from the container.
+    ///	
+    /// It notifies all the registed observers about more item erased from 
+    /// the container.
+    /// 
+    void erase(const std::vector<Item>& items) {
+      typename Observers::iterator it = _observers.begin();
+      while (it != _observers.end()) {
+        try {
+          (*it)->erase(items);
+          ++it;
+        } catch (const ImmediateDetach&) {
+          it = _observers.erase(it);
+          (*it)->_index = _observers.end();
+          (*it)->_notifier = 0;
+        }
+      }
+    }
+
+    /// \brief Notifies all the registed observers about the container is 
+    /// built.
+    ///		
+    /// Notifies all the registed observers about the container is built
+    /// from an empty container.
+    void build() {
+      typename Observers::reverse_iterator it;
+      try {
+        for (it = _observers.rbegin(); it != _observers.rend(); ++it) {
+          (*it)->build();
+        }
+      } catch (...) {
+        typename Observers::iterator jt;
+        for (jt = it.base(); jt != _observers.end(); ++jt) {
+          (*jt)->clear();
+        }
+        throw;
+      }
+    }
+
+    /// \brief Notifies all the registed observers about all items are 
+    /// erased.
+    ///
+    /// Notifies all the registed observers about all items are erased
+    /// from the container.
+    void clear() {
+      typename Observers::iterator it = _observers.begin();
+      while (it != _observers.end()) {
+        try {
+          (*it)->clear();
+          ++it;
+        } catch (const ImmediateDetach&) {
+          it = _observers.erase(it);
+          (*it)->_index = _observers.end();
+          (*it)->_notifier = 0;
+        }
+      }
+    }
+  };
+
+}
+
+#endif
Index: lemon/bits/array_map.h
===================================================================
--- lemon/bits/array_map.h	(revision 57)
+++ lemon/bits/array_map.h	(revision 57)
@@ -0,0 +1,346 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2007
+ * 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_ARRAY_MAP_H
+#define LEMON_BITS_ARRAY_MAP_H
+
+#include <memory>
+
+#include <lemon/bits/traits.h>
+#include <lemon/bits/alteration_notifier.h>
+#include <lemon/concept_check.h>
+#include <lemon/concepts/maps.h>
+
+/// \ingroup graphbits
+/// \file
+/// \brief Graph map based on the array storage.
+
+namespace lemon {
+
+  /// \ingroup graphbits
+  ///
+  /// \brief Graph map based on the array storage.
+  ///
+  /// The ArrayMap template class is graph map structure what
+  /// automatically updates the map when a key is added to or erased from
+  /// the map. This map uses the allocators to implement 
+  /// the container functionality.
+  ///
+  /// The template parameters are the Graph the current Item type and
+  /// the Value type of the map.
+  template <typename _Graph, typename _Item, typename _Value>
+  class ArrayMap 
+    : public ItemSetTraits<_Graph, _Item>::ItemNotifier::ObserverBase {
+  public:
+    /// The graph type of the maps. 
+    typedef _Graph Graph;
+    /// The item type of the map.
+    typedef _Item Item;
+    /// The reference map tag.
+    typedef True ReferenceMapTag;
+
+    /// The key type of the maps.
+    typedef _Item Key;
+    /// The value type of the map.
+    typedef _Value Value;
+
+    /// The const reference type of the map.
+    typedef const _Value& ConstReference;
+    /// The reference type of the map.
+    typedef _Value& Reference;
+
+    /// The notifier type.
+    typedef typename ItemSetTraits<_Graph, _Item>::ItemNotifier Notifier;
+
+    /// The MapBase of the Map which imlements the core regisitry function.
+    typedef typename Notifier::ObserverBase Parent;
+		
+  private:
+    typedef std::allocator<Value> Allocator;
+
+  public:
+
+    /// \brief Graph initialized map constructor.
+    ///
+    /// Graph initialized map constructor.
+    explicit ArrayMap(const Graph& graph) {
+      Parent::attach(graph.notifier(Item()));
+      allocate_memory();
+      Notifier* nf = Parent::notifier();
+      Item it;
+      for (nf->first(it); it != INVALID; nf->next(it)) {
+	int id = nf->id(it);;
+	allocator.construct(&(values[id]), Value());
+      }								
+    }
+
+    /// \brief Constructor to use default value to initialize the map. 
+    ///
+    /// It constructs a map and initialize all of the the map. 
+    ArrayMap(const Graph& graph, const Value& value) {
+      Parent::attach(graph.notifier(Item()));
+      allocate_memory();
+      Notifier* nf = Parent::notifier();
+      Item it;
+      for (nf->first(it); it != INVALID; nf->next(it)) {
+	int id = nf->id(it);;
+	allocator.construct(&(values[id]), value);
+      }								
+    }
+
+    /// \brief Constructor to copy a map of the same map type.
+    ///
+    /// Constructor to copy a map of the same map type.     
+    ArrayMap(const ArrayMap& copy) : Parent() {
+      if (copy.attached()) {
+	attach(*copy.notifier());
+      }
+      capacity = copy.capacity;
+      if (capacity == 0) return;
+      values = allocator.allocate(capacity);
+      Notifier* nf = Parent::notifier();
+      Item it;
+      for (nf->first(it); it != INVALID; nf->next(it)) {
+	int id = nf->id(it);;
+	allocator.construct(&(values[id]), copy.values[id]);
+      }
+    }
+
+    /// \brief Assign operator.
+    ///
+    /// This operator assigns for each item in the map the
+    /// value mapped to the same item in the copied map.  
+    /// The parameter map should be indiced with the same
+    /// itemset because this assign operator does not change
+    /// the container of the map. 
+    ArrayMap& operator=(const ArrayMap& cmap) {
+      return operator=<ArrayMap>(cmap);
+    }
+
+
+    /// \brief Template assign operator.
+    ///
+    /// The given parameter should be conform to the ReadMap
+    /// concecpt and could be indiced by the current item set of
+    /// the NodeMap. In this case the value for each item
+    /// is assigned by the value of the given ReadMap. 
+    template <typename CMap>
+    ArrayMap& operator=(const CMap& cmap) {
+      checkConcept<concepts::ReadMap<Key, _Value>, CMap>();
+      const typename Parent::Notifier* nf = Parent::notifier();
+      Item it;
+      for (nf->first(it); it != INVALID; nf->next(it)) {
+        set(it, cmap[it]);
+      }
+      return *this;
+    }
+
+    /// \brief The destructor of the map.
+    ///     
+    /// The destructor of the map.
+    virtual ~ArrayMap() {      
+      if (attached()) {
+	clear();
+	detach();
+      }
+    }
+		
+  protected:
+
+    using Parent::attach;
+    using Parent::detach;
+    using Parent::attached;
+
+  public:
+
+    /// \brief The subscript operator. 
+    ///
+    /// The subscript operator. The map can be subscripted by the
+    /// actual keys of the graph. 
+    Value& operator[](const Key& key) {
+      int id = Parent::notifier()->id(key);
+      return values[id];
+    } 
+		
+    /// \brief The const subscript operator.
+    ///
+    /// The const subscript operator. The map can be subscripted by the
+    /// actual keys of the graph. 
+    const Value& operator[](const Key& key) const {
+      int id = Parent::notifier()->id(key);
+      return values[id];
+    }
+
+    /// \brief Setter function of the map.
+    ///	
+    /// Setter function of the map. Equivalent with map[key] = val.
+    /// This is a compatibility feature with the not dereferable maps.
+    void set(const Key& key, const Value& val) {
+      (*this)[key] = val;
+    }
+
+  protected:
+
+    /// \brief Adds a new key to the map.
+    ///		
+    /// It adds a new key to the map. It called by the observer notifier
+    /// and it overrides the add() member function of the observer base.     
+    virtual void add(const Key& key) {
+      Notifier* nf = Parent::notifier();
+      int id = nf->id(key);
+      if (id >= capacity) {
+	int new_capacity = (capacity == 0 ? 1 : capacity);
+	while (new_capacity <= id) {
+	  new_capacity <<= 1;
+	}
+	Value* new_values = allocator.allocate(new_capacity);
+	Item it;
+	for (nf->first(it); it != INVALID; nf->next(it)) {
+	  int jd = nf->id(it);;
+	  if (id != jd) {
+	    allocator.construct(&(new_values[jd]), values[jd]);
+	    allocator.destroy(&(values[jd]));
+	  }
+	}
+	if (capacity != 0) allocator.deallocate(values, capacity);
+	values = new_values;
+	capacity = new_capacity;
+      }
+      allocator.construct(&(values[id]), Value());
+    }
+
+    /// \brief Adds more new keys to the map.
+    ///		
+    /// It adds more new keys to the map. It called by the observer notifier
+    /// and it overrides the add() member function of the observer base.     
+    virtual void add(const std::vector<Key>& keys) {
+      Notifier* nf = Parent::notifier();
+      int max_id = -1;
+      for (int i = 0; i < int(keys.size()); ++i) {
+	int id = nf->id(keys[i]);
+	if (id > max_id) {
+	  max_id = id;
+	}
+      }
+      if (max_id >= capacity) {
+	int new_capacity = (capacity == 0 ? 1 : capacity);
+	while (new_capacity <= max_id) {
+	  new_capacity <<= 1;
+	}
+	Value* new_values = allocator.allocate(new_capacity);
+	Item it;
+	for (nf->first(it); it != INVALID; nf->next(it)) {
+	  int id = nf->id(it);
+	  bool found = false;
+	  for (int i = 0; i < int(keys.size()); ++i) {
+	    int jd = nf->id(keys[i]);
+	    if (id == jd) {
+	      found = true;
+	      break;
+	    }
+	  }
+	  if (found) continue;
+	  allocator.construct(&(new_values[id]), values[id]);
+	  allocator.destroy(&(values[id]));
+	}
+	if (capacity != 0) allocator.deallocate(values, capacity);
+	values = new_values;
+	capacity = new_capacity;
+      }
+      for (int i = 0; i < int(keys.size()); ++i) {
+	int id = nf->id(keys[i]);
+	allocator.construct(&(values[id]), Value());
+      }
+    }
+		
+    /// \brief Erase a key from the map.
+    ///
+    /// Erase a key from the map. It called by the observer notifier
+    /// and it overrides the erase() member function of the observer base.     
+    virtual void erase(const Key& key) {
+      int id = Parent::notifier()->id(key);
+      allocator.destroy(&(values[id]));
+    }
+
+    /// \brief Erase more keys from the map.
+    ///
+    /// Erase more keys from the map. It called by the observer notifier
+    /// and it overrides the erase() member function of the observer base.     
+    virtual void erase(const std::vector<Key>& keys) {
+      for (int i = 0; i < int(keys.size()); ++i) {
+	int id = Parent::notifier()->id(keys[i]);
+	allocator.destroy(&(values[id]));
+      }
+    }
+
+    /// \brief Buildes the map.
+    ///	
+    /// It buildes the map. It called by the observer notifier
+    /// and it overrides the build() member function of the observer base. 
+    virtual void build() {
+      Notifier* nf = Parent::notifier();
+      allocate_memory();
+      Item it;
+      for (nf->first(it); it != INVALID; nf->next(it)) {
+	int id = nf->id(it);;
+	allocator.construct(&(values[id]), Value());
+      }								
+    }
+
+    /// \brief Clear the map.
+    ///
+    /// It erase all items from the map. It called by the observer notifier
+    /// and it overrides the clear() member function of the observer base.     
+    virtual void clear() {	
+      Notifier* nf = Parent::notifier();
+      if (capacity != 0) {
+	Item it;
+	for (nf->first(it); it != INVALID; nf->next(it)) {
+	  int id = nf->id(it);
+	  allocator.destroy(&(values[id]));
+	}								
+	allocator.deallocate(values, capacity);
+	capacity = 0;
+      }
+    }
+
+  private:
+      
+    void allocate_memory() {
+      int max_id = Parent::notifier()->maxId();
+      if (max_id == -1) {
+	capacity = 0;
+	values = 0;
+	return;
+      }
+      capacity = 1;
+      while (capacity <= max_id) {
+	capacity <<= 1;
+      }
+      values = allocator.allocate(capacity);	
+    }      
+
+    int capacity;
+    Value* values;
+    Allocator allocator;
+
+  };		
+
+}
+
+#endif 
Index: lemon/bits/base_extender.h
===================================================================
--- lemon/bits/base_extender.h	(revision 57)
+++ lemon/bits/base_extender.h	(revision 57)
@@ -0,0 +1,495 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2007
+ * 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_BASE_EXTENDER_H
+#define LEMON_BITS_BASE_EXTENDER_H
+
+#include <lemon/bits/invalid.h>
+#include <lemon/error.h>
+
+#include <lemon/bits/map_extender.h>
+#include <lemon/bits/default_map.h>
+
+#include <lemon/concept_check.h>
+#include <lemon/concepts/maps.h>
+
+///\ingroup digraphbits
+///\file
+///\brief Extenders for the digraph types
+namespace lemon {
+
+  /// \ingroup digraphbits
+  ///
+  /// \brief BaseDigraph to BaseGraph extender
+  template <typename Base>
+  class UndirDigraphExtender : public Base {
+
+  public:
+
+    typedef Base Parent;
+    typedef typename Parent::Arc Edge;
+    typedef typename Parent::Node Node;
+
+    typedef True UndirectedTag;
+
+    class Arc : public Edge {
+      friend class UndirDigraphExtender;
+
+    protected:
+      bool forward;
+
+      Arc(const Edge &ue, bool _forward) :
+        Edge(ue), forward(_forward) {}
+
+    public:
+      Arc() {}
+
+      /// Invalid arc constructor
+      Arc(Invalid i) : Edge(i), forward(true) {}
+
+      bool operator==(const Arc &that) const {
+	return forward==that.forward && Edge(*this)==Edge(that);
+      }
+      bool operator!=(const Arc &that) const {
+	return forward!=that.forward || Edge(*this)!=Edge(that);
+      }
+      bool operator<(const Arc &that) const {
+	return forward<that.forward ||
+	  (!(that.forward<forward) && Edge(*this)<Edge(that));
+      }
+    };
+
+
+
+    using Parent::source;
+
+    /// Source of the given Arc.
+    Node source(const Arc &e) const {
+      return e.forward ? Parent::source(e) : Parent::target(e);
+    }
+
+    using Parent::target;
+
+    /// Target of the given Arc.
+    Node target(const Arc &e) const {
+      return e.forward ? Parent::target(e) : Parent::source(e);
+    }
+
+    /// \brief Directed arc from an edge.
+    ///
+    /// Returns a directed arc corresponding to the specified Edge.
+    /// If the given bool is true the given edge and the
+    /// returned arc have the same source node.
+    static Arc direct(const Edge &ue, bool d) {
+      return Arc(ue, d);
+    }
+
+    /// Returns whether the given directed arc is same orientation as the
+    /// corresponding edge.
+    ///
+    /// \todo reference to the corresponding point of the undirected digraph
+    /// concept. "What does the direction of an edge mean?"
+    static bool direction(const Arc &e) { return e.forward; }
+
+
+    using Parent::first;
+    using Parent::next;
+
+    void first(Arc &e) const {
+      Parent::first(e);
+      e.forward=true;
+    }
+
+    void next(Arc &e) const {
+      if( e.forward ) {
+	e.forward = false;
+      }
+      else {
+	Parent::next(e);
+	e.forward = true;
+      }
+    }
+
+    void firstOut(Arc &e, const Node &n) const {
+      Parent::firstIn(e,n);
+      if( Edge(e) != INVALID ) {
+	e.forward = false;
+      }
+      else {
+	Parent::firstOut(e,n);
+	e.forward = true;
+      }
+    }
+    void nextOut(Arc &e) const {
+      if( ! e.forward ) {
+	Node n = Parent::target(e);
+	Parent::nextIn(e);
+	if( Edge(e) == INVALID ) {
+	  Parent::firstOut(e, n);
+	  e.forward = true;
+	}
+      }
+      else {
+	Parent::nextOut(e);
+      }
+    }
+
+    void firstIn(Arc &e, const Node &n) const {
+      Parent::firstOut(e,n);
+      if( Edge(e) != INVALID ) {
+	e.forward = false;
+      }
+      else {
+	Parent::firstIn(e,n);
+	e.forward = true;
+      }
+    }
+    void nextIn(Arc &e) const {
+      if( ! e.forward ) {
+	Node n = Parent::source(e);
+	Parent::nextOut(e);
+	if( Edge(e) == INVALID ) {
+	  Parent::firstIn(e, n);
+	  e.forward = true;
+	}
+      }
+      else {
+	Parent::nextIn(e);
+      }
+    }
+
+    void firstInc(Edge &e, bool &d, const Node &n) const {
+      d = true;
+      Parent::firstOut(e, n);
+      if (e != INVALID) return;
+      d = false;
+      Parent::firstIn(e, n);
+    }
+
+    void nextInc(Edge &e, bool &d) const {
+      if (d) {
+	Node s = Parent::source(e);
+	Parent::nextOut(e);
+	if (e != INVALID) return;
+	d = false;
+	Parent::firstIn(e, s);
+      } else {
+	Parent::nextIn(e);
+      }
+    }
+
+    Node nodeFromId(int ix) const {
+      return Parent::nodeFromId(ix);
+    }
+
+    Arc arcFromId(int ix) const {
+      return direct(Parent::arcFromId(ix >> 1), bool(ix & 1));
+    }
+
+    Edge edgeFromId(int ix) const {
+      return Parent::arcFromId(ix);
+    }
+
+    int id(const Node &n) const {
+      return Parent::id(n);
+    }
+
+    int id(const Edge &e) const {
+      return Parent::id(e);
+    }
+
+    int id(const Arc &e) const {
+      return 2 * Parent::id(e) + int(e.forward);
+    }
+
+    int maxNodeId() const {
+      return Parent::maxNodeId();
+    }
+
+    int maxArcId() const {
+      return 2 * Parent::maxArcId() + 1;
+    }
+
+    int maxEdgeId() const {
+      return Parent::maxArcId();
+    }
+
+
+    int arcNum() const {
+      return 2 * Parent::arcNum();
+    }
+
+    int edgeNum() const {
+      return Parent::arcNum();
+    }
+
+    Arc findArc(Node s, Node t, Arc p = INVALID) const {
+      if (p == INVALID) {
+	Edge arc = Parent::findArc(s, t);
+	if (arc != INVALID) return direct(arc, true);
+	arc = Parent::findArc(t, s);
+	if (arc != INVALID) return direct(arc, false);
+      } else if (direction(p)) {
+	Edge arc = Parent::findArc(s, t, p);
+	if (arc != INVALID) return direct(arc, true);
+	arc = Parent::findArc(t, s);
+	if (arc != INVALID) return direct(arc, false);	
+      } else {
+	Edge arc = Parent::findArc(t, s, p);
+	if (arc != INVALID) return direct(arc, false);	      
+      }
+      return INVALID;
+    }
+
+    Edge findEdge(Node s, Node t, Edge p = INVALID) const {
+      if (s != t) {
+        if (p == INVALID) {
+          Edge arc = Parent::findArc(s, t);
+          if (arc != INVALID) return arc;
+          arc = Parent::findArc(t, s);
+          if (arc != INVALID) return arc;
+        } else if (Parent::s(p) == s) {
+          Edge arc = Parent::findArc(s, t, p);
+          if (arc != INVALID) return arc;
+          arc = Parent::findArc(t, s);
+          if (arc != INVALID) return arc;	
+        } else {
+          Edge arc = Parent::findArc(t, s, p);
+          if (arc != INVALID) return arc;	      
+        }
+      } else {
+        return Parent::findArc(s, t, p);
+      }
+      return INVALID;
+    }
+  };
+
+  template <typename Base>
+  class BidirBpGraphExtender : public Base {
+  public:
+    typedef Base Parent;
+    typedef BidirBpGraphExtender Digraph;
+
+    typedef typename Parent::Node Node;
+    typedef typename Parent::Edge Edge;
+
+
+    using Parent::first;
+    using Parent::next;
+
+    using Parent::id;
+
+    class Red : public Node {
+      friend class BidirBpGraphExtender;
+    public:
+      Red() {}
+      Red(const Node& node) : Node(node) {
+	LEMON_ASSERT(Parent::red(node) || node == INVALID, 
+		     typename Parent::NodeSetError());
+      }
+      Red& operator=(const Node& node) {
+	LEMON_ASSERT(Parent::red(node) || node == INVALID, 
+		     typename Parent::NodeSetError());
+        Node::operator=(node);
+        return *this;
+      }
+      Red(Invalid) : Node(INVALID) {}
+      Red& operator=(Invalid) {
+        Node::operator=(INVALID);
+        return *this;
+      }
+    };
+
+    void first(Red& node) const {
+      Parent::firstRed(static_cast<Node&>(node));
+    }
+    void next(Red& node) const {
+      Parent::nextRed(static_cast<Node&>(node));
+    }
+
+    int id(const Red& node) const {
+      return Parent::redId(node);
+    }
+
+    class Blue : public Node {
+      friend class BidirBpGraphExtender;
+    public:
+      Blue() {}
+      Blue(const Node& node) : Node(node) {
+	LEMON_ASSERT(Parent::blue(node) || node == INVALID,
+		     typename Parent::NodeSetError());
+      }
+      Blue& operator=(const Node& node) {
+	LEMON_ASSERT(Parent::blue(node) || node == INVALID, 
+		     typename Parent::NodeSetError());
+        Node::operator=(node);
+        return *this;
+      }
+      Blue(Invalid) : Node(INVALID) {}
+      Blue& operator=(Invalid) {
+        Node::operator=(INVALID);
+        return *this;
+      }
+    };
+
+    void first(Blue& node) const {
+      Parent::firstBlue(static_cast<Node&>(node));
+    }
+    void next(Blue& node) const {
+      Parent::nextBlue(static_cast<Node&>(node));
+    }
+  
+    int id(const Blue& node) const {
+      return Parent::redId(node);
+    }
+
+    Node source(const Edge& arc) const {
+      return red(arc);
+    }
+    Node target(const Edge& arc) const {
+      return blue(arc);
+    }
+
+    void firstInc(Edge& arc, bool& dir, const Node& node) const {
+      if (Parent::red(node)) {
+	Parent::firstFromRed(arc, node);
+	dir = true;
+      } else {
+	Parent::firstFromBlue(arc, node);
+	dir = static_cast<Edge&>(arc) == INVALID;
+      }
+    }
+    void nextInc(Edge& arc, bool& dir) const {
+      if (dir) {
+	Parent::nextFromRed(arc);
+      } else {
+	Parent::nextFromBlue(arc);
+	if (arc == INVALID) dir = true;
+      }
+    }
+
+    class Arc : public Edge {
+      friend class BidirBpGraphExtender;
+    protected:
+      bool forward;
+
+      Arc(const Edge& arc, bool _forward)
+	: Edge(arc), forward(_forward) {}
+
+    public:
+      Arc() {}
+      Arc (Invalid) : Edge(INVALID), forward(true) {}
+      bool operator==(const Arc& i) const {
+	return Edge::operator==(i) && forward == i.forward;
+      }
+      bool operator!=(const Arc& i) const {
+	return Edge::operator!=(i) || forward != i.forward;
+      }
+      bool operator<(const Arc& i) const {
+	return Edge::operator<(i) || 
+	  (!(i.forward<forward) && Edge(*this)<Edge(i));
+      }
+    };
+
+    void first(Arc& arc) const {
+      Parent::first(static_cast<Edge&>(arc));
+      arc.forward = true;
+    }
+
+    void next(Arc& arc) const {
+      if (!arc.forward) {
+	Parent::next(static_cast<Edge&>(arc));
+      }
+      arc.forward = !arc.forward;
+    }
+
+    void firstOut(Arc& arc, const Node& node) const {
+      if (Parent::red(node)) {
+	Parent::firstFromRed(arc, node);
+	arc.forward = true;
+      } else {
+	Parent::firstFromBlue(arc, node);
+	arc.forward = static_cast<Edge&>(arc) == INVALID;
+      }
+    }
+    void nextOut(Arc& arc) const {
+      if (arc.forward) {
+	Parent::nextFromRed(arc);
+      } else {
+	Parent::nextFromBlue(arc);
+        arc.forward = static_cast<Edge&>(arc) == INVALID;
+      }
+    }
+
+    void firstIn(Arc& arc, const Node& node) const {
+      if (Parent::blue(node)) {
+	Parent::firstFromBlue(arc, node);
+	arc.forward = true;	
+      } else {
+	Parent::firstFromRed(arc, node);
+	arc.forward = static_cast<Edge&>(arc) == INVALID;
+      }
+    }
+    void nextIn(Arc& arc) const {
+      if (arc.forward) {
+	Parent::nextFromBlue(arc);
+      } else {
+	Parent::nextFromRed(arc);
+	arc.forward = static_cast<Edge&>(arc) == INVALID;
+      }
+    }
+
+    Node source(const Arc& arc) const {
+      return arc.forward ? Parent::red(arc) : Parent::blue(arc);
+    }
+    Node target(const Arc& arc) const {
+      return arc.forward ? Parent::blue(arc) : Parent::red(arc);
+    }
+
+    int id(const Arc& arc) const {
+      return (Parent::id(static_cast<const Edge&>(arc)) << 1) + 
+        (arc.forward ? 0 : 1);
+    }
+    Arc arcFromId(int ix) const {
+      return Arc(Parent::fromEdgeId(ix >> 1), (ix & 1) == 0);
+    }
+    int maxArcId() const {
+      return (Parent::maxEdgeId() << 1) + 1;
+    }
+
+    bool direction(const Arc& arc) const {
+      return arc.forward;
+    }
+
+    Arc direct(const Edge& arc, bool dir) const {
+      return Arc(arc, dir);
+    }
+
+    int arcNum() const {
+      return 2 * Parent::edgeNum();
+    }
+
+    int edgeNum() const {
+      return Parent::edgeNum();
+    }
+
+
+  };
+}
+
+#endif
Index: lemon/bits/default_map.h
===================================================================
--- lemon/bits/default_map.h	(revision 57)
+++ lemon/bits/default_map.h	(revision 57)
@@ -0,0 +1,181 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2007
+ * 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_DEFAULT_MAP_H
+#define LEMON_BITS_DEFAULT_MAP_H
+
+
+#include <lemon/bits/array_map.h>
+#include <lemon/bits/vector_map.h>
+//#include <lemon/bits/debug_map.h>
+
+///\ingroup graphbits
+///\file
+///\brief Graph maps that construct and destruct their elements dynamically.
+
+namespace lemon {
+  
+  
+  //#ifndef LEMON_USE_DEBUG_MAP
+
+  template <typename _Graph, typename _Item, typename _Value>
+  struct DefaultMapSelector {
+    typedef ArrayMap<_Graph, _Item, _Value> Map;
+  };
+
+  // bool
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, bool> {
+    typedef VectorMap<_Graph, _Item, bool> Map;
+  };
+
+  // char
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, char> {
+    typedef VectorMap<_Graph, _Item, char> Map;
+  };
+
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, signed char> {
+    typedef VectorMap<_Graph, _Item, signed char> Map;
+  };
+
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, unsigned char> {
+    typedef VectorMap<_Graph, _Item, unsigned char> Map;
+  };
+
+
+  // int
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, signed int> {
+    typedef VectorMap<_Graph, _Item, signed int> Map;
+  };
+
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, unsigned int> {
+    typedef VectorMap<_Graph, _Item, unsigned int> Map;
+  };
+
+
+  // short
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, signed short> {
+    typedef VectorMap<_Graph, _Item, signed short> Map;
+  };
+
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, unsigned short> {
+    typedef VectorMap<_Graph, _Item, unsigned short> Map;
+  };
+
+
+  // long
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, signed long> {
+    typedef VectorMap<_Graph, _Item, signed long> Map;
+  };
+
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, unsigned long> {
+    typedef VectorMap<_Graph, _Item, unsigned long> Map;
+  };
+
+
+#if defined __GNUC__ && !defined __STRICT_ANSI__
+
+  // long long
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, signed long long> {
+    typedef VectorMap<_Graph, _Item, signed long long> Map;
+  };
+
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, unsigned long long> {
+    typedef VectorMap<_Graph, _Item, unsigned long long> Map;
+  };
+
+#endif
+
+
+  // float
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, float> {
+    typedef VectorMap<_Graph, _Item, float> Map;
+  };
+
+
+  // double
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, double> {
+    typedef VectorMap<_Graph, _Item,  double> Map;
+  };
+
+
+  // long double
+  template <typename _Graph, typename _Item>
+  struct DefaultMapSelector<_Graph, _Item, long double> {
+    typedef VectorMap<_Graph, _Item, long double> Map;
+  };
+
+
+  // pointer
+  template <typename _Graph, typename _Item, typename _Ptr>
+  struct DefaultMapSelector<_Graph, _Item, _Ptr*> {
+    typedef VectorMap<_Graph, _Item, _Ptr*> Map;
+  };
+
+// #else 
+
+//   template <typename _Graph, typename _Item, typename _Value>
+//   struct DefaultMapSelector {
+//     typedef DebugMap<_Graph, _Item, _Value> Map;
+//   };
+
+// #endif  
+
+  /// \e
+  template <typename _Graph, typename _Item, typename _Value>
+  class DefaultMap 
+    : public DefaultMapSelector<_Graph, _Item, _Value>::Map {
+  public:
+    typedef typename DefaultMapSelector<_Graph, _Item, _Value>::Map Parent;
+    typedef DefaultMap<_Graph, _Item, _Value> Map;
+    
+    typedef typename Parent::Graph Graph;
+    typedef typename Parent::Value Value;
+
+    explicit DefaultMap(const Graph& graph) : Parent(graph) {}
+    DefaultMap(const Graph& graph, const Value& value) 
+      : Parent(graph, value) {}
+
+    DefaultMap& operator=(const DefaultMap& cmap) {
+      return operator=<DefaultMap>(cmap);
+    }
+
+    template <typename CMap>
+    DefaultMap& operator=(const CMap& cmap) {
+      Parent::operator=(cmap);
+      return *this;
+    }
+
+  };
+
+}
+
+#endif
Index: lemon/bits/graph_extender.h
===================================================================
--- lemon/bits/graph_extender.h	(revision 57)
+++ lemon/bits/graph_extender.h	(revision 57)
@@ -0,0 +1,747 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2007
+ * 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_GRAPH_EXTENDER_H
+#define LEMON_BITS_GRAPH_EXTENDER_H
+
+#include <lemon/bits/invalid.h>
+
+#include <lemon/bits/map_extender.h>
+#include <lemon/bits/default_map.h>
+
+#include <lemon/concept_check.h>
+#include <lemon/concepts/maps.h>
+
+///\ingroup graphbits
+///\file
+///\brief Extenders for the digraph types
+namespace lemon {
+
+  /// \ingroup graphbits
+  ///
+  /// \brief Extender for the Digraphs
+  template <typename Base>
+  class DigraphExtender : public Base {
+  public:
+
+    typedef Base Parent;
+    typedef DigraphExtender Digraph;
+
+    // Base extensions
+
+    typedef typename Parent::Node Node;
+    typedef typename Parent::Arc Arc;
+
+    int maxId(Node) const {
+      return Parent::maxNodeId();
+    }
+
+    int maxId(Arc) const {
+      return Parent::maxArcId();
+    }
+
+    Node fromId(int id, Node) const {
+      return Parent::nodeFromId(id);
+    }
+
+    Arc fromId(int id, Arc) const {
+      return Parent::arcFromId(id);
+    }
+
+    Node oppositeNode(const Node &n, const Arc &e) const {
+      if (n == Parent::source(e))
+	return Parent::target(e);
+      else if(n==Parent::target(e))
+	return Parent::source(e);
+      else
+	return INVALID;
+    }
+
+    // Alterable extension
+
+    typedef AlterationNotifier<DigraphExtender, Node> NodeNotifier;
+    typedef AlterationNotifier<DigraphExtender, Arc> ArcNotifier;
+
+
+  protected:
+
+    mutable NodeNotifier node_notifier;
+    mutable ArcNotifier arc_notifier;
+
+  public:
+
+    NodeNotifier& notifier(Node) const {
+      return node_notifier;
+    }
+    
+    ArcNotifier& notifier(Arc) const {
+      return arc_notifier;
+    }
+
+    class NodeIt : public Node { 
+      const Digraph* digraph;
+    public:
+
+      NodeIt() {}
+
+      NodeIt(Invalid i) : Node(i) { }
+
+      explicit NodeIt(const Digraph& _digraph) : digraph(&_digraph) {
+	_digraph.first(static_cast<Node&>(*this));
+      }
+
+      NodeIt(const Digraph& _digraph, const Node& node) 
+	: Node(node), digraph(&_digraph) {}
+
+      NodeIt& operator++() { 
+	digraph->next(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class ArcIt : public Arc { 
+      const Digraph* digraph;
+    public:
+
+      ArcIt() { }
+
+      ArcIt(Invalid i) : Arc(i) { }
+
+      explicit ArcIt(const Digraph& _digraph) : digraph(&_digraph) {
+	_digraph.first(static_cast<Arc&>(*this));
+      }
+
+      ArcIt(const Digraph& _digraph, const Arc& e) : 
+	Arc(e), digraph(&_digraph) { }
+
+      ArcIt& operator++() { 
+	digraph->next(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class OutArcIt : public Arc { 
+      const Digraph* digraph;
+    public:
+
+      OutArcIt() { }
+
+      OutArcIt(Invalid i) : Arc(i) { }
+
+      OutArcIt(const Digraph& _digraph, const Node& node) 
+	: digraph(&_digraph) {
+	_digraph.firstOut(*this, node);
+      }
+
+      OutArcIt(const Digraph& _digraph, const Arc& arc) 
+	: Arc(arc), digraph(&_digraph) {}
+
+      OutArcIt& operator++() { 
+	digraph->nextOut(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class InArcIt : public Arc { 
+      const Digraph* digraph;
+    public:
+
+      InArcIt() { }
+
+      InArcIt(Invalid i) : Arc(i) { }
+
+      InArcIt(const Digraph& _digraph, const Node& node) 
+	: digraph(&_digraph) {
+	_digraph.firstIn(*this, node);
+      }
+
+      InArcIt(const Digraph& _digraph, const Arc& arc) : 
+	Arc(arc), digraph(&_digraph) {}
+
+      InArcIt& operator++() { 
+	digraph->nextIn(*this);
+	return *this; 
+      }
+
+    };
+
+    /// \brief Base node of the iterator
+    ///
+    /// Returns the base node (i.e. the source in this case) of the iterator
+    Node baseNode(const OutArcIt &e) const {
+      return Parent::source(e);
+    }
+    /// \brief Running node of the iterator
+    ///
+    /// Returns the running node (i.e. the target in this case) of the
+    /// iterator
+    Node runningNode(const OutArcIt &e) const {
+      return Parent::target(e);
+    }
+
+    /// \brief Base node of the iterator
+    ///
+    /// Returns the base node (i.e. the target in this case) of the iterator
+    Node baseNode(const InArcIt &e) const {
+      return Parent::target(e);
+    }
+    /// \brief Running node of the iterator
+    ///
+    /// Returns the running node (i.e. the source in this case) of the
+    /// iterator
+    Node runningNode(const InArcIt &e) const {
+      return Parent::source(e);
+    }
+
+    
+    template <typename _Value>
+    class NodeMap 
+      : public MapExtender<DefaultMap<Digraph, Node, _Value> > {
+    public:
+      typedef DigraphExtender Digraph;
+      typedef MapExtender<DefaultMap<Digraph, Node, _Value> > Parent;
+
+      explicit NodeMap(const Digraph& digraph) 
+	: Parent(digraph) {}
+      NodeMap(const Digraph& digraph, const _Value& value) 
+	: Parent(digraph, value) {}
+
+      NodeMap& operator=(const NodeMap& cmap) {
+	return operator=<NodeMap>(cmap);
+      }
+
+      template <typename CMap>
+      NodeMap& operator=(const CMap& cmap) {
+        Parent::operator=(cmap);
+	return *this;
+      }
+
+    };
+
+    template <typename _Value>
+    class ArcMap 
+      : public MapExtender<DefaultMap<Digraph, Arc, _Value> > {
+    public:
+      typedef DigraphExtender Digraph;
+      typedef MapExtender<DefaultMap<Digraph, Arc, _Value> > Parent;
+
+      explicit ArcMap(const Digraph& digraph) 
+	: Parent(digraph) {}
+      ArcMap(const Digraph& digraph, const _Value& value) 
+	: Parent(digraph, value) {}
+
+      ArcMap& operator=(const ArcMap& cmap) {
+	return operator=<ArcMap>(cmap);
+      }
+
+      template <typename CMap>
+      ArcMap& operator=(const CMap& cmap) {
+        Parent::operator=(cmap);
+	return *this;
+      }
+    };
+
+
+    Node addNode() {
+      Node node = Parent::addNode();
+      notifier(Node()).add(node);
+      return node;
+    }
+    
+    Arc addArc(const Node& from, const Node& to) {
+      Arc arc = Parent::addArc(from, to);
+      notifier(Arc()).add(arc);
+      return arc;
+    }
+
+    void clear() {
+      notifier(Arc()).clear();
+      notifier(Node()).clear();
+      Parent::clear();
+    }
+
+    template <typename Digraph, typename NodeRefMap, typename ArcRefMap>
+    void build(const Digraph& digraph, NodeRefMap& nodeRef, ArcRefMap& arcRef) {
+      Parent::build(digraph, nodeRef, arcRef);
+      notifier(Node()).build();
+      notifier(Arc()).build();
+    }
+
+    void erase(const Node& node) {
+      Arc arc;
+      Parent::firstOut(arc, node);
+      while (arc != INVALID ) {
+	erase(arc);
+	Parent::firstOut(arc, node);
+      } 
+
+      Parent::firstIn(arc, node);
+      while (arc != INVALID ) {
+	erase(arc);
+	Parent::firstIn(arc, node);
+      }
+
+      notifier(Node()).erase(node);
+      Parent::erase(node);
+    }
+    
+    void erase(const Arc& arc) {
+      notifier(Arc()).erase(arc);
+      Parent::erase(arc);
+    }
+
+    DigraphExtender() {
+      node_notifier.setContainer(*this);
+      arc_notifier.setContainer(*this);
+    } 
+    
+
+    ~DigraphExtender() {
+      arc_notifier.clear();
+      node_notifier.clear();
+    }
+  };
+
+  /// \ingroup graphbits
+  ///
+  /// \brief Extender for the Graphs
+  template <typename Base> 
+  class GraphExtender : public Base {
+  public:
+    
+    typedef Base Parent;
+    typedef GraphExtender Digraph;
+
+    typedef typename Parent::Node Node;
+    typedef typename Parent::Arc Arc;
+    typedef typename Parent::Edge Edge;
+
+    // Graph extension    
+
+    int maxId(Node) const {
+      return Parent::maxNodeId();
+    }
+
+    int maxId(Arc) const {
+      return Parent::maxArcId();
+    }
+
+    int maxId(Edge) const {
+      return Parent::maxEdgeId();
+    }
+
+    Node fromId(int id, Node) const {
+      return Parent::nodeFromId(id);
+    }
+
+    Arc fromId(int id, Arc) const {
+      return Parent::arcFromId(id);
+    }
+
+    Edge fromId(int id, Edge) const {
+      return Parent::edgeFromId(id);
+    }
+
+    Node oppositeNode(const Node &n, const Edge &e) const {
+      if( n == Parent::source(e))
+	return Parent::target(e);
+      else if( n == Parent::target(e))
+	return Parent::source(e);
+      else
+	return INVALID;
+    }
+
+    Arc oppositeArc(const Arc &e) const {
+      return Parent::direct(e, !Parent::direction(e));
+    }
+
+    using Parent::direct;
+    Arc direct(const Edge &ue, const Node &s) const {
+      return Parent::direct(ue, Parent::source(ue) == s);
+    }
+
+    // Alterable extension
+
+    typedef AlterationNotifier<GraphExtender, Node> NodeNotifier;
+    typedef AlterationNotifier<GraphExtender, Arc> ArcNotifier;
+    typedef AlterationNotifier<GraphExtender, Edge> EdgeNotifier;
+
+
+  protected:
+
+    mutable NodeNotifier node_notifier;
+    mutable ArcNotifier arc_notifier;
+    mutable EdgeNotifier edge_notifier;
+
+  public:
+
+    NodeNotifier& notifier(Node) const {
+      return node_notifier;
+    }
+    
+    ArcNotifier& notifier(Arc) const {
+      return arc_notifier;
+    }
+
+    EdgeNotifier& notifier(Edge) const {
+      return edge_notifier;
+    }
+
+
+
+    class NodeIt : public Node { 
+      const Digraph* digraph;
+    public:
+
+      NodeIt() {}
+
+      NodeIt(Invalid i) : Node(i) { }
+
+      explicit NodeIt(const Digraph& _digraph) : digraph(&_digraph) {
+	_digraph.first(static_cast<Node&>(*this));
+      }
+
+      NodeIt(const Digraph& _digraph, const Node& node) 
+	: Node(node), digraph(&_digraph) {}
+
+      NodeIt& operator++() { 
+	digraph->next(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class ArcIt : public Arc { 
+      const Digraph* digraph;
+    public:
+
+      ArcIt() { }
+
+      ArcIt(Invalid i) : Arc(i) { }
+
+      explicit ArcIt(const Digraph& _digraph) : digraph(&_digraph) {
+	_digraph.first(static_cast<Arc&>(*this));
+      }
+
+      ArcIt(const Digraph& _digraph, const Arc& e) : 
+	Arc(e), digraph(&_digraph) { }
+
+      ArcIt& operator++() { 
+	digraph->next(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class OutArcIt : public Arc { 
+      const Digraph* digraph;
+    public:
+
+      OutArcIt() { }
+
+      OutArcIt(Invalid i) : Arc(i) { }
+
+      OutArcIt(const Digraph& _digraph, const Node& node) 
+	: digraph(&_digraph) {
+	_digraph.firstOut(*this, node);
+      }
+
+      OutArcIt(const Digraph& _digraph, const Arc& arc) 
+	: Arc(arc), digraph(&_digraph) {}
+
+      OutArcIt& operator++() { 
+	digraph->nextOut(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class InArcIt : public Arc { 
+      const Digraph* digraph;
+    public:
+
+      InArcIt() { }
+
+      InArcIt(Invalid i) : Arc(i) { }
+
+      InArcIt(const Digraph& _digraph, const Node& node) 
+	: digraph(&_digraph) {
+	_digraph.firstIn(*this, node);
+      }
+
+      InArcIt(const Digraph& _digraph, const Arc& arc) : 
+	Arc(arc), digraph(&_digraph) {}
+
+      InArcIt& operator++() { 
+	digraph->nextIn(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class EdgeIt : public Parent::Edge { 
+      const Digraph* digraph;
+    public:
+
+      EdgeIt() { }
+
+      EdgeIt(Invalid i) : Edge(i) { }
+
+      explicit EdgeIt(const Digraph& _digraph) : digraph(&_digraph) {
+	_digraph.first(static_cast<Edge&>(*this));
+      }
+
+      EdgeIt(const Digraph& _digraph, const Edge& e) : 
+	Edge(e), digraph(&_digraph) { }
+
+      EdgeIt& operator++() { 
+	digraph->next(*this);
+	return *this; 
+      }
+
+    };
+
+    class IncArcIt : public Parent::Edge {
+      friend class GraphExtender;
+      const Digraph* digraph;
+      bool direction;
+    public:
+
+      IncArcIt() { }
+
+      IncArcIt(Invalid i) : Edge(i), direction(false) { }
+
+      IncArcIt(const Digraph& _digraph, const Node &n) : digraph(&_digraph) {
+	_digraph.firstInc(*this, direction, n);
+      }
+
+      IncArcIt(const Digraph& _digraph, const Edge &ue, const Node &n)
+	: digraph(&_digraph), Edge(ue) {
+	direction = (_digraph.source(ue) == n);
+      }
+
+      IncArcIt& operator++() {
+	digraph->nextInc(*this, direction);
+	return *this; 
+      }
+    };
+
+    /// \brief Base node of the iterator
+    ///
+    /// Returns the base node (ie. the source in this case) of the iterator
+    Node baseNode(const OutArcIt &e) const {
+      return Parent::source(static_cast<const Arc&>(e));
+    }
+    /// \brief Running node of the iterator
+    ///
+    /// Returns the running node (ie. the target in this case) of the
+    /// iterator
+    Node runningNode(const OutArcIt &e) const {
+      return Parent::target(static_cast<const Arc&>(e));
+    }
+
+    /// \brief Base node of the iterator
+    ///
+    /// Returns the base node (ie. the target in this case) of the iterator
+    Node baseNode(const InArcIt &e) const {
+      return Parent::target(static_cast<const Arc&>(e));
+    }
+    /// \brief Running node of the iterator
+    ///
+    /// Returns the running node (ie. the source in this case) of the
+    /// iterator
+    Node runningNode(const InArcIt &e) const {
+      return Parent::source(static_cast<const Arc&>(e));
+    }
+
+    /// Base node of the iterator
+    ///
+    /// Returns the base node of the iterator
+    Node baseNode(const IncArcIt &e) const {
+      return e.direction ? source(e) : target(e);
+    }
+    /// Running node of the iterator
+    ///
+    /// Returns the running node of the iterator
+    Node runningNode(const IncArcIt &e) const {
+      return e.direction ? target(e) : source(e);
+    }
+
+    // Mappable extension
+
+    template <typename _Value>
+    class NodeMap 
+      : public MapExtender<DefaultMap<Digraph, Node, _Value> > {
+    public:
+      typedef GraphExtender Digraph;
+      typedef MapExtender<DefaultMap<Digraph, Node, _Value> > Parent;
+
+      NodeMap(const Digraph& digraph) 
+	: Parent(digraph) {}
+      NodeMap(const Digraph& digraph, const _Value& value) 
+	: Parent(digraph, value) {}
+
+      NodeMap& operator=(const NodeMap& cmap) {
+	return operator=<NodeMap>(cmap);
+      }
+
+      template <typename CMap>
+      NodeMap& operator=(const CMap& cmap) {
+        Parent::operator=(cmap);
+	return *this;
+      }
+
+    };
+
+    template <typename _Value>
+    class ArcMap 
+      : public MapExtender<DefaultMap<Digraph, Arc, _Value> > {
+    public:
+      typedef GraphExtender Digraph;
+      typedef MapExtender<DefaultMap<Digraph, Arc, _Value> > Parent;
+
+      ArcMap(const Digraph& digraph) 
+	: Parent(digraph) {}
+      ArcMap(const Digraph& digraph, const _Value& value) 
+	: Parent(digraph, value) {}
+
+      ArcMap& operator=(const ArcMap& cmap) {
+	return operator=<ArcMap>(cmap);
+      }
+
+      template <typename CMap>
+      ArcMap& operator=(const CMap& cmap) {
+        Parent::operator=(cmap);
+	return *this;
+      }
+    };
+
+
+    template <typename _Value>
+    class EdgeMap 
+      : public MapExtender<DefaultMap<Digraph, Edge, _Value> > {
+    public:
+      typedef GraphExtender Digraph;
+      typedef MapExtender<DefaultMap<Digraph, Edge, _Value> > Parent;
+
+      EdgeMap(const Digraph& digraph) 
+	: Parent(digraph) {}
+
+      EdgeMap(const Digraph& digraph, const _Value& value) 
+	: Parent(digraph, value) {}
+
+      EdgeMap& operator=(const EdgeMap& cmap) {
+	return operator=<EdgeMap>(cmap);
+      }
+
+      template <typename CMap>
+      EdgeMap& operator=(const CMap& cmap) {
+        Parent::operator=(cmap);
+	return *this;
+      }
+
+    };
+
+    // Alteration extension
+
+    Node addNode() {
+      Node node = Parent::addNode();
+      notifier(Node()).add(node);
+      return node;
+    }
+
+    Edge addEdge(const Node& from, const Node& to) {
+      Edge edge = Parent::addEdge(from, to);
+      notifier(Edge()).add(edge);
+      std::vector<Arc> ev;
+      ev.push_back(Parent::direct(edge, true));
+      ev.push_back(Parent::direct(edge, false));      
+      notifier(Arc()).add(ev);
+      return edge;
+    }
+    
+    void clear() {
+      notifier(Arc()).clear();
+      notifier(Edge()).clear();
+      notifier(Node()).clear();
+      Parent::clear();
+    }
+
+    template <typename Digraph, typename NodeRefMap, typename EdgeRefMap>
+    void build(const Digraph& digraph, NodeRefMap& nodeRef, 
+               EdgeRefMap& edgeRef) {
+      Parent::build(digraph, nodeRef, edgeRef);
+      notifier(Node()).build();
+      notifier(Edge()).build();
+      notifier(Arc()).build();
+    }
+
+    void erase(const Node& node) {
+      Arc arc;
+      Parent::firstOut(arc, node);
+      while (arc != INVALID ) {
+	erase(arc);
+	Parent::firstOut(arc, node);
+      } 
+
+      Parent::firstIn(arc, node);
+      while (arc != INVALID ) {
+	erase(arc);
+	Parent::firstIn(arc, node);
+      }
+
+      notifier(Node()).erase(node);
+      Parent::erase(node);
+    }
+
+    void erase(const Edge& edge) {
+      std::vector<Arc> ev;
+      ev.push_back(Parent::direct(edge, true));
+      ev.push_back(Parent::direct(edge, false));      
+      notifier(Arc()).erase(ev);
+      notifier(Edge()).erase(edge);
+      Parent::erase(edge);
+    }
+
+    GraphExtender() {
+      node_notifier.setContainer(*this); 
+      arc_notifier.setContainer(*this);
+      edge_notifier.setContainer(*this);
+    } 
+
+    ~GraphExtender() {
+      edge_notifier.clear();
+      arc_notifier.clear();
+      node_notifier.clear(); 
+    } 
+
+  };
+
+}
+
+#endif
Index: lemon/bits/map_extender.h
===================================================================
--- lemon/bits/map_extender.h	(revision 57)
+++ lemon/bits/map_extender.h	(revision 57)
@@ -0,0 +1,321 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2007
+ * 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_MAP_EXTENDER_H
+#define LEMON_BITS_MAP_EXTENDER_H
+
+#include <iterator>
+
+#include <lemon/bits/traits.h>
+
+#include <lemon/concept_check.h>
+#include <lemon/concepts/maps.h>
+
+///\file
+///\brief Extenders for iterable maps.
+
+namespace lemon {
+
+  /// \ingroup graphbits
+  /// 
+  /// \brief Extender for maps
+  template <typename _Map>
+  class MapExtender : public _Map {
+  public:
+
+    typedef _Map Parent;
+    typedef MapExtender Map;
+
+
+    typedef typename Parent::Graph Graph;
+    typedef typename Parent::Key Item;
+
+    typedef typename Parent::Key Key;
+    typedef typename Parent::Value Value;
+
+    class MapIt;
+    class ConstMapIt;
+
+    friend class MapIt;
+    friend class ConstMapIt;
+
+  public:
+
+    MapExtender(const Graph& graph) 
+      : Parent(graph) {}
+
+    MapExtender(const Graph& graph, const Value& value) 
+      : Parent(graph, value) {}
+
+    MapExtender& operator=(const MapExtender& cmap) {
+      return operator=<MapExtender>(cmap);
+    }
+
+    template <typename CMap>
+    MapExtender& operator=(const CMap& cmap) {
+      Parent::operator=(cmap);
+      return *this;
+    } 
+
+    class MapIt : public Item {
+    public:
+      
+      typedef Item Parent;
+      typedef typename Map::Value Value;
+      
+      MapIt() {}
+
+      MapIt(Invalid i) : Parent(i) { }
+
+      explicit MapIt(Map& _map) : map(_map) {
+        map.notifier()->first(*this);
+      }
+
+      MapIt(const Map& _map, const Item& item) 
+	: Parent(item), map(_map) {}
+
+      MapIt& operator++() { 
+	map.notifier()->next(*this);
+	return *this; 
+      }
+      
+      typename MapTraits<Map>::ConstReturnValue operator*() const {
+	return map[*this];
+      }
+
+      typename MapTraits<Map>::ReturnValue operator*() {
+	return map[*this];
+      }
+      
+      void set(const Value& value) {
+	map.set(*this, value);
+      }
+      
+    protected:
+      Map& map;
+      
+    };
+
+    class ConstMapIt : public Item {
+    public:
+
+      typedef Item Parent;
+
+      typedef typename Map::Value Value;
+      
+      ConstMapIt() {}
+
+      ConstMapIt(Invalid i) : Parent(i) { }
+
+      explicit ConstMapIt(Map& _map) : map(_map) {
+        map.notifier()->first(*this);
+      }
+
+      ConstMapIt(const Map& _map, const Item& item) 
+	: Parent(item), map(_map) {}
+
+      ConstMapIt& operator++() { 
+	map.notifier()->next(*this);
+	return *this; 
+      }
+
+      typename MapTraits<Map>::ConstReturnValue operator*() const {
+	return map[*this];
+      }
+
+    protected:
+      const Map& map;
+    };
+
+    class ItemIt : public Item {
+    public:
+      
+      typedef Item Parent;
+      
+      ItemIt() {}
+
+      ItemIt(Invalid i) : Parent(i) { }
+
+      explicit ItemIt(Map& _map) : map(_map) {
+        map.notifier()->first(*this);
+      }
+
+      ItemIt(const Map& _map, const Item& item) 
+	: Parent(item), map(_map) {}
+
+      ItemIt& operator++() { 
+	map.notifier()->next(*this);
+	return *this; 
+      }
+
+    protected:
+      const Map& map;
+      
+    };
+  };
+
+  /// \ingroup graphbits
+  /// 
+  /// \brief Extender for maps which use a subset of the items.
+  template <typename _Graph, typename _Map>
+  class SubMapExtender : public _Map {
+  public:
+
+    typedef _Map Parent;
+    typedef SubMapExtender Map;
+
+    typedef _Graph Graph;
+
+    typedef typename Parent::Key Item;
+
+    typedef typename Parent::Key Key;
+    typedef typename Parent::Value Value;
+
+    class MapIt;
+    class ConstMapIt;
+
+    friend class MapIt;
+    friend class ConstMapIt;
+
+  public:
+
+    SubMapExtender(const Graph& _graph) 
+      : Parent(_graph), graph(_graph) {}
+
+    SubMapExtender(const Graph& _graph, const Value& _value) 
+      : Parent(_graph, _value), graph(_graph) {}
+
+    SubMapExtender& operator=(const SubMapExtender& cmap) {
+      return operator=<MapExtender>(cmap);
+    }
+
+    template <typename CMap>
+    SubMapExtender& operator=(const CMap& cmap) {
+      checkConcept<concepts::ReadMap<Key, Value>, CMap>();
+      Item it;
+      for (graph.first(it); it != INVALID; graph.next(it)) {
+        Parent::set(it, cmap[it]);
+      }
+      return *this;
+    } 
+
+    class MapIt : public Item {
+    public:
+      
+      typedef Item Parent;
+      typedef typename Map::Value Value;
+      
+      MapIt() {}
+
+      MapIt(Invalid i) : Parent(i) { }
+
+      explicit MapIt(Map& _map) : map(_map) {
+        map.graph.first(*this);
+      }
+
+      MapIt(const Map& _map, const Item& item) 
+	: Parent(item), map(_map) {}
+
+      MapIt& operator++() { 
+	map.graph.next(*this);
+	return *this; 
+      }
+      
+      typename MapTraits<Map>::ConstReturnValue operator*() const {
+	return map[*this];
+      }
+
+      typename MapTraits<Map>::ReturnValue operator*() {
+	return map[*this];
+      }
+      
+      void set(const Value& value) {
+	map.set(*this, value);
+      }
+      
+    protected:
+      Map& map;
+      
+    };
+
+    class ConstMapIt : public Item {
+    public:
+
+      typedef Item Parent;
+
+      typedef typename Map::Value Value;
+      
+      ConstMapIt() {}
+
+      ConstMapIt(Invalid i) : Parent(i) { }
+
+      explicit ConstMapIt(Map& _map) : map(_map) {
+        map.graph.first(*this);
+      }
+
+      ConstMapIt(const Map& _map, const Item& item) 
+	: Parent(item), map(_map) {}
+
+      ConstMapIt& operator++() { 
+	map.graph.next(*this);
+	return *this; 
+      }
+
+      typename MapTraits<Map>::ConstReturnValue operator*() const {
+	return map[*this];
+      }
+
+    protected:
+      const Map& map;
+    };
+
+    class ItemIt : public Item {
+    public:
+      
+      typedef Item Parent;
+      
+      ItemIt() {}
+
+      ItemIt(Invalid i) : Parent(i) { }
+
+      explicit ItemIt(Map& _map) : map(_map) {
+        map.graph.first(*this);
+      }
+
+      ItemIt(const Map& _map, const Item& item) 
+	: Parent(item), map(_map) {}
+
+      ItemIt& operator++() { 
+	map.graph.next(*this);
+	return *this; 
+      }
+
+    protected:
+      const Map& map;
+      
+    };
+    
+  private:
+
+    const Graph& graph;
+    
+  };
+
+}
+
+#endif
Index: lemon/bits/traits.h
===================================================================
--- lemon/bits/traits.h	(revision 57)
+++ lemon/bits/traits.h	(revision 57)
@@ -0,0 +1,272 @@
+
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2007
+ * 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_TRAITS_H
+#define LEMON_BITS_TRAITS_H
+
+#include <lemon/bits/utility.h>
+
+///\file
+///\brief Traits for graphs and maps
+///
+
+namespace lemon {
+  template <typename _Graph, typename _Item>
+  class ItemSetTraits {};
+  
+
+  template <typename Graph, typename Enable = void>
+  struct NodeNotifierIndicator {
+    typedef InvalidType Type;
+  };
+  template <typename Graph>
+  struct NodeNotifierIndicator<
+    Graph, 
+    typename enable_if<typename Graph::NodeNotifier::Notifier, void>::type
+  > { 
+    typedef typename Graph::NodeNotifier Type;
+  };
+
+  template <typename _Graph>
+  class ItemSetTraits<_Graph, typename _Graph::Node> {
+  public:
+    
+    typedef _Graph Graph;
+
+    typedef typename Graph::Node Item;
+    typedef typename Graph::NodeIt ItemIt;
+
+    typedef typename NodeNotifierIndicator<Graph>::Type ItemNotifier;
+
+    template <typename _Value>
+    class Map : public Graph::template NodeMap<_Value> {
+    public:
+      typedef typename Graph::template NodeMap<_Value> Parent; 
+      typedef typename Graph::template NodeMap<_Value> Type; 
+      typedef typename Parent::Value Value;
+
+      Map(const Graph& _digraph) : Parent(_digraph) {}
+      Map(const Graph& _digraph, const Value& _value) 
+	: Parent(_digraph, _value) {}
+
+     };
+
+  };
+
+  template <typename Graph, typename Enable = void>
+  struct ArcNotifierIndicator {
+    typedef InvalidType Type;
+  };
+  template <typename Graph>
+  struct ArcNotifierIndicator<
+    Graph, 
+    typename enable_if<typename Graph::ArcNotifier::Notifier, void>::type
+  > { 
+    typedef typename Graph::ArcNotifier Type;
+  };
+
+  template <typename _Graph>
+  class ItemSetTraits<_Graph, typename _Graph::Arc> {
+  public:
+    
+    typedef _Graph Graph;
+
+    typedef typename Graph::Arc Item;
+    typedef typename Graph::ArcIt ItemIt;
+
+    typedef typename ArcNotifierIndicator<Graph>::Type ItemNotifier;
+
+    template <typename _Value>
+    class Map : public Graph::template ArcMap<_Value> {
+    public:
+      typedef typename Graph::template ArcMap<_Value> Parent; 
+      typedef typename Graph::template ArcMap<_Value> Type; 
+      typedef typename Parent::Value Value;
+
+      Map(const Graph& _digraph) : Parent(_digraph) {}
+      Map(const Graph& _digraph, const Value& _value) 
+	: Parent(_digraph, _value) {}
+    };
+
+  };
+
+  template <typename Graph, typename Enable = void>
+  struct EdgeNotifierIndicator {
+    typedef InvalidType Type;
+  };
+  template <typename Graph>
+  struct EdgeNotifierIndicator<
+    Graph, 
+    typename enable_if<typename Graph::EdgeNotifier::Notifier, void>::type
+  > { 
+    typedef typename Graph::EdgeNotifier Type;
+  };
+
+  template <typename _Graph>
+  class ItemSetTraits<_Graph, typename _Graph::Edge> {
+  public:
+    
+    typedef _Graph Graph;
+
+    typedef typename Graph::Edge Item;
+    typedef typename Graph::EdgeIt ItemIt;
+
+    typedef typename EdgeNotifierIndicator<Graph>::Type ItemNotifier;
+
+    template <typename _Value>
+    class Map : public Graph::template EdgeMap<_Value> {
+    public:
+      typedef typename Graph::template EdgeMap<_Value> Parent; 
+      typedef typename Graph::template EdgeMap<_Value> Type; 
+      typedef typename Parent::Value Value;
+
+      Map(const Graph& _digraph) : Parent(_digraph) {}
+      Map(const Graph& _digraph, const Value& _value) 
+	: Parent(_digraph, _value) {}
+    };
+
+  };
+
+  template <typename Map, typename Enable = void>
+  struct MapTraits {
+    typedef False ReferenceMapTag;
+
+    typedef typename Map::Key Key;
+    typedef typename Map::Value Value;
+
+    typedef const Value ConstReturnValue;
+    typedef const Value ReturnValue;
+  };
+
+  template <typename Map>
+  struct MapTraits<
+    Map, typename enable_if<typename Map::ReferenceMapTag, void>::type > 
+  {
+    typedef True ReferenceMapTag;
+    
+    typedef typename Map::Key Key;
+    typedef typename Map::Value Value;
+
+    typedef typename Map::ConstReference ConstReturnValue;
+    typedef typename Map::Reference ReturnValue;
+
+    typedef typename Map::ConstReference ConstReference; 
+    typedef typename Map::Reference Reference;
+ };
+
+  template <typename MatrixMap, typename Enable = void>
+  struct MatrixMapTraits {
+    typedef False ReferenceMapTag;
+
+    typedef typename MatrixMap::FirstKey FirstKey;
+    typedef typename MatrixMap::SecondKey SecondKey;
+    typedef typename MatrixMap::Value Value;
+
+    typedef const Value ConstReturnValue;
+    typedef const Value ReturnValue;
+  };
+
+  template <typename MatrixMap>
+  struct MatrixMapTraits<
+    MatrixMap, typename enable_if<typename MatrixMap::ReferenceMapTag, 
+                                  void>::type > 
+  {
+    typedef True ReferenceMapTag;
+    
+    typedef typename MatrixMap::FirstKey FirstKey;
+    typedef typename MatrixMap::SecondKey SecondKey;
+    typedef typename MatrixMap::Value Value;
+
+    typedef typename MatrixMap::ConstReference ConstReturnValue;
+    typedef typename MatrixMap::Reference ReturnValue;
+
+    typedef typename MatrixMap::ConstReference ConstReference; 
+    typedef typename MatrixMap::Reference Reference;
+ };
+
+  // Indicators for the tags
+
+  template <typename Graph, typename Enable = void>
+  struct NodeNumTagIndicator {
+    static const bool value = false;
+  };
+
+  template <typename Graph>
+  struct NodeNumTagIndicator<
+    Graph, 
+    typename enable_if<typename Graph::NodeNumTag, void>::type
+  > {
+    static const bool value = true;
+  };
+
+  template <typename Graph, typename Enable = void>
+  struct ArcNumTagIndicator {
+    static const bool value = false;
+  };
+
+  template <typename Graph>
+  struct ArcNumTagIndicator<
+    Graph, 
+    typename enable_if<typename Graph::ArcNumTag, void>::type
+  > {
+    static const bool value = true;
+  };
+
+  template <typename Graph, typename Enable = void>
+  struct FindArcTagIndicator {
+    static const bool value = false;
+  };
+
+  template <typename Graph>
+  struct FindArcTagIndicator<
+    Graph, 
+    typename enable_if<typename Graph::FindArcTag, void>::type
+  > {
+    static const bool value = true;
+  };
+
+  template <typename Graph, typename Enable = void>
+  struct UndirectedTagIndicator {
+    static const bool value = false;
+  };
+
+  template <typename Graph>
+  struct UndirectedTagIndicator<
+    Graph, 
+    typename enable_if<typename Graph::UndirectedTag, void>::type
+  > {
+    static const bool value = true;
+  };
+
+  template <typename Graph, typename Enable = void>
+  struct BuildTagIndicator {
+    static const bool value = false;
+  };
+
+  template <typename Graph>
+  struct BuildTagIndicator<
+    Graph, 
+    typename enable_if<typename Graph::BuildTag, void>::type
+  > {
+    static const bool value = true;
+  };
+
+}
+
+#endif
Index: lemon/bits/vector_map.h
===================================================================
--- lemon/bits/vector_map.h	(revision 57)
+++ lemon/bits/vector_map.h	(revision 57)
@@ -0,0 +1,243 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2007
+ * 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_VECTOR_MAP_H
+#define LEMON_BITS_VECTOR_MAP_H
+
+#include <vector>
+#include <algorithm>
+
+#include <lemon/bits/traits.h>
+#include <lemon/bits/utility.h>
+
+#include <lemon/bits/alteration_notifier.h>
+
+#include <lemon/concept_check.h>
+#include <lemon/concepts/maps.h>
+
+///\ingroup graphbits
+///
+///\file
+///\brief Vector based graph maps.
+namespace lemon {
+
+  /// \ingroup graphbits
+  ///
+  /// \brief Graph map based on the std::vector storage.
+  ///
+  /// The VectorMap template class is graph map structure what
+  /// automatically updates the map when a key is added to or erased from
+  /// the map. This map type uses the std::vector to store the values.
+  ///
+  /// \param Notifier The AlterationNotifier that will notify this map.
+  /// \param Item The item type of the graph items.
+  /// \param Value The value type of the map.
+  /// 
+  /// \author Balazs Dezso  	
+  template <typename _Graph, typename _Item, typename _Value>
+  class VectorMap 
+    : public ItemSetTraits<_Graph, _Item>::ItemNotifier::ObserverBase {
+  private:
+		
+    /// The container type of the map.
+    typedef std::vector<_Value> Container;	
+
+  public:
+
+    /// The graph type of the map. 
+    typedef _Graph Graph;
+    /// The item type of the map.
+    typedef _Item Item;
+    /// The reference map tag.
+    typedef True ReferenceMapTag;
+
+    /// The key type of the map.
+    typedef _Item Key;
+    /// The value type of the map.
+    typedef _Value Value;
+
+    /// The notifier type.
+    typedef typename ItemSetTraits<_Graph, _Item>::ItemNotifier Notifier;
+
+    /// The map type.
+    typedef VectorMap Map;
+    /// The base class of the map.
+    typedef typename Notifier::ObserverBase Parent;
+
+    /// The reference type of the map;
+    typedef typename Container::reference Reference;
+    /// The const reference type of the map;
+    typedef typename Container::const_reference ConstReference;
+
+
+    /// \brief Constructor to attach the new map into the notifier.
+    ///
+    /// It constructs a map and attachs it into the notifier.
+    /// It adds all the items of the graph to the map.
+    VectorMap(const Graph& graph) {
+      Parent::attach(graph.notifier(Item()));
+      container.resize(Parent::notifier()->maxId() + 1);
+    }
+
+    /// \brief Constructor uses given value to initialize the map. 
+    ///
+    /// It constructs a map uses a given value to initialize the map. 
+    /// It adds all the items of the graph to the map.
+    VectorMap(const Graph& graph, const Value& value) {
+      Parent::attach(graph.notifier(Item()));
+      container.resize(Parent::notifier()->maxId() + 1, value);
+    }
+
+    /// \brief Copy constructor
+    ///
+    /// Copy constructor.
+    VectorMap(const VectorMap& _copy) : Parent() {
+      if (_copy.attached()) {
+	Parent::attach(*_copy.notifier());
+	container = _copy.container;
+      }
+    }
+
+    /// \brief Assign operator.
+    ///
+    /// This operator assigns for each item in the map the
+    /// value mapped to the same item in the copied map.  
+    /// The parameter map should be indiced with the same
+    /// itemset because this assign operator does not change
+    /// the container of the map. 
+    VectorMap& operator=(const VectorMap& cmap) {
+      return operator=<VectorMap>(cmap);
+    }
+
+
+    /// \brief Template assign operator.
+    ///
+    /// The given parameter should be conform to the ReadMap
+    /// concecpt and could be indiced by the current item set of
+    /// the NodeMap. In this case the value for each item
+    /// is assigned by the value of the given ReadMap. 
+    template <typename CMap>
+    VectorMap& operator=(const CMap& cmap) {
+      checkConcept<concepts::ReadMap<Key, _Value>, CMap>();
+      const typename Parent::Notifier* nf = Parent::notifier();
+      Item it;
+      for (nf->first(it); it != INVALID; nf->next(it)) {
+        set(it, cmap[it]);
+      }
+      return *this;
+    }
+    
+  public:
+
+    /// \brief The subcript operator.
+    ///
+    /// The subscript operator. The map can be subscripted by the
+    /// actual items of the graph.      
+    Reference operator[](const Key& key) {
+      return container[Parent::notifier()->id(key)];
+    } 
+		
+    /// \brief The const subcript operator.
+    ///
+    /// The const subscript operator. The map can be subscripted by the
+    /// actual items of the graph. 
+    ConstReference operator[](const Key& key) const {
+      return container[Parent::notifier()->id(key)];
+    }
+
+
+    /// \brief The setter function of the map.
+    ///
+    /// It the same as operator[](key) = value expression.
+    void set(const Key& key, const Value& value) {
+      (*this)[key] = value;
+    }
+
+  protected:
+
+    /// \brief Adds a new key to the map.
+    ///		
+    /// It adds a new key to the map. It called by the observer notifier
+    /// and it overrides the add() member function of the observer base.     
+    virtual void add(const Key& key) {
+      int id = Parent::notifier()->id(key);
+      if (id >= int(container.size())) {
+	container.resize(id + 1);
+      }
+    }
+
+    /// \brief Adds more new keys to the map.
+    ///		
+    /// It adds more new keys to the map. It called by the observer notifier
+    /// and it overrides the add() member function of the observer base.     
+    virtual void add(const std::vector<Key>& keys) {
+      int max = container.size() - 1;
+      for (int i = 0; i < int(keys.size()); ++i) {
+        int id = Parent::notifier()->id(keys[i]);
+        if (id >= max) {
+          max = id;
+        }
+      }
+      container.resize(max + 1);
+    }
+
+    /// \brief Erase a key from the map.
+    ///
+    /// Erase a key from the map. It called by the observer notifier
+    /// and it overrides the erase() member function of the observer base.     
+    virtual void erase(const Key& key) {
+      container[Parent::notifier()->id(key)] = Value();
+    }
+
+    /// \brief Erase more keys from the map.
+    ///
+    /// Erase more keys from the map. It called by the observer notifier
+    /// and it overrides the erase() member function of the observer base.     
+    virtual void erase(const std::vector<Key>& keys) {
+      for (int i = 0; i < int(keys.size()); ++i) {
+	container[Parent::notifier()->id(keys[i])] = Value();
+      }
+    }
+    
+    /// \brief Buildes the map.
+    ///	
+    /// It buildes the map. It called by the observer notifier
+    /// and it overrides the build() member function of the observer base.
+    virtual void build() { 
+      int size = Parent::notifier()->maxId() + 1;
+      container.reserve(size);
+      container.resize(size);
+    }
+
+    /// \brief Clear the map.
+    ///
+    /// It erase all items from the map. It called by the observer notifier
+    /// and it overrides the clear() member function of the observer base.     
+    virtual void clear() { 
+      container.clear();
+    }
+    
+  private:
+		
+    Container container;
+
+  };
+
+}
+
+#endif
Index: lemon/concepts/digraph.h
===================================================================
--- lemon/concepts/digraph.h	(revision 57)
+++ lemon/concepts/digraph.h	(revision 57)
@@ -0,0 +1,453 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2007
+ * 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_CONCEPT_DIGRAPH_H
+#define LEMON_CONCEPT_DIGRAPH_H
+
+///\ingroup graph_concepts
+///\file
+///\brief The concept of directed graphs.
+
+#include <lemon/bits/invalid.h>
+#include <lemon/bits/utility.h>
+#include <lemon/concepts/maps.h>
+#include <lemon/concept_check.h>
+#include <lemon/concepts/graph_components.h>
+
+namespace lemon {
+  namespace concepts {
+
+    /// \ingroup graph_concepts
+    ///
+    /// \brief Class describing the concept of directed graphs.
+    ///
+    /// This class describes the \ref concept "concept" of the
+    /// immutable directed digraphs.
+    ///
+    /// Note that actual digraph implementation like @ref ListDigraph or
+    /// @ref SmartDigraph may have several additional functionality.
+    ///
+    /// \sa concept
+    class Digraph {
+    private:
+      ///Digraphs are \e not copy constructible. Use DigraphCopy() instead.
+      
+      ///Digraphs are \e not copy constructible. Use DigraphCopy() instead.
+      ///
+      Digraph(const Digraph &) {};
+      ///\brief Assignment of \ref Digraph "Digraph"s to another ones are
+      ///\e not allowed. Use DigraphCopy() instead.
+      
+      ///Assignment of \ref Digraph "Digraph"s to another ones are
+      ///\e not allowed.  Use DigraphCopy() instead.
+
+      void operator=(const Digraph &) {}
+    public:
+      ///\e
+
+      /// Defalult constructor.
+
+      /// Defalult constructor.
+      ///
+      Digraph() { }
+      /// Class for identifying a node of the digraph
+
+      /// This class identifies a node of the digraph. It also serves
+      /// as a base class of the node iterators,
+      /// thus they will convert to this type.
+      class Node {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        Node() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        Node(const Node&) { }
+
+        /// Invalid constructor \& conversion.
+
+        /// This constructor initializes the iterator to be invalid.
+        /// \sa Invalid for more details.
+        Node(Invalid) { }
+        /// Equality operator
+
+        /// Two iterators are equal if and only if they point to the
+        /// same object or both are invalid.
+        bool operator==(Node) const { return true; }
+
+        /// Inequality operator
+        
+        /// \sa operator==(Node n)
+        ///
+        bool operator!=(Node) const { return true; }
+
+	/// Artificial ordering operator.
+	
+	/// To allow the use of digraph descriptors as key type in std::map or
+	/// similar associative container we require this.
+	///
+	/// \note This operator only have to define some strict ordering of
+	/// the items; this order has nothing to do with the iteration
+	/// ordering of the items.
+	bool operator<(Node) const { return false; }
+
+      };
+    
+      /// This iterator goes through each node.
+
+      /// This iterator goes through each node.
+      /// Its usage is quite simple, for example you can count the number
+      /// of nodes in digraph \c g of type \c Digraph like this:
+      ///\code
+      /// int count=0;
+      /// for (Digraph::NodeIt n(g); n!=INVALID; ++n) ++count;
+      ///\endcode
+      class NodeIt : public Node {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        NodeIt() { }
+        /// Copy constructor.
+        
+        /// Copy constructor.
+        ///
+        NodeIt(const NodeIt& n) : Node(n) { }
+        /// Invalid constructor \& conversion.
+
+        /// Initialize the iterator to be invalid.
+        /// \sa Invalid for more details.
+        NodeIt(Invalid) { }
+        /// Sets the iterator to the first node.
+
+        /// Sets the iterator to the first node of \c g.
+        ///
+        NodeIt(const Digraph&) { }
+        /// Node -> NodeIt conversion.
+
+        /// Sets the iterator to the node of \c the digraph pointed by 
+	/// the trivial iterator.
+        /// This feature necessitates that each time we 
+        /// iterate the arc-set, the iteration order is the same.
+        NodeIt(const Digraph&, const Node&) { }
+        /// Next node.
+
+        /// Assign the iterator to the next node.
+        ///
+        NodeIt& operator++() { return *this; }
+      };
+    
+    
+      /// Class for identifying an arc of the digraph
+
+      /// This class identifies an arc of the digraph. It also serves
+      /// as a base class of the arc iterators,
+      /// thus they will convert to this type.
+      class Arc {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        Arc() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        Arc(const Arc&) { }
+        /// Initialize the iterator to be invalid.
+
+        /// Initialize the iterator to be invalid.
+        ///
+        Arc(Invalid) { }
+        /// Equality operator
+
+        /// Two iterators are equal if and only if they point to the
+        /// same object or both are invalid.
+        bool operator==(Arc) const { return true; }
+        /// Inequality operator
+
+        /// \sa operator==(Arc n)
+        ///
+        bool operator!=(Arc) const { return true; }
+
+	/// Artificial ordering operator.
+	
+	/// To allow the use of digraph descriptors as key type in std::map or
+	/// similar associative container we require this.
+	///
+	/// \note This operator only have to define some strict ordering of
+	/// the items; this order has nothing to do with the iteration
+	/// ordering of the items.
+	bool operator<(Arc) const { return false; }
+      };
+    
+      /// This iterator goes trough the outgoing arcs of a node.
+
+      /// This iterator goes trough the \e outgoing arcs of a certain node
+      /// of a digraph.
+      /// Its usage is quite simple, for example you can count the number
+      /// of outgoing arcs of a node \c n
+      /// in digraph \c g of type \c Digraph as follows.
+      ///\code
+      /// int count=0;
+      /// for (Digraph::OutArcIt e(g, n); e!=INVALID; ++e) ++count;
+      ///\endcode
+    
+      class OutArcIt : public Arc {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        OutArcIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        OutArcIt(const OutArcIt& e) : Arc(e) { }
+        /// Initialize the iterator to be invalid.
+
+        /// Initialize the iterator to be invalid.
+        ///
+        OutArcIt(Invalid) { }
+        /// This constructor sets the iterator to the first outgoing arc.
+    
+        /// This constructor sets the iterator to the first outgoing arc of
+        /// the node.
+        OutArcIt(const Digraph&, const Node&) { }
+        /// Arc -> OutArcIt conversion
+
+        /// Sets the iterator to the value of the trivial iterator.
+	/// This feature necessitates that each time we 
+        /// iterate the arc-set, the iteration order is the same.
+        OutArcIt(const Digraph&, const Arc&) { }
+        ///Next outgoing arc
+        
+        /// Assign the iterator to the next 
+        /// outgoing arc of the corresponding node.
+        OutArcIt& operator++() { return *this; }
+      };
+
+      /// This iterator goes trough the incoming arcs of a node.
+
+      /// This iterator goes trough the \e incoming arcs of a certain node
+      /// of a digraph.
+      /// Its usage is quite simple, for example you can count the number
+      /// of outgoing arcs of a node \c n
+      /// in digraph \c g of type \c Digraph as follows.
+      ///\code
+      /// int count=0;
+      /// for(Digraph::InArcIt e(g, n); e!=INVALID; ++e) ++count;
+      ///\endcode
+
+      class InArcIt : public Arc {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        InArcIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        InArcIt(const InArcIt& e) : Arc(e) { }
+        /// Initialize the iterator to be invalid.
+
+        /// Initialize the iterator to be invalid.
+        ///
+        InArcIt(Invalid) { }
+        /// This constructor sets the iterator to first incoming arc.
+    
+        /// This constructor set the iterator to the first incoming arc of
+        /// the node.
+        InArcIt(const Digraph&, const Node&) { }
+        /// Arc -> InArcIt conversion
+
+        /// Sets the iterator to the value of the trivial iterator \c e.
+        /// This feature necessitates that each time we 
+        /// iterate the arc-set, the iteration order is the same.
+        InArcIt(const Digraph&, const Arc&) { }
+        /// Next incoming arc
+
+        /// Assign the iterator to the next inarc of the corresponding node.
+        ///
+        InArcIt& operator++() { return *this; }
+      };
+      /// This iterator goes through each arc.
+
+      /// This iterator goes through each arc of a digraph.
+      /// Its usage is quite simple, for example you can count the number
+      /// of arcs in a digraph \c g of type \c Digraph as follows:
+      ///\code
+      /// int count=0;
+      /// for(Digraph::ArcIt e(g); e!=INVALID; ++e) ++count;
+      ///\endcode
+      class ArcIt : public Arc {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        ArcIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        ArcIt(const ArcIt& e) : Arc(e) { }
+        /// Initialize the iterator to be invalid.
+
+        /// Initialize the iterator to be invalid.
+        ///
+        ArcIt(Invalid) { }
+        /// This constructor sets the iterator to the first arc.
+    
+        /// This constructor sets the iterator to the first arc of \c g.
+        ///@param g the digraph
+        ArcIt(const Digraph& g) { ignore_unused_variable_warning(g); }
+        /// Arc -> ArcIt conversion
+
+        /// Sets the iterator to the value of the trivial iterator \c e.
+        /// This feature necessitates that each time we 
+        /// iterate the arc-set, the iteration order is the same.
+        ArcIt(const Digraph&, const Arc&) { } 
+        ///Next arc
+        
+        /// Assign the iterator to the next arc.
+        ArcIt& operator++() { return *this; }
+      };
+      ///Gives back the target node of an arc.
+
+      ///Gives back the target node of an arc.
+      ///
+      Node target(Arc) const { return INVALID; }
+      ///Gives back the source node of an arc.
+
+      ///Gives back the source node of an arc.
+      ///
+      Node source(Arc) const { return INVALID; }
+
+      void first(Node&) const {}
+      void next(Node&) const {}
+
+      void first(Arc&) const {}
+      void next(Arc&) const {}
+
+
+      void firstIn(Arc&, const Node&) const {}
+      void nextIn(Arc&) const {}
+
+      void firstOut(Arc&, const Node&) const {}
+      void nextOut(Arc&) const {}
+
+      /// \brief The base node of the iterator.
+      ///
+      /// Gives back the base node of the iterator.
+      /// It is always the target of the pointed arc.
+      Node baseNode(const InArcIt&) const { return INVALID; }
+
+      /// \brief The running node of the iterator.
+      ///
+      /// Gives back the running node of the iterator.
+      /// It is always the source of the pointed arc.
+      Node runningNode(const InArcIt&) const { return INVALID; }
+
+      /// \brief The base node of the iterator.
+      ///
+      /// Gives back the base node of the iterator.
+      /// It is always the source of the pointed arc.
+      Node baseNode(const OutArcIt&) const { return INVALID; }
+
+      /// \brief The running node of the iterator.
+      ///
+      /// Gives back the running node of the iterator.
+      /// It is always the target of the pointed arc.
+      Node runningNode(const OutArcIt&) const { return INVALID; }
+
+      /// \brief The opposite node on the given arc.
+      ///
+      /// Gives back the opposite node on the given arc.
+      Node oppositeNode(const Node&, const Arc&) const { return INVALID; }
+
+      /// \brief Read write map of the nodes to type \c T.
+      /// 
+      /// ReadWrite map of the nodes to type \c T.
+      /// \sa Reference
+      template<class T> 
+      class NodeMap : public ReadWriteMap< Node, T > {
+      public:
+
+        ///\e
+        NodeMap(const Digraph&) { }
+        ///\e
+        NodeMap(const Digraph&, T) { }
+
+        ///Copy constructor
+        NodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }
+        ///Assignment operator
+        template <typename CMap>
+        NodeMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<Node, T>, CMap>();
+          return *this; 
+        }
+      };
+
+      /// \brief Read write map of the arcs to type \c T.
+      ///
+      /// Reference map of the arcs to type \c T.
+      /// \sa Reference
+      template<class T> 
+      class ArcMap : public ReadWriteMap<Arc,T> {
+      public:
+
+        ///\e
+        ArcMap(const Digraph&) { }
+        ///\e
+        ArcMap(const Digraph&, T) { }
+        ///Copy constructor
+        ArcMap(const ArcMap& em) : ReadWriteMap<Arc,T>(em) { }
+        ///Assignment operator
+        template <typename CMap>
+        ArcMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<Arc, T>, CMap>();
+          return *this; 
+        }
+      };
+
+      template <typename RDigraph>
+      struct Constraints {
+        void constraints() {
+          checkConcept<IterableDigraphComponent<>, Digraph>();
+          checkConcept<MappableDigraphComponent<>, Digraph>();
+        }
+      };
+
+    };
+    
+  } //namespace concepts  
+} //namespace lemon
+
+
+
+#endif // LEMON_CONCEPT_DIGRAPH_H
Index: lemon/concepts/graph.h
===================================================================
--- lemon/concepts/graph.h	(revision 57)
+++ lemon/concepts/graph.h	(revision 57)
@@ -0,0 +1,702 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2007
+ * 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.
+ *
+ */
+
+///\ingroup graph_concepts
+///\file
+///\brief The concept of Undirected Graphs.
+
+#ifndef LEMON_CONCEPT_GRAPH_H
+#define LEMON_CONCEPT_GRAPH_H
+
+#include <lemon/concepts/graph_components.h>
+#include <lemon/concepts/graph.h>
+#include <lemon/bits/utility.h>
+
+namespace lemon {
+  namespace concepts {
+
+    /// \ingroup graph_concepts
+    ///
+    /// \brief Class describing the concept of Undirected Graphs.
+    ///
+    /// This class describes the common interface of all Undirected
+    /// Graphs.
+    ///
+    /// As all concept describing classes it provides only interface
+    /// without any sensible implementation. So any algorithm for
+    /// undirected graph should compile with this class, but it will not
+    /// run properly, of course.
+    ///
+    /// The LEMON undirected graphs also fulfill the concept of
+    /// directed graphs (\ref lemon::concepts::Digraph "Digraph
+    /// Concept"). Each edges can be seen as two opposite
+    /// directed arc and consequently the undirected graph can be
+    /// seen as the direceted graph of these directed arcs. The
+    /// Graph has the Edge inner class for the edges and
+    /// the Arc type for the directed arcs. The Arc type is
+    /// convertible to Edge or inherited from it so from a directed
+    /// arc we can get the represented edge.
+    ///
+    /// In the sense of the LEMON each edge has a default
+    /// direction (it should be in every computer implementation,
+    /// because the order of edge's nodes defines an
+    /// orientation). With the default orientation we can define that
+    /// the directed arc is forward or backward directed. With the \c
+    /// direction() and \c direct() function we can get the direction
+    /// of the directed arc and we can direct an edge.
+    ///
+    /// The EdgeIt is an iterator for the edges. We can use
+    /// the EdgeMap to map values for the edges. The InArcIt and
+    /// OutArcIt iterates on the same edges but with opposite
+    /// direction. The IncArcIt iterates also on the same edges
+    /// as the OutArcIt and InArcIt but it is not convertible to Arc just
+    /// to Edge.  
+    class Graph {
+    public:
+      /// \brief The undirected graph should be tagged by the
+      /// UndirectedTag.
+      ///
+      /// The undirected graph should be tagged by the UndirectedTag. This
+      /// tag helps the enable_if technics to make compile time 
+      /// specializations for undirected graphs.  
+      typedef True UndirectedTag;
+
+      /// \brief The base type of node iterators, 
+      /// or in other words, the trivial node iterator.
+      ///
+      /// This is the base type of each node iterator,
+      /// thus each kind of node iterator converts to this.
+      /// More precisely each kind of node iterator should be inherited 
+      /// from the trivial node iterator.
+      class Node {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        Node() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        Node(const Node&) { }
+
+        /// Invalid constructor \& conversion.
+
+        /// This constructor initializes the iterator to be invalid.
+        /// \sa Invalid for more details.
+        Node(Invalid) { }
+        /// Equality operator
+
+        /// Two iterators are equal if and only if they point to the
+        /// same object or both are invalid.
+        bool operator==(Node) const { return true; }
+
+        /// Inequality operator
+        
+        /// \sa operator==(Node n)
+        ///
+        bool operator!=(Node) const { return true; }
+
+	/// Artificial ordering operator.
+	
+	/// To allow the use of graph descriptors as key type in std::map or
+	/// similar associative container we require this.
+	///
+	/// \note This operator only have to define some strict ordering of
+	/// the items; this order has nothing to do with the iteration
+	/// ordering of the items.
+	bool operator<(Node) const { return false; }
+
+      };
+    
+      /// This iterator goes through each node.
+
+      /// This iterator goes through each node.
+      /// Its usage is quite simple, for example you can count the number
+      /// of nodes in graph \c g of type \c Graph like this:
+      ///\code
+      /// int count=0;
+      /// for (Graph::NodeIt n(g); n!=INVALID; ++n) ++count;
+      ///\endcode
+      class NodeIt : public Node {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        NodeIt() { }
+        /// Copy constructor.
+        
+        /// Copy constructor.
+        ///
+        NodeIt(const NodeIt& n) : Node(n) { }
+        /// Invalid constructor \& conversion.
+
+        /// Initialize the iterator to be invalid.
+        /// \sa Invalid for more details.
+        NodeIt(Invalid) { }
+        /// Sets the iterator to the first node.
+
+        /// Sets the iterator to the first node of \c g.
+        ///
+        NodeIt(const Graph&) { }
+        /// Node -> NodeIt conversion.
+
+        /// Sets the iterator to the node of \c the graph pointed by 
+	/// the trivial iterator.
+        /// This feature necessitates that each time we 
+        /// iterate the arc-set, the iteration order is the same.
+        NodeIt(const Graph&, const Node&) { }
+        /// Next node.
+
+        /// Assign the iterator to the next node.
+        ///
+        NodeIt& operator++() { return *this; }
+      };
+    
+    
+      /// The base type of the edge iterators.
+
+      /// The base type of the edge iterators.
+      ///
+      class Edge {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        Edge() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        Edge(const Edge&) { }
+        /// Initialize the iterator to be invalid.
+
+        /// Initialize the iterator to be invalid.
+        ///
+        Edge(Invalid) { }
+        /// Equality operator
+
+        /// Two iterators are equal if and only if they point to the
+        /// same object or both are invalid.
+        bool operator==(Edge) const { return true; }
+        /// Inequality operator
+
+        /// \sa operator==(Edge n)
+        ///
+        bool operator!=(Edge) const { return true; }
+
+	/// Artificial ordering operator.
+	
+	/// To allow the use of graph descriptors as key type in std::map or
+	/// similar associative container we require this.
+	///
+	/// \note This operator only have to define some strict ordering of
+	/// the items; this order has nothing to do with the iteration
+	/// ordering of the items.
+	bool operator<(Edge) const { return false; }
+      };
+
+      /// This iterator goes through each edge.
+
+      /// This iterator goes through each edge of a graph.
+      /// Its usage is quite simple, for example you can count the number
+      /// of edges in a graph \c g of type \c Graph as follows:
+      ///\code
+      /// int count=0;
+      /// for(Graph::EdgeIt e(g); e!=INVALID; ++e) ++count;
+      ///\endcode
+      class EdgeIt : public Edge {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        EdgeIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        EdgeIt(const EdgeIt& e) : Edge(e) { }
+        /// Initialize the iterator to be invalid.
+
+        /// Initialize the iterator to be invalid.
+        ///
+        EdgeIt(Invalid) { }
+        /// This constructor sets the iterator to the first edge.
+    
+        /// This constructor sets the iterator to the first edge.
+        EdgeIt(const Graph&) { }
+        /// Edge -> EdgeIt conversion
+
+        /// Sets the iterator to the value of the trivial iterator.
+        /// This feature necessitates that each time we
+        /// iterate the edge-set, the iteration order is the 
+	/// same.
+        EdgeIt(const Graph&, const Edge&) { } 
+        /// Next edge
+        
+        /// Assign the iterator to the next edge.
+        EdgeIt& operator++() { return *this; }
+      };
+
+      /// \brief This iterator goes trough the incident undirected 
+      /// arcs of a node.
+      ///
+      /// This iterator goes trough the incident edges
+      /// of a certain node of a graph. You should assume that the 
+      /// loop arcs will be iterated twice.
+      /// 
+      /// Its usage is quite simple, for example you can compute the
+      /// degree (i.e. count the number of incident arcs of a node \c n
+      /// in graph \c g of type \c Graph as follows. 
+      ///
+      ///\code
+      /// int count=0;
+      /// for(Graph::IncArcIt e(g, n); e!=INVALID; ++e) ++count;
+      ///\endcode
+      class IncArcIt : public Edge {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        IncArcIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        IncArcIt(const IncArcIt& e) : Edge(e) { }
+        /// Initialize the iterator to be invalid.
+
+        /// Initialize the iterator to be invalid.
+        ///
+        IncArcIt(Invalid) { }
+        /// This constructor sets the iterator to first incident arc.
+    
+        /// This constructor set the iterator to the first incident arc of
+        /// the node.
+        IncArcIt(const Graph&, const Node&) { }
+        /// Edge -> IncArcIt conversion
+
+        /// Sets the iterator to the value of the trivial iterator \c e.
+        /// This feature necessitates that each time we 
+        /// iterate the arc-set, the iteration order is the same.
+        IncArcIt(const Graph&, const Edge&) { }
+        /// Next incident arc
+
+        /// Assign the iterator to the next incident arc
+	/// of the corresponding node.
+        IncArcIt& operator++() { return *this; }
+      };
+
+      /// The directed arc type.
+
+      /// The directed arc type. It can be converted to the
+      /// edge or it should be inherited from the undirected
+      /// arc.
+      class Arc : public Edge {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        Arc() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        Arc(const Arc& e) : Edge(e) { }
+        /// Initialize the iterator to be invalid.
+
+        /// Initialize the iterator to be invalid.
+        ///
+        Arc(Invalid) { }
+        /// Equality operator
+
+        /// Two iterators are equal if and only if they point to the
+        /// same object or both are invalid.
+        bool operator==(Arc) const { return true; }
+        /// Inequality operator
+
+        /// \sa operator==(Arc n)
+        ///
+        bool operator!=(Arc) const { return true; }
+
+	/// Artificial ordering operator.
+	
+	/// To allow the use of graph descriptors as key type in std::map or
+	/// similar associative container we require this.
+	///
+	/// \note This operator only have to define some strict ordering of
+	/// the items; this order has nothing to do with the iteration
+	/// ordering of the items.
+	bool operator<(Arc) const { return false; }
+	
+      }; 
+      /// This iterator goes through each directed arc.
+
+      /// This iterator goes through each arc of a graph.
+      /// Its usage is quite simple, for example you can count the number
+      /// of arcs in a graph \c g of type \c Graph as follows:
+      ///\code
+      /// int count=0;
+      /// for(Graph::ArcIt e(g); e!=INVALID; ++e) ++count;
+      ///\endcode
+      class ArcIt : public Arc {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        ArcIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        ArcIt(const ArcIt& e) : Arc(e) { }
+        /// Initialize the iterator to be invalid.
+
+        /// Initialize the iterator to be invalid.
+        ///
+        ArcIt(Invalid) { }
+        /// This constructor sets the iterator to the first arc.
+    
+        /// This constructor sets the iterator to the first arc of \c g.
+        ///@param g the graph
+        ArcIt(const Graph &g) { ignore_unused_variable_warning(g); }
+        /// Arc -> ArcIt conversion
+
+        /// Sets the iterator to the value of the trivial iterator \c e.
+        /// This feature necessitates that each time we 
+        /// iterate the arc-set, the iteration order is the same.
+        ArcIt(const Graph&, const Arc&) { } 
+        ///Next arc
+        
+        /// Assign the iterator to the next arc.
+        ArcIt& operator++() { return *this; }
+      };
+   
+      /// This iterator goes trough the outgoing directed arcs of a node.
+
+      /// This iterator goes trough the \e outgoing arcs of a certain node
+      /// of a graph.
+      /// Its usage is quite simple, for example you can count the number
+      /// of outgoing arcs of a node \c n
+      /// in graph \c g of type \c Graph as follows.
+      ///\code
+      /// int count=0;
+      /// for (Graph::OutArcIt e(g, n); e!=INVALID; ++e) ++count;
+      ///\endcode
+    
+      class OutArcIt : public Arc {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        OutArcIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        OutArcIt(const OutArcIt& e) : Arc(e) { }
+        /// Initialize the iterator to be invalid.
+
+        /// Initialize the iterator to be invalid.
+        ///
+        OutArcIt(Invalid) { }
+        /// This constructor sets the iterator to the first outgoing arc.
+    
+        /// This constructor sets the iterator to the first outgoing arc of
+        /// the node.
+        ///@param n the node
+        ///@param g the graph
+        OutArcIt(const Graph& n, const Node& g) {
+	  ignore_unused_variable_warning(n);
+	  ignore_unused_variable_warning(g);
+	}
+        /// Arc -> OutArcIt conversion
+
+        /// Sets the iterator to the value of the trivial iterator.
+	/// This feature necessitates that each time we 
+        /// iterate the arc-set, the iteration order is the same.
+        OutArcIt(const Graph&, const Arc&) { }
+        ///Next outgoing arc
+        
+        /// Assign the iterator to the next 
+        /// outgoing arc of the corresponding node.
+        OutArcIt& operator++() { return *this; }
+      };
+
+      /// This iterator goes trough the incoming directed arcs of a node.
+
+      /// This iterator goes trough the \e incoming arcs of a certain node
+      /// of a graph.
+      /// Its usage is quite simple, for example you can count the number
+      /// of outgoing arcs of a node \c n
+      /// in graph \c g of type \c Graph as follows.
+      ///\code
+      /// int count=0;
+      /// for(Graph::InArcIt e(g, n); e!=INVALID; ++e) ++count;
+      ///\endcode
+
+      class InArcIt : public Arc {
+      public:
+        /// Default constructor
+
+        /// @warning The default constructor sets the iterator
+        /// to an undefined value.
+        InArcIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        InArcIt(const InArcIt& e) : Arc(e) { }
+        /// Initialize the iterator to be invalid.
+
+        /// Initialize the iterator to be invalid.
+        ///
+        InArcIt(Invalid) { }
+        /// This constructor sets the iterator to first incoming arc.
+    
+        /// This constructor set the iterator to the first incoming arc of
+        /// the node.
+        ///@param n the node
+        ///@param g the graph
+        InArcIt(const Graph& g, const Node& n) { 
+	  ignore_unused_variable_warning(n);
+	  ignore_unused_variable_warning(g);
+	}
+        /// Arc -> InArcIt conversion
+
+        /// Sets the iterator to the value of the trivial iterator \c e.
+        /// This feature necessitates that each time we 
+        /// iterate the arc-set, the iteration order is the same.
+        InArcIt(const Graph&, const Arc&) { }
+        /// Next incoming arc
+
+        /// Assign the iterator to the next inarc of the corresponding node.
+        ///
+        InArcIt& operator++() { return *this; }
+      };
+
+      /// \brief Read write map of the nodes to type \c T.
+      /// 
+      /// ReadWrite map of the nodes to type \c T.
+      /// \sa Reference
+      template<class T> 
+      class NodeMap : public ReadWriteMap< Node, T >
+      {
+      public:
+
+        ///\e
+        NodeMap(const Graph&) { }
+        ///\e
+        NodeMap(const Graph&, T) { }
+
+        ///Copy constructor
+        NodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }
+        ///Assignment operator
+        template <typename CMap>
+        NodeMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<Node, T>, CMap>();
+          return *this; 
+        }
+      };
+
+      /// \brief Read write map of the directed arcs to type \c T.
+      ///
+      /// Reference map of the directed arcs to type \c T.
+      /// \sa Reference
+      template<class T> 
+      class ArcMap : public ReadWriteMap<Arc,T>
+      {
+      public:
+
+        ///\e
+        ArcMap(const Graph&) { }
+        ///\e
+        ArcMap(const Graph&, T) { }
+        ///Copy constructor
+        ArcMap(const ArcMap& em) : ReadWriteMap<Arc,T>(em) { }
+        ///Assignment operator
+        template <typename CMap>
+        ArcMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<Arc, T>, CMap>();
+          return *this; 
+        }
+      };
+
+      /// Read write map of the edges to type \c T.
+
+      /// Reference map of the arcs to type \c T.
+      /// \sa Reference
+      template<class T> 
+      class EdgeMap : public ReadWriteMap<Edge,T>
+      {
+      public:
+
+        ///\e
+        EdgeMap(const Graph&) { }
+        ///\e
+        EdgeMap(const Graph&, T) { }
+        ///Copy constructor
+        EdgeMap(const EdgeMap& em) : ReadWriteMap<Edge,T>(em) {}
+        ///Assignment operator
+        template <typename CMap>
+        EdgeMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<Edge, T>, CMap>();
+          return *this; 
+        }
+      };
+
+      /// \brief Direct the given edge.
+      ///
+      /// Direct the given edge. The returned arc source
+      /// will be the given node.
+      Arc direct(const Edge&, const Node&) const {
+	return INVALID;
+      }
+
+      /// \brief Direct the given edge.
+      ///
+      /// Direct the given edge. The returned arc
+      /// represents the given edge and the direction comes
+      /// from the bool parameter. The source of the edge and
+      /// the directed arc is the same when the given bool is true.
+      Arc direct(const Edge&, bool) const {
+	return INVALID;
+      }
+
+      /// \brief Returns true if the arc has default orientation.
+      ///
+      /// Returns whether the given directed arc is same orientation as
+      /// the corresponding edge's default orientation.
+      bool direction(Arc) const { return true; }
+
+      /// \brief Returns the opposite directed arc.
+      ///
+      /// Returns the opposite directed arc.
+      Arc oppositeArc(Arc) const { return INVALID; }
+
+      /// \brief Opposite node on an arc
+      ///
+      /// \return the opposite of the given Node on the given Edge
+      Node oppositeNode(Node, Edge) const { return INVALID; }
+
+      /// \brief First node of the edge.
+      ///
+      /// \return the first node of the given Edge.
+      ///
+      /// Naturally edges don't have direction and thus
+      /// don't have source and target node. But we use these two methods
+      /// to query the two nodes of the arc. The direction of the arc
+      /// which arises this way is called the inherent direction of the
+      /// edge, and is used to define the "default" direction
+      /// of the directed versions of the arcs.
+      /// \sa direction
+      Node u(Edge) const { return INVALID; }
+
+      /// \brief Second node of the edge.
+      Node v(Edge) const { return INVALID; }
+
+      /// \brief Source node of the directed arc.
+      Node source(Arc) const { return INVALID; }
+
+      /// \brief Target node of the directed arc.
+      Node target(Arc) const { return INVALID; }
+
+      void first(Node&) const {}
+      void next(Node&) const {}
+
+      void first(Edge&) const {}
+      void next(Edge&) const {}
+
+      void first(Arc&) const {}
+      void next(Arc&) const {}
+
+      void firstOut(Arc&, Node) const {}
+      void nextOut(Arc&) const {}
+
+      void firstIn(Arc&, Node) const {}
+      void nextIn(Arc&) const {}
+
+
+      void firstInc(Edge &, bool &, const Node &) const {}
+      void nextInc(Edge &, bool &) const {}
+
+      /// \brief Base node of the iterator
+      ///
+      /// Returns the base node (the source in this case) of the iterator
+      Node baseNode(OutArcIt e) const {
+	return source(e);
+      }
+      /// \brief Running node of the iterator
+      ///
+      /// Returns the running node (the target in this case) of the
+      /// iterator
+      Node runningNode(OutArcIt e) const {
+	return target(e);
+      }
+
+      /// \brief Base node of the iterator
+      ///
+      /// Returns the base node (the target in this case) of the iterator
+      Node baseNode(InArcIt e) const {
+	return target(e);
+      }
+      /// \brief Running node of the iterator
+      ///
+      /// Returns the running node (the source in this case) of the
+      /// iterator
+      Node runningNode(InArcIt e) const {
+	return source(e);
+      }
+
+      /// \brief Base node of the iterator
+      ///
+      /// Returns the base node of the iterator
+      Node baseNode(IncArcIt) const {
+	return INVALID;
+      }
+      
+      /// \brief Running node of the iterator
+      ///
+      /// Returns the running node of the iterator
+      Node runningNode(IncArcIt) const {
+	return INVALID;
+      }
+
+      template <typename Graph>
+      struct Constraints {
+	void constraints() {
+	  checkConcept<IterableGraphComponent<>, Graph>();
+	  checkConcept<MappableGraphComponent<>, Graph>();
+	}
+      };
+
+    };
+
+  }
+
+}
+
+#endif
Index: lemon/concepts/graph_components.h
===================================================================
--- lemon/concepts/graph_components.h	(revision 57)
+++ lemon/concepts/graph_components.h	(revision 57)
@@ -0,0 +1,1490 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2007
+ * 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.
+ *
+ */
+
+///\ingroup graph_concepts
+///\file
+///\brief The concept of graph components.
+
+
+#ifndef LEMON_CONCEPT_GRAPH_COMPONENTS_H
+#define LEMON_CONCEPT_GRAPH_COMPONENTS_H
+
+#include <lemon/bits/invalid.h>
+#include <lemon/concepts/maps.h>
+
+#include <lemon/bits/alteration_notifier.h>
+
+namespace lemon {
+  namespace concepts {
+
+    /// \brief Skeleton class for graph Node and Arc types
+    ///
+    /// This class describes the interface of Node and Arc (and Edge
+    /// in undirected graphs) subtypes of graph types.
+    ///
+    /// \note This class is a template class so that we can use it to
+    /// create graph skeleton classes. The reason for this is than Node
+    /// and Arc types should \em not derive from the same base class.
+    /// For Node you should instantiate it with character 'n' and for Arc
+    /// with 'a'.
+
+#ifndef DOXYGEN
+    template <char _selector = '0'>
+#endif
+    class GraphItem {
+    public:
+      /// \brief Default constructor.
+      ///      
+      /// \warning The default constructor is not required to set
+      /// the item to some well-defined value. So you should consider it
+      /// as uninitialized.
+      GraphItem() {}
+      /// \brief Copy constructor.
+      ///
+      /// Copy constructor.
+      ///
+      GraphItem(const GraphItem &) {}
+      /// \brief Invalid constructor \& conversion.
+      ///
+      /// This constructor initializes the item to be invalid.
+      /// \sa Invalid for more details.
+      GraphItem(Invalid) {}
+      /// \brief Assign operator for nodes.
+      ///
+      /// The nodes are assignable. 
+      ///
+      GraphItem& operator=(GraphItem const&) { return *this; }
+      /// \brief Equality operator.
+      ///
+      /// Two iterators are equal if and only if they represents the
+      /// same node in the graph or both are invalid.
+      bool operator==(GraphItem) const { return false; }
+      /// \brief Inequality operator.
+      ///
+      /// \sa operator==(const Node& n)
+      ///
+      bool operator!=(GraphItem) const { return false; }
+
+      /// \brief Artificial ordering operator.
+      ///
+      /// To allow the use of graph descriptors as key type in std::map or
+      /// similar associative container we require this.
+      ///
+      /// \note This operator only have to define some strict ordering of
+      /// the items; this order has nothing to do with the iteration
+      /// ordering of the items.
+      bool operator<(GraphItem) const { return false; }
+
+      template<typename _GraphItem>
+      struct Constraints {
+	void constraints() {
+	  _GraphItem i1;
+	  _GraphItem i2 = i1;
+	  _GraphItem i3 = INVALID;
+	  
+	  i1 = i2 = i3;
+
+	  bool b;
+	  //	  b = (ia == ib) && (ia != ib) && (ia < ib);
+	  b = (ia == ib) && (ia != ib);
+	  b = (ia == INVALID) && (ib != INVALID);
+          b = (ia < ib);
+	}
+
+	const _GraphItem &ia;
+	const _GraphItem &ib;
+      };
+    };
+
+    /// \brief An empty base directed graph class.
+    ///  
+    /// This class provides the minimal set of features needed for a
+    /// directed graph structure. All digraph concepts have to be
+    /// conform to this base directed graph. It just provides types
+    /// for nodes and arcs and functions to get the source and the
+    /// target of the arcs.
+    class BaseDigraphComponent {
+    public:
+
+      typedef BaseDigraphComponent Digraph;
+      
+      /// \brief Node class of the digraph.
+      ///
+      /// This class represents the Nodes of the digraph. 
+      ///
+      typedef GraphItem<'n'> Node;
+
+      /// \brief Arc class of the digraph.
+      ///
+      /// This class represents the Arcs of the digraph. 
+      ///
+      typedef GraphItem<'e'> Arc;
+
+      /// \brief Gives back the target node of an arc.
+      ///
+      /// Gives back the target node of an arc.
+      ///
+      Node target(const Arc&) const { return INVALID;}
+
+      /// \brief Gives back the source node of an arc.
+      ///
+      /// Gives back the source node of an arc.
+      ///
+      Node source(const Arc&) const { return INVALID;}
+
+      /// \brief Gives back the opposite node on the given arc.
+      ///
+      /// Gives back the opposite node on the given arc.
+      Node oppositeNode(const Node&, const Arc&) const {
+        return INVALID;
+      }
+
+      template <typename _Digraph>
+      struct Constraints {
+	typedef typename _Digraph::Node Node;
+	typedef typename _Digraph::Arc Arc;
+      
+	void constraints() {
+	  checkConcept<GraphItem<'n'>, Node>();
+	  checkConcept<GraphItem<'a'>, Arc>();
+	  {
+	    Node n;
+	    Arc e(INVALID);
+	    n = digraph.source(e);
+	    n = digraph.target(e);
+            n = digraph.oppositeNode(n, e);
+	  }      
+	}
+      
+	const _Digraph& digraph;
+      };
+    };
+
+    /// \brief An empty base undirected graph class.
+    ///  
+    /// This class provides the minimal set of features needed for an
+    /// undirected graph structure. All undirected graph concepts have
+    /// to be conform to this base graph. It just provides types for
+    /// nodes, arcs and edges and functions to get the
+    /// source and the target of the arcs and edges,
+    /// conversion from arcs to edges and function to get
+    /// both direction of the edges.
+    class BaseGraphComponent : public BaseDigraphComponent {
+    public:
+      typedef BaseDigraphComponent::Node Node;
+      typedef BaseDigraphComponent::Arc Arc;
+      /// \brief Undirected arc class of the graph.
+      ///
+      /// This class represents the edges of the graph.
+      /// The undirected graphs can be used as a directed graph which
+      /// for each arc contains the opposite arc too so the graph is
+      /// bidirected. The edge represents two opposite
+      /// directed arcs.
+      class Edge : public GraphItem<'u'> {
+      public:
+        typedef GraphItem<'u'> Parent;
+        /// \brief Default constructor.
+        ///      
+        /// \warning The default constructor is not required to set
+        /// the item to some well-defined value. So you should consider it
+        /// as uninitialized.
+        Edge() {}
+        /// \brief Copy constructor.
+        ///
+        /// Copy constructor.
+        ///
+        Edge(const Edge &) : Parent() {}
+        /// \brief Invalid constructor \& conversion.
+        ///
+        /// This constructor initializes the item to be invalid.
+        /// \sa Invalid for more details.
+        Edge(Invalid) {}
+        /// \brief Converter from arc to edge.
+        ///
+        /// Besides the core graph item functionality each arc should
+        /// be convertible to the represented edge. 
+        Edge(const Arc&) {}
+        /// \brief Assign arc to edge.
+        ///
+        /// Besides the core graph item functionality each arc should
+        /// be convertible to the represented edge. 
+        Edge& operator=(const Arc&) { return *this; }
+      };
+
+      /// \brief Returns the direction of the arc.
+      ///
+      /// Returns the direction of the arc. Each arc represents an
+      /// edge with a direction. It gives back the
+      /// direction.
+      bool direction(const Arc&) const { return true; }
+
+      /// \brief Returns the directed arc.
+      ///
+      /// Returns the directed arc from its direction and the
+      /// represented edge.
+      Arc direct(const Edge&, bool) const { return INVALID;} 
+
+      /// \brief Returns the directed arc.
+      ///
+      /// Returns the directed arc from its source and the
+      /// represented edge.
+      Arc direct(const Edge&, const Node&) const { return INVALID;} 
+
+      /// \brief Returns the opposite arc.
+      ///
+      /// Returns the opposite arc. It is the arc representing the
+      /// same edge and has opposite direction.
+      Arc oppositeArc(const Arc&) const { return INVALID;}
+
+      /// \brief Gives back one ending of an edge.
+      ///
+      /// Gives back one ending of an edge.
+      Node u(const Edge&) const { return INVALID;}
+
+      /// \brief Gives back the other ending of an edge.
+      ///
+      /// Gives back the other ending of an edge.
+      Node v(const Edge&) const { return INVALID;}
+      
+      template <typename _Graph>
+      struct Constraints {
+	typedef typename _Graph::Node Node;
+	typedef typename _Graph::Arc Arc;
+	typedef typename _Graph::Edge Edge;
+      
+	void constraints() {
+          checkConcept<BaseDigraphComponent, _Graph>();
+	  checkConcept<GraphItem<'u'>, Edge>();
+	  {
+	    Node n;
+	    Edge ue(INVALID);
+            Arc e;
+	    n = graph.u(ue);
+	    n = graph.v(ue);
+            e = graph.direct(ue, true);
+            e = graph.direct(ue, n);
+            e = graph.oppositeArc(e);
+            ue = e;
+            bool d = graph.direction(e);
+            ignore_unused_variable_warning(d);
+	  }      
+	}
+      
+	const _Graph& graph;
+      };
+
+    };
+
+    /// \brief An empty idable base digraph class.
+    ///  
+    /// This class provides beside the core digraph features
+    /// core id functions for the digraph structure.
+    /// The most of the base digraphs should be conform to this concept.
+    /// The id's are unique and immutable.
+    template <typename _Base = BaseDigraphComponent>
+    class IDableDigraphComponent : public _Base {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::Arc Arc;
+
+      /// \brief Gives back an unique integer id for the Node. 
+      ///
+      /// Gives back an unique integer id for the Node. 
+      ///
+      int id(const Node&) const { return -1;}
+
+      /// \brief Gives back the node by the unique id.
+      ///
+      /// Gives back the node by the unique id.
+      /// If the digraph does not contain node with the given id
+      /// then the result of the function is undetermined. 
+      Node nodeFromId(int) const { return INVALID;}
+
+      /// \brief Gives back an unique integer id for the Arc. 
+      ///
+      /// Gives back an unique integer id for the Arc. 
+      ///
+      int id(const Arc&) const { return -1;}
+
+      /// \brief Gives back the arc by the unique id.
+      ///
+      /// Gives back the arc by the unique id.
+      /// If the digraph does not contain arc with the given id
+      /// then the result of the function is undetermined. 
+      Arc arcFromId(int) const { return INVALID;}
+
+      /// \brief Gives back an integer greater or equal to the maximum
+      /// Node id.
+      ///
+      /// Gives back an integer greater or equal to the maximum Node
+      /// id.
+      int maxNodeId() const { return -1;}
+
+      /// \brief Gives back an integer greater or equal to the maximum
+      /// Arc id.
+      ///
+      /// Gives back an integer greater or equal to the maximum Arc
+      /// id.
+      int maxArcId() const { return -1;}
+
+      template <typename _Digraph>
+      struct Constraints {
+
+	void constraints() {
+	  checkConcept<Base, _Digraph >();
+	  typename _Digraph::Node node;
+	  int nid = digraph.id(node);
+	  nid = digraph.id(node);
+	  node = digraph.nodeFromId(nid);
+	  typename _Digraph::Arc arc;
+	  int eid = digraph.id(arc);
+	  eid = digraph.id(arc);
+	  arc = digraph.arcFromId(eid);
+
+	  nid = digraph.maxNodeId();
+	  ignore_unused_variable_warning(nid);
+	  eid = digraph.maxArcId();
+	  ignore_unused_variable_warning(eid);
+	}
+
+	const _Digraph& digraph;
+      };
+    };
+
+    /// \brief An empty idable base undirected graph class.
+    ///  
+    /// This class provides beside the core undirected graph features
+    /// core id functions for the undirected graph structure.  The
+    /// most of the base undirected graphs should be conform to this
+    /// concept.  The id's are unique and immutable.
+    template <typename _Base = BaseGraphComponent>
+    class IDableGraphComponent : public IDableDigraphComponent<_Base> {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Edge Edge;
+
+      using IDableDigraphComponent<_Base>::id;
+
+      /// \brief Gives back an unique integer id for the Edge. 
+      ///
+      /// Gives back an unique integer id for the Edge. 
+      ///
+      int id(const Edge&) const { return -1;}
+
+      /// \brief Gives back the edge by the unique id.
+      ///
+      /// Gives back the edge by the unique id.  If the
+      /// graph does not contain arc with the given id then the
+      /// result of the function is undetermined.
+      Edge edgeFromId(int) const { return INVALID;}
+
+      /// \brief Gives back an integer greater or equal to the maximum
+      /// Edge id.
+      ///
+      /// Gives back an integer greater or equal to the maximum Edge
+      /// id.
+      int maxEdgeId() const { return -1;}
+
+      template <typename _Graph>
+      struct Constraints {
+
+	void constraints() {
+	  checkConcept<Base, _Graph >();
+	  checkConcept<IDableDigraphComponent<Base>, _Graph >();
+	  typename _Graph::Edge edge;
+	  int ueid = graph.id(edge);
+	  ueid = graph.id(edge);
+	  edge = graph.edgeFromId(ueid);
+	  ueid = graph.maxEdgeId();
+	  ignore_unused_variable_warning(ueid);
+	}
+
+	const _Graph& graph;
+      };
+    };
+
+    /// \brief Skeleton class for graph NodeIt and ArcIt
+    ///
+    /// Skeleton class for graph NodeIt and ArcIt.
+    ///
+    template <typename _Graph, typename _Item>
+    class GraphItemIt : public _Item {
+    public:
+      /// \brief Default constructor.
+      ///
+      /// @warning The default constructor sets the iterator
+      /// to an undefined value.
+      GraphItemIt() {}
+      /// \brief Copy constructor.
+      ///
+      /// Copy constructor.
+      ///
+      GraphItemIt(const GraphItemIt& ) {}
+      /// \brief Sets the iterator to the first item.
+      ///
+      /// Sets the iterator to the first item of \c the graph.
+      ///
+      explicit GraphItemIt(const _Graph&) {}
+      /// \brief Invalid constructor \& conversion.
+      ///
+      /// This constructor initializes the item to be invalid.
+      /// \sa Invalid for more details.
+      GraphItemIt(Invalid) {}
+      /// \brief Assign operator for items.
+      ///
+      /// The items are assignable. 
+      ///
+      GraphItemIt& operator=(const GraphItemIt&) { return *this; }      
+      /// \brief Next item.
+      /// 
+      /// Assign the iterator to the next item.
+      ///
+      GraphItemIt& operator++() { return *this; }
+      /// \brief Equality operator
+      /// 
+      /// Two iterators are equal if and only if they point to the
+      /// same object or both are invalid.
+      bool operator==(const GraphItemIt&) const { return true;}
+      /// \brief Inequality operator
+      ///	
+      /// \sa operator==(Node n)
+      ///
+      bool operator!=(const GraphItemIt&) const { return true;}
+      
+      template<typename _GraphItemIt>
+      struct Constraints {
+	void constraints() {
+	  _GraphItemIt it1(g);	
+	  _GraphItemIt it2;
+
+	  it2 = ++it1;
+	  ++it2 = it1;
+	  ++(++it1);
+
+	  _Item bi = it1;
+	  bi = it2;
+	}
+	_Graph& g;
+      };
+    };
+
+    /// \brief Skeleton class for graph InArcIt and OutArcIt
+    ///
+    /// \note Because InArcIt and OutArcIt may not inherit from the same
+    /// base class, the _selector is a additional template parameter. For 
+    /// InArcIt you should instantiate it with character 'i' and for 
+    /// OutArcIt with 'o'.
+    template <typename _Graph,
+	      typename _Item = typename _Graph::Arc,
+              typename _Base = typename _Graph::Node, 
+	      char _selector = '0'>
+    class GraphIncIt : public _Item {
+    public:
+      /// \brief Default constructor.
+      ///
+      /// @warning The default constructor sets the iterator
+      /// to an undefined value.
+      GraphIncIt() {}
+      /// \brief Copy constructor.
+      ///
+      /// Copy constructor.
+      ///
+      GraphIncIt(GraphIncIt const& gi) : _Item(gi) {}
+      /// \brief Sets the iterator to the first arc incoming into or outgoing 
+      /// from the node.
+      ///
+      /// Sets the iterator to the first arc incoming into or outgoing 
+      /// from the node.
+      ///
+      explicit GraphIncIt(const _Graph&, const _Base&) {}
+      /// \brief Invalid constructor \& conversion.
+      ///
+      /// This constructor initializes the item to be invalid.
+      /// \sa Invalid for more details.
+      GraphIncIt(Invalid) {}
+      /// \brief Assign operator for iterators.
+      ///
+      /// The iterators are assignable. 
+      ///
+      GraphIncIt& operator=(GraphIncIt const&) { return *this; }      
+      /// \brief Next item.
+      ///
+      /// Assign the iterator to the next item.
+      ///
+      GraphIncIt& operator++() { return *this; }
+
+      /// \brief Equality operator
+      ///
+      /// Two iterators are equal if and only if they point to the
+      /// same object or both are invalid.
+      bool operator==(const GraphIncIt&) const { return true;}
+
+      /// \brief Inequality operator
+      ///
+      /// \sa operator==(Node n)
+      ///
+      bool operator!=(const GraphIncIt&) const { return true;}
+
+      template <typename _GraphIncIt>
+      struct Constraints {
+	void constraints() {
+	  checkConcept<GraphItem<_selector>, _GraphIncIt>();
+	  _GraphIncIt it1(graph, node);
+	  _GraphIncIt it2;
+
+	  it2 = ++it1;
+	  ++it2 = it1;
+	  ++(++it1);
+	  _Item e = it1;
+	  e = it2;
+
+	}
+
+	_Item arc;
+	_Base node;
+	_Graph graph;
+	_GraphIncIt it;
+      };
+    };
+
+
+    /// \brief An empty iterable digraph class.
+    ///
+    /// This class provides beside the core digraph features
+    /// iterator based iterable interface for the digraph structure.
+    /// This concept is part of the Digraph concept.
+    template <typename _Base = BaseDigraphComponent>
+    class IterableDigraphComponent : public _Base {
+
+    public:
+    
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::Arc Arc;
+
+      typedef IterableDigraphComponent Digraph;
+
+      /// \name Base iteration
+      /// 
+      /// This interface provides functions for iteration on digraph items
+      ///
+      /// @{  
+
+      /// \brief Gives back the first node in the iterating order.
+      ///      
+      /// Gives back the first node in the iterating order.
+      ///     
+      void first(Node&) const {}
+
+      /// \brief Gives back the next node in the iterating order.
+      ///
+      /// Gives back the next node in the iterating order.
+      ///     
+      void next(Node&) const {}
+
+      /// \brief Gives back the first arc in the iterating order.
+      ///
+      /// Gives back the first arc in the iterating order.
+      ///     
+      void first(Arc&) const {}
+
+      /// \brief Gives back the next arc in the iterating order.
+      ///
+      /// Gives back the next arc in the iterating order.
+      ///     
+      void next(Arc&) const {}
+
+
+      /// \brief Gives back the first of the arcs point to the given
+      /// node.
+      ///
+      /// Gives back the first of the arcs point to the given node.
+      ///     
+      void firstIn(Arc&, const Node&) const {}
+
+      /// \brief Gives back the next of the arcs points to the given
+      /// node.
+      ///
+      /// Gives back the next of the arcs points to the given node.
+      ///
+      void nextIn(Arc&) const {}
+
+      /// \brief Gives back the first of the arcs start from the
+      /// given node.
+      ///      
+      /// Gives back the first of the arcs start from the given node.
+      ///     
+      void firstOut(Arc&, const Node&) const {}
+
+      /// \brief Gives back the next of the arcs start from the given
+      /// node.
+      ///
+      /// Gives back the next of the arcs start from the given node.
+      ///     
+      void nextOut(Arc&) const {}
+
+      /// @}
+
+      /// \name Class based iteration
+      /// 
+      /// This interface provides functions for iteration on digraph items
+      ///
+      /// @{
+
+      /// \brief This iterator goes through each node.
+      ///
+      /// This iterator goes through each node.
+      ///
+      typedef GraphItemIt<Digraph, Node> NodeIt;
+
+      /// \brief This iterator goes through each node.
+      ///
+      /// This iterator goes through each node.
+      ///
+      typedef GraphItemIt<Digraph, Arc> ArcIt;
+
+      /// \brief This iterator goes trough the incoming arcs of a node.
+      ///
+      /// This iterator goes trough the \e inccoming arcs of a certain node
+      /// of a digraph.
+      typedef GraphIncIt<Digraph, Arc, Node, 'i'> InArcIt;
+
+      /// \brief This iterator goes trough the outgoing arcs of a node.
+      ///
+      /// This iterator goes trough the \e outgoing arcs of a certain node
+      /// of a digraph.
+      typedef GraphIncIt<Digraph, Arc, Node, 'o'> OutArcIt;
+
+      /// \brief The base node of the iterator.
+      ///
+      /// Gives back the base node of the iterator.
+      /// It is always the target of the pointed arc.
+      Node baseNode(const InArcIt&) const { return INVALID; }
+
+      /// \brief The running node of the iterator.
+      ///
+      /// Gives back the running node of the iterator.
+      /// It is always the source of the pointed arc.
+      Node runningNode(const InArcIt&) const { return INVALID; }
+
+      /// \brief The base node of the iterator.
+      ///
+      /// Gives back the base node of the iterator.
+      /// It is always the source of the pointed arc.
+      Node baseNode(const OutArcIt&) const { return INVALID; }
+
+      /// \brief The running node of the iterator.
+      ///
+      /// Gives back the running node of the iterator.
+      /// It is always the target of the pointed arc.
+      Node runningNode(const OutArcIt&) const { return INVALID; }
+
+      /// @}
+
+      template <typename _Digraph> 
+      struct Constraints {
+	void constraints() {
+	  checkConcept<Base, _Digraph>();
+
+          {
+            typename _Digraph::Node node(INVALID);      
+            typename _Digraph::Arc arc(INVALID);
+            {
+              digraph.first(node);
+              digraph.next(node);
+            }
+            {
+              digraph.first(arc);
+              digraph.next(arc);
+            }
+            {
+              digraph.firstIn(arc, node);
+              digraph.nextIn(arc);
+            }
+            {
+              digraph.firstOut(arc, node);
+              digraph.nextOut(arc);
+            }
+          }           
+
+          {
+            checkConcept<GraphItemIt<_Digraph, typename _Digraph::Arc>,
+              typename _Digraph::ArcIt >();
+            checkConcept<GraphItemIt<_Digraph, typename _Digraph::Node>,
+              typename _Digraph::NodeIt >();
+            checkConcept<GraphIncIt<_Digraph, typename _Digraph::Arc, 
+              typename _Digraph::Node, 'i'>, typename _Digraph::InArcIt>();
+            checkConcept<GraphIncIt<_Digraph, typename _Digraph::Arc, 
+              typename _Digraph::Node, 'o'>, typename _Digraph::OutArcIt>();
+
+            typename _Digraph::Node n;
+            typename _Digraph::InArcIt ieit(INVALID);
+            typename _Digraph::OutArcIt oeit(INVALID);
+            n = digraph.baseNode(ieit);
+            n = digraph.runningNode(ieit);
+            n = digraph.baseNode(oeit);
+            n = digraph.runningNode(oeit);
+            ignore_unused_variable_warning(n);
+          }
+        }
+	
+	const _Digraph& digraph;
+	
+      };
+    };
+
+    /// \brief An empty iterable undirected graph class.
+    ///
+    /// This class provides beside the core graph features iterator
+    /// based iterable interface for the undirected graph structure.
+    /// This concept is part of the Graph concept.
+    template <typename _Base = BaseGraphComponent>
+    class IterableGraphComponent : public IterableDigraphComponent<_Base> {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::Arc Arc;
+      typedef typename Base::Edge Edge;
+
+    
+      typedef IterableGraphComponent Graph;
+
+      /// \name Base iteration
+      /// 
+      /// This interface provides functions for iteration on graph items
+      /// @{  
+
+      using IterableDigraphComponent<_Base>::first;
+      using IterableDigraphComponent<_Base>::next;
+
+      /// \brief Gives back the first edge in the iterating
+      /// order.
+      ///
+      /// Gives back the first edge in the iterating order.
+      ///     
+      void first(Edge&) const {}
+
+      /// \brief Gives back the next edge in the iterating
+      /// order.
+      ///
+      /// Gives back the next edge in the iterating order.
+      ///     
+      void next(Edge&) const {}
+
+
+      /// \brief Gives back the first of the edges from the
+      /// given node.
+      ///
+      /// Gives back the first of the edges from the given
+      /// node. The bool parameter gives back that direction which
+      /// gives a good direction of the edge so the source of the
+      /// directed arc is the given node.
+      void firstInc(Edge&, bool&, const Node&) const {}
+
+      /// \brief Gives back the next of the edges from the
+      /// given node.
+      ///
+      /// Gives back the next of the edges from the given
+      /// node. The bool parameter should be used as the \c firstInc()
+      /// use it.
+      void nextInc(Edge&, bool&) const {}
+
+      using IterableDigraphComponent<_Base>::baseNode;
+      using IterableDigraphComponent<_Base>::runningNode;
+
+      /// @}
+
+      /// \name Class based iteration
+      /// 
+      /// This interface provides functions for iteration on graph items
+      ///
+      /// @{
+
+      /// \brief This iterator goes through each node.
+      ///
+      /// This iterator goes through each node.
+      typedef GraphItemIt<Graph, Edge> EdgeIt;
+      /// \brief This iterator goes trough the incident arcs of a
+      /// node.
+      ///
+      /// This iterator goes trough the incident arcs of a certain
+      /// node of a graph.
+      typedef GraphIncIt<Graph, Edge, Node, 'u'> IncArcIt;
+      /// \brief The base node of the iterator.
+      ///
+      /// Gives back the base node of the iterator.
+      Node baseNode(const IncArcIt&) const { return INVALID; }
+
+      /// \brief The running node of the iterator.
+      ///
+      /// Gives back the running node of the iterator.
+      Node runningNode(const IncArcIt&) const { return INVALID; }
+
+      /// @}
+
+      template <typename _Graph> 
+      struct Constraints {
+	void constraints() {
+	  checkConcept<IterableDigraphComponent<Base>, _Graph>();
+
+          {
+            typename _Graph::Node node(INVALID);
+            typename _Graph::Edge edge(INVALID);
+            bool dir;
+            {
+              graph.first(edge);
+              graph.next(edge);
+            }
+            {
+              graph.firstInc(edge, dir, node);
+              graph.nextInc(edge, dir);
+            }
+            
+          }	
+  
+          {
+            checkConcept<GraphItemIt<_Graph, typename _Graph::Edge>,
+              typename _Graph::EdgeIt >();
+            checkConcept<GraphIncIt<_Graph, typename _Graph::Edge, 
+              typename _Graph::Node, 'u'>, typename _Graph::IncArcIt>();
+            
+            typename _Graph::Node n;
+            typename _Graph::IncArcIt ueit(INVALID);
+            n = graph.baseNode(ueit);
+            n = graph.runningNode(ueit);
+          }
+        }
+	
+	const _Graph& graph;
+	
+      };
+    };
+
+    /// \brief An empty alteration notifier digraph class.
+    ///  
+    /// This class provides beside the core digraph features alteration
+    /// notifier interface for the digraph structure.  This implements
+    /// an observer-notifier pattern for each digraph item. More
+    /// obsevers can be registered into the notifier and whenever an
+    /// alteration occured in the digraph all the observers will
+    /// notified about it.
+    template <typename _Base = BaseDigraphComponent>
+    class AlterableDigraphComponent : public _Base {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::Arc Arc;
+
+
+      /// The node observer registry.
+      typedef AlterationNotifier<AlterableDigraphComponent, Node> 
+      NodeNotifier;
+      /// The arc observer registry.
+      typedef AlterationNotifier<AlterableDigraphComponent, Arc> 
+      ArcNotifier;
+      
+      /// \brief Gives back the node alteration notifier.
+      ///
+      /// Gives back the node alteration notifier.
+      NodeNotifier& notifier(Node) const {
+	return NodeNotifier();
+      }
+      
+      /// \brief Gives back the arc alteration notifier.
+      ///
+      /// Gives back the arc alteration notifier.
+      ArcNotifier& notifier(Arc) const {
+	return ArcNotifier();
+      }
+
+      template <typename _Digraph> 
+      struct Constraints {
+	void constraints() {
+	  checkConcept<Base, _Digraph>();
+          typename _Digraph::NodeNotifier& nn 
+            = digraph.notifier(typename _Digraph::Node());
+
+          typename _Digraph::ArcNotifier& en 
+            = digraph.notifier(typename _Digraph::Arc());
+          
+          ignore_unused_variable_warning(nn);
+          ignore_unused_variable_warning(en);
+	}
+	
+	const _Digraph& digraph;
+	
+      };
+      
+    };
+
+    /// \brief An empty alteration notifier undirected graph class.
+    ///  
+    /// This class provides beside the core graph features alteration
+    /// notifier interface for the graph structure.  This implements
+    /// an observer-notifier pattern for each graph item. More
+    /// obsevers can be registered into the notifier and whenever an
+    /// alteration occured in the graph all the observers will
+    /// notified about it.
+    template <typename _Base = BaseGraphComponent>
+    class AlterableGraphComponent : public AlterableDigraphComponent<_Base> {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Edge Edge;
+
+
+      /// The arc observer registry.
+      typedef AlterationNotifier<AlterableGraphComponent, Edge> 
+      EdgeNotifier;
+      
+      /// \brief Gives back the arc alteration notifier.
+      ///
+      /// Gives back the arc alteration notifier.
+      EdgeNotifier& notifier(Edge) const {
+	return EdgeNotifier();
+      }
+
+      template <typename _Graph> 
+      struct Constraints {
+	void constraints() {
+	  checkConcept<AlterableGraphComponent<Base>, _Graph>();
+          typename _Graph::EdgeNotifier& uen 
+            = graph.notifier(typename _Graph::Edge());
+          ignore_unused_variable_warning(uen);
+	}
+	
+	const _Graph& graph;
+	
+      };
+      
+    };
+
+    /// \brief Class describing the concept of graph maps
+    /// 
+    /// This class describes the common interface of the graph maps
+    /// (NodeMap, ArcMap), that is \ref maps-page "maps" which can be used to
+    /// associate data to graph descriptors (nodes or arcs).
+    template <typename _Graph, typename _Item, typename _Value>
+    class GraphMap : public ReadWriteMap<_Item, _Value> {
+    public:
+
+      typedef ReadWriteMap<_Item, _Value> Parent;
+
+      /// The graph type of the map.
+      typedef _Graph Graph;
+      /// The key type of the map.
+      typedef _Item Key;
+      /// The value type of the map.
+      typedef _Value Value;
+
+      /// \brief Construct a new map.
+      ///
+      /// Construct a new map for the graph.
+      explicit GraphMap(const Graph&) {}
+      /// \brief Construct a new map with default value.
+      ///
+      /// Construct a new map for the graph and initalise the values.
+      GraphMap(const Graph&, const Value&) {}
+      /// \brief Copy constructor.
+      ///
+      /// Copy Constructor.
+      GraphMap(const GraphMap&) : Parent() {}
+      
+      /// \brief Assign operator.
+      ///
+      /// Assign operator. It does not mofify the underlying graph,
+      /// it just iterates on the current item set and set the  map
+      /// with the value returned by the assigned map. 
+      template <typename CMap>
+      GraphMap& operator=(const CMap&) { 
+        checkConcept<ReadMap<Key, Value>, CMap>();
+        return *this;
+      }
+
+      template<typename _Map>
+      struct Constraints {
+	void constraints() {
+	  checkConcept<ReadWriteMap<Key, Value>, _Map >();
+	  // Construction with a graph parameter
+	  _Map a(g);
+	  // Constructor with a graph and a default value parameter
+	  _Map a2(g,t);
+	  // Copy constructor.
+	  _Map b(c);
+          
+          ReadMap<Key, Value> cmap;
+          b = cmap;
+
+	  ignore_unused_variable_warning(a2);
+	  ignore_unused_variable_warning(b);
+	}
+
+	const _Map &c;
+	const Graph &g;
+	const typename GraphMap::Value &t;
+      };
+
+    };
+
+    /// \brief An empty mappable digraph class.
+    ///
+    /// This class provides beside the core digraph features
+    /// map interface for the digraph structure.
+    /// This concept is part of the Digraph concept.
+    template <typename _Base = BaseDigraphComponent>
+    class MappableDigraphComponent : public _Base  {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::Arc Arc;
+
+      typedef MappableDigraphComponent Digraph;
+
+      /// \brief ReadWrite map of the nodes.
+      ///
+      /// ReadWrite map of the nodes.
+      ///
+      template <typename _Value>
+      class NodeMap : public GraphMap<Digraph, Node, _Value> {
+      public:
+        typedef GraphMap<MappableDigraphComponent, Node, _Value> Parent;
+
+	/// \brief Construct a new map.
+	///
+	/// Construct a new map for the digraph.
+	explicit NodeMap(const MappableDigraphComponent& digraph) 
+          : Parent(digraph) {}
+
+	/// \brief Construct a new map with default value.
+	///
+	/// Construct a new map for the digraph and initalise the values.
+	NodeMap(const MappableDigraphComponent& digraph, const _Value& value)
+          : Parent(digraph, value) {}
+
+	/// \brief Copy constructor.
+	///
+	/// Copy Constructor.
+	NodeMap(const NodeMap& nm) : Parent(nm) {}
+
+	/// \brief Assign operator.
+	///
+	/// Assign operator.
+        template <typename CMap>
+        NodeMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<Node, _Value>, CMap>();
+          return *this;
+        }
+
+      };
+
+      /// \brief ReadWrite map of the arcs.
+      ///
+      /// ReadWrite map of the arcs.
+      ///
+      template <typename _Value>
+      class ArcMap : public GraphMap<Digraph, Arc, _Value> {
+      public:
+        typedef GraphMap<MappableDigraphComponent, Arc, _Value> Parent;
+
+	/// \brief Construct a new map.
+	///
+	/// Construct a new map for the digraph.
+	explicit ArcMap(const MappableDigraphComponent& digraph) 
+          : Parent(digraph) {}
+
+	/// \brief Construct a new map with default value.
+	///
+	/// Construct a new map for the digraph and initalise the values.
+	ArcMap(const MappableDigraphComponent& digraph, const _Value& value)
+          : Parent(digraph, value) {}
+
+	/// \brief Copy constructor.
+	///
+	/// Copy Constructor.
+	ArcMap(const ArcMap& nm) : Parent(nm) {}
+
+	/// \brief Assign operator.
+	///
+	/// Assign operator.
+        template <typename CMap>
+        ArcMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<Arc, _Value>, CMap>();
+          return *this;
+        }
+
+      };
+
+
+      template <typename _Digraph>
+      struct Constraints {
+
+	struct Dummy {
+	  int value;
+	  Dummy() : value(0) {}
+	  Dummy(int _v) : value(_v) {}
+	};
+
+	void constraints() {
+	  checkConcept<Base, _Digraph>();
+	  { // int map test
+	    typedef typename _Digraph::template NodeMap<int> IntNodeMap;
+	    checkConcept<GraphMap<_Digraph, typename _Digraph::Node, int>, 
+	      IntNodeMap >();
+	  } { // bool map test
+	    typedef typename _Digraph::template NodeMap<bool> BoolNodeMap;
+	    checkConcept<GraphMap<_Digraph, typename _Digraph::Node, bool>,
+	      BoolNodeMap >();
+	  } { // Dummy map test
+	    typedef typename _Digraph::template NodeMap<Dummy> DummyNodeMap;
+	    checkConcept<GraphMap<_Digraph, typename _Digraph::Node, Dummy>,
+	      DummyNodeMap >();
+	  } 
+
+	  { // int map test
+	    typedef typename _Digraph::template ArcMap<int> IntArcMap;
+	    checkConcept<GraphMap<_Digraph, typename _Digraph::Arc, int>,
+	      IntArcMap >();
+	  } { // bool map test
+	    typedef typename _Digraph::template ArcMap<bool> BoolArcMap;
+	    checkConcept<GraphMap<_Digraph, typename _Digraph::Arc, bool>,
+	      BoolArcMap >();
+	  } { // Dummy map test
+	    typedef typename _Digraph::template ArcMap<Dummy> DummyArcMap;
+	    checkConcept<GraphMap<_Digraph, typename _Digraph::Arc, Dummy>, 
+	      DummyArcMap >();
+	  } 
+	}
+
+	_Digraph& digraph;
+      };
+    };
+
+    /// \brief An empty mappable base bipartite graph class.
+    ///
+    /// This class provides beside the core graph features
+    /// map interface for the graph structure.
+    /// This concept is part of the Graph concept.
+    template <typename _Base = BaseGraphComponent>
+    class MappableGraphComponent : public MappableDigraphComponent<_Base>  {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Edge Edge;
+
+      typedef MappableGraphComponent Graph;
+
+      /// \brief ReadWrite map of the edges.
+      ///
+      /// ReadWrite map of the edges.
+      ///
+      template <typename _Value>
+      class EdgeMap : public GraphMap<Graph, Edge, _Value> {  
+      public:
+        typedef GraphMap<MappableGraphComponent, Edge, _Value> Parent;
+
+	/// \brief Construct a new map.
+	///
+	/// Construct a new map for the graph.
+	explicit EdgeMap(const MappableGraphComponent& graph) 
+          : Parent(graph) {}
+
+	/// \brief Construct a new map with default value.
+	///
+	/// Construct a new map for the graph and initalise the values.
+	EdgeMap(const MappableGraphComponent& graph, const _Value& value)
+          : Parent(graph, value) {}
+
+	/// \brief Copy constructor.
+	///
+	/// Copy Constructor.
+	EdgeMap(const EdgeMap& nm) : Parent(nm) {}
+
+	/// \brief Assign operator.
+	///
+	/// Assign operator.
+        template <typename CMap>
+        EdgeMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<Edge, _Value>, CMap>();
+          return *this;
+        }
+
+      };
+
+
+      template <typename _Graph>
+      struct Constraints {
+
+	struct Dummy {
+	  int value;
+	  Dummy() : value(0) {}
+	  Dummy(int _v) : value(_v) {}
+	};
+
+	void constraints() {
+	  checkConcept<MappableGraphComponent<Base>, _Graph>();
+
+	  { // int map test
+	    typedef typename _Graph::template EdgeMap<int> IntEdgeMap;
+	    checkConcept<GraphMap<_Graph, typename _Graph::Edge, int>,
+	      IntEdgeMap >();
+	  } { // bool map test
+	    typedef typename _Graph::template EdgeMap<bool> BoolEdgeMap;
+	    checkConcept<GraphMap<_Graph, typename _Graph::Edge, bool>,
+	      BoolEdgeMap >();
+	  } { // Dummy map test
+	    typedef typename _Graph::template EdgeMap<Dummy> DummyEdgeMap;
+	    checkConcept<GraphMap<_Graph, typename _Graph::Edge, Dummy>, 
+	      DummyEdgeMap >();
+	  } 
+	}
+
+	_Graph& graph;
+      };
+    };
+
+    /// \brief An empty extendable digraph class.
+    ///
+    /// This class provides beside the core digraph features digraph
+    /// extendable interface for the digraph structure.  The main
+    /// difference between the base and this interface is that the
+    /// digraph alterations should handled already on this level.
+    template <typename _Base = BaseDigraphComponent>
+    class ExtendableDigraphComponent : public _Base {
+    public:
+      typedef _Base Base;
+
+      typedef typename _Base::Node Node;
+      typedef typename _Base::Arc Arc;
+
+      /// \brief Adds a new node to the digraph.
+      ///
+      /// Adds a new node to the digraph.
+      ///
+      Node addNode() {
+	return INVALID;
+      }
+    
+      /// \brief Adds a new arc connects the given two nodes.
+      ///
+      /// Adds a new arc connects the the given two nodes.
+      Arc addArc(const Node&, const Node&) {
+	return INVALID;
+      }
+
+      template <typename _Digraph>
+      struct Constraints {
+	void constraints() {
+          checkConcept<Base, _Digraph>();
+	  typename _Digraph::Node node_a, node_b;
+	  node_a = digraph.addNode();
+	  node_b = digraph.addNode();
+	  typename _Digraph::Arc arc;
+	  arc = digraph.addArc(node_a, node_b);
+	}
+
+	_Digraph& digraph;
+      };
+    };
+
+    /// \brief An empty extendable base undirected graph class.
+    ///
+    /// This class provides beside the core undirected graph features
+    /// core undircted graph extend interface for the graph structure.
+    /// The main difference between the base and this interface is
+    /// that the graph alterations should handled already on this
+    /// level.
+    template <typename _Base = BaseGraphComponent>
+    class ExtendableGraphComponent : public _Base {
+    public:
+
+      typedef _Base Base;
+      typedef typename _Base::Node Node;
+      typedef typename _Base::Edge Edge;
+
+      /// \brief Adds a new node to the graph.
+      ///
+      /// Adds a new node to the graph.
+      ///
+      Node addNode() {
+	return INVALID;
+      }
+    
+      /// \brief Adds a new arc connects the given two nodes.
+      ///
+      /// Adds a new arc connects the the given two nodes.
+      Edge addArc(const Node&, const Node&) {
+	return INVALID;
+      }
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+	  checkConcept<Base, _Graph>();
+	  typename _Graph::Node node_a, node_b;
+	  node_a = graph.addNode();
+	  node_b = graph.addNode();
+	  typename _Graph::Edge edge;
+	  edge = graph.addEdge(node_a, node_b);
+	}
+
+	_Graph& graph;
+      };
+    };
+
+    /// \brief An empty erasable digraph class.
+    ///  
+    /// This class provides beside the core digraph features core erase
+    /// functions for the digraph structure. The main difference between
+    /// the base and this interface is that the digraph alterations
+    /// should handled already on this level.
+    template <typename _Base = BaseDigraphComponent>
+    class ErasableDigraphComponent : public _Base {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::Arc Arc;
+
+      /// \brief Erase a node from the digraph.
+      ///
+      /// Erase a node from the digraph. This function should 
+      /// erase all arcs connecting to the node.
+      void erase(const Node&) {}    
+
+      /// \brief Erase an arc from the digraph.
+      ///
+      /// Erase an arc from the digraph.
+      ///
+      void erase(const Arc&) {}
+
+      template <typename _Digraph>
+      struct Constraints {
+	void constraints() {
+          checkConcept<Base, _Digraph>();
+	  typename _Digraph::Node node;
+	  digraph.erase(node);
+	  typename _Digraph::Arc arc;
+	  digraph.erase(arc);
+	}
+
+	_Digraph& digraph;
+      };
+    };
+
+    /// \brief An empty erasable base undirected graph class.
+    ///  
+    /// This class provides beside the core undirected graph features
+    /// core erase functions for the undirceted graph structure. The
+    /// main difference between the base and this interface is that
+    /// the graph alterations should handled already on this level.
+    template <typename _Base = BaseGraphComponent>
+    class ErasableGraphComponent : public _Base {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::Edge Edge;
+
+      /// \brief Erase a node from the graph.
+      ///
+      /// Erase a node from the graph. This function should erase
+      /// arcs connecting to the node.
+      void erase(const Node&) {}    
+
+      /// \brief Erase an arc from the graph.
+      ///
+      /// Erase an arc from the graph.
+      ///
+      void erase(const Edge&) {}
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+          checkConcept<Base, _Graph>();
+	  typename _Graph::Node node;
+	  graph.erase(node);
+	  typename _Graph::Arc arc;
+	  graph.erase(arc);
+	}
+
+	_Graph& graph;
+      };
+    };
+
+    /// \brief An empty clearable base digraph class.
+    ///
+    /// This class provides beside the core digraph features core clear
+    /// functions for the digraph structure. The main difference between
+    /// the base and this interface is that the digraph alterations
+    /// should handled already on this level.
+    template <typename _Base = BaseDigraphComponent>
+    class ClearableDigraphComponent : public _Base {
+    public:
+
+      typedef _Base Base;
+
+      /// \brief Erase all nodes and arcs from the digraph.
+      ///
+      /// Erase all nodes and arcs from the digraph.
+      ///
+      void clear() {}    
+
+      template <typename _Digraph>
+      struct Constraints {
+	void constraints() {
+          checkConcept<Base, _Digraph>();
+	  digraph.clear();
+	}
+
+	_Digraph digraph;
+      };
+    };
+
+    /// \brief An empty clearable base undirected graph class.
+    ///
+    /// This class provides beside the core undirected graph features
+    /// core clear functions for the undirected graph structure. The
+    /// main difference between the base and this interface is that
+    /// the graph alterations should handled already on this level.
+    template <typename _Base = BaseGraphComponent>
+    class ClearableGraphComponent : public ClearableDigraphComponent<_Base> {
+    public:
+
+      typedef _Base Base;
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+          checkConcept<ClearableGraphComponent<Base>, _Graph>();
+	}
+
+	_Graph graph;
+      };
+    };
+
+  }
+
+}
+
+#endif
Index: lemon/list_graph.h
===================================================================
--- lemon/list_graph.h	(revision 39)
+++ lemon/list_graph.h	(revision 57)
@@ -17,2 +17,1451 @@
  */
 
+#ifndef LEMON_LIST_GRAPH_H
+#define LEMON_LIST_GRAPH_H
+
+///\ingroup graphs
+///\file
+///\brief ListDigraph, ListGraph classes.
+
+#include <lemon/bits/graph_extender.h>
+
+#include <vector>
+#include <list>
+
+namespace lemon {
+
+  class ListDigraphBase {
+
+  protected:
+    struct NodeT {
+      int first_in, first_out;
+      int prev, next;
+    };
+ 
+    struct ArcT {
+      int target, source;
+      int prev_in, prev_out;
+      int next_in, next_out;
+    };
+
+    std::vector<NodeT> nodes;
+
+    int first_node;
+
+    int first_free_node;
+
+    std::vector<ArcT> arcs;
+
+    int first_free_arc;
+    
+  public:
+    
+    typedef ListDigraphBase Digraph;
+    
+    class Node {
+      friend class ListDigraphBase;
+    protected:
+
+      int id;
+      explicit Node(int pid) { id = pid;}
+
+    public:
+      Node() {}
+      Node (Invalid) { id = -1; }
+      bool operator==(const Node& node) const {return id == node.id;}
+      bool operator!=(const Node& node) const {return id != node.id;}
+      bool operator<(const Node& node) const {return id < node.id;}
+    };
+
+    class Arc {
+      friend class ListDigraphBase;
+    protected:
+
+      int id;
+      explicit Arc(int pid) { id = pid;}
+
+    public:
+      Arc() {}
+      Arc (Invalid) { id = -1; }
+      bool operator==(const Arc& arc) const {return id == arc.id;}
+      bool operator!=(const Arc& arc) const {return id != arc.id;}
+      bool operator<(const Arc& arc) const {return id < arc.id;}
+    };
+
+
+
+    ListDigraphBase()
+      : nodes(), first_node(-1),
+	first_free_node(-1), arcs(), first_free_arc(-1) {}
+
+    
+    int maxNodeId() const { return nodes.size()-1; } 
+    int maxArcId() const { return arcs.size()-1; }
+
+    Node source(Arc e) const { return Node(arcs[e.id].source); }
+    Node target(Arc e) const { return Node(arcs[e.id].target); }
+
+
+    void first(Node& node) const { 
+      node.id = first_node;
+    }
+
+    void next(Node& node) const {
+      node.id = nodes[node.id].next;
+    }
+
+
+    void first(Arc& e) const { 
+      int n;
+      for(n = first_node; 
+	  n!=-1 && nodes[n].first_in == -1; 
+	  n = nodes[n].next);
+      e.id = (n == -1) ? -1 : nodes[n].first_in;
+    }
+
+    void next(Arc& arc) const {
+      if (arcs[arc.id].next_in != -1) {
+	arc.id = arcs[arc.id].next_in;
+      } else {
+	int n;
+	for(n = nodes[arcs[arc.id].target].next;
+	  n!=-1 && nodes[n].first_in == -1; 
+	  n = nodes[n].next);
+	arc.id = (n == -1) ? -1 : nodes[n].first_in;
+      }      
+    }
+
+    void firstOut(Arc &e, const Node& v) const {
+      e.id = nodes[v.id].first_out;
+    }
+    void nextOut(Arc &e) const {
+      e.id=arcs[e.id].next_out;
+    }
+
+    void firstIn(Arc &e, const Node& v) const {
+      e.id = nodes[v.id].first_in;
+    }
+    void nextIn(Arc &e) const {
+      e.id=arcs[e.id].next_in;
+    }
+
+    
+    static int id(Node v) { return v.id; }
+    static int id(Arc e) { return e.id; }
+
+    static Node nodeFromId(int id) { return Node(id);}
+    static Arc arcFromId(int id) { return Arc(id);}
+
+    Node addNode() {     
+      int n;
+      
+      if(first_free_node==-1) {
+	n = nodes.size();
+	nodes.push_back(NodeT());
+      } else {
+	n = first_free_node;
+	first_free_node = nodes[n].next;
+      }
+      
+      nodes[n].next = first_node;
+      if(first_node != -1) nodes[first_node].prev = n;
+      first_node = n;
+      nodes[n].prev = -1;
+      
+      nodes[n].first_in = nodes[n].first_out = -1;
+      
+      return Node(n);
+    }
+    
+    Arc addArc(Node u, Node v) {
+      int n;      
+
+      if (first_free_arc == -1) {
+	n = arcs.size();
+	arcs.push_back(ArcT());
+      } else {
+	n = first_free_arc;
+	first_free_arc = arcs[n].next_in;
+      }
+      
+      arcs[n].source = u.id; 
+      arcs[n].target = v.id;
+
+      arcs[n].next_out = nodes[u.id].first_out;
+      if(nodes[u.id].first_out != -1) {
+	arcs[nodes[u.id].first_out].prev_out = n;
+      }
+      
+      arcs[n].next_in = nodes[v.id].first_in;
+      if(nodes[v.id].first_in != -1) {
+	arcs[nodes[v.id].first_in].prev_in = n;
+      }
+      
+      arcs[n].prev_in = arcs[n].prev_out = -1;
+	
+      nodes[u.id].first_out = nodes[v.id].first_in = n;
+
+      return Arc(n);
+    }
+    
+    void erase(const Node& node) {
+      int n = node.id;
+      
+      if(nodes[n].next != -1) {
+	nodes[nodes[n].next].prev = nodes[n].prev;
+      }
+      
+      if(nodes[n].prev != -1) {
+	nodes[nodes[n].prev].next = nodes[n].next;
+      } else {
+	first_node = nodes[n].next;
+      }
+      
+      nodes[n].next = first_free_node;
+      first_free_node = n;
+
+    }
+    
+    void erase(const Arc& arc) {
+      int n = arc.id;
+      
+      if(arcs[n].next_in!=-1) {
+	arcs[arcs[n].next_in].prev_in = arcs[n].prev_in;
+      }
+
+      if(arcs[n].prev_in!=-1) {
+	arcs[arcs[n].prev_in].next_in = arcs[n].next_in;
+      } else {
+	nodes[arcs[n].target].first_in = arcs[n].next_in;
+      }
+
+      
+      if(arcs[n].next_out!=-1) {
+	arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;
+      } 
+
+      if(arcs[n].prev_out!=-1) {
+	arcs[arcs[n].prev_out].next_out = arcs[n].next_out;
+      } else {
+	nodes[arcs[n].source].first_out = arcs[n].next_out;
+      }
+      
+      arcs[n].next_in = first_free_arc;
+      first_free_arc = n;      
+
+    }
+
+    void clear() {
+      arcs.clear();
+      nodes.clear();
+      first_node = first_free_node = first_free_arc = -1;
+    }
+
+  protected:
+    void changeTarget(Arc e, Node n) 
+    {
+      if(arcs[e.id].next_in != -1)
+	arcs[arcs[e.id].next_in].prev_in = arcs[e.id].prev_in;
+      if(arcs[e.id].prev_in != -1)
+	arcs[arcs[e.id].prev_in].next_in = arcs[e.id].next_in;
+      else nodes[arcs[e.id].target].first_in = arcs[e.id].next_in;
+      if (nodes[n.id].first_in != -1) {
+	arcs[nodes[n.id].first_in].prev_in = e.id;
+      }
+      arcs[e.id].target = n.id;
+      arcs[e.id].prev_in = -1;
+      arcs[e.id].next_in = nodes[n.id].first_in;
+      nodes[n.id].first_in = e.id;
+    }
+    void changeSource(Arc e, Node n) 
+    {
+      if(arcs[e.id].next_out != -1)
+	arcs[arcs[e.id].next_out].prev_out = arcs[e.id].prev_out;
+      if(arcs[e.id].prev_out != -1)
+	arcs[arcs[e.id].prev_out].next_out = arcs[e.id].next_out;
+      else nodes[arcs[e.id].source].first_out = arcs[e.id].next_out;
+      if (nodes[n.id].first_out != -1) {
+	arcs[nodes[n.id].first_out].prev_out = e.id;
+      }
+      arcs[e.id].source = n.id;
+      arcs[e.id].prev_out = -1;
+      arcs[e.id].next_out = nodes[n.id].first_out;
+      nodes[n.id].first_out = e.id;
+    }
+
+  };
+
+  typedef DigraphExtender<ListDigraphBase> ExtendedListDigraphBase;
+
+  /// \addtogroup digraphs
+  /// @{
+
+  ///A list digraph class.
+
+  ///This is a simple and fast digraph implementation.
+  ///
+  ///It conforms to the \ref concepts::Digraph "Digraph concept" and it
+  ///also provides several additional useful extra functionalities.
+  ///The most of the member functions and nested classes are
+  ///documented only in the concept class.
+  ///
+  ///An important extra feature of this digraph implementation is that
+  ///its maps are real \ref concepts::ReferenceMap "reference map"s.
+  ///
+  ///\sa concepts::Digraph.
+
+  class ListDigraph : public ExtendedListDigraphBase {
+  private:
+    ///ListDigraph is \e not copy constructible. Use DigraphCopy() instead.
+    
+    ///ListDigraph is \e not copy constructible. Use DigraphCopy() instead.
+    ///
+    ListDigraph(const ListDigraph &) :ExtendedListDigraphBase() {};
+    ///\brief Assignment of ListDigraph to another one is \e not allowed.
+    ///Use DigraphCopy() instead.
+
+    ///Assignment of ListDigraph to another one is \e not allowed.
+    ///Use DigraphCopy() instead.
+    void operator=(const ListDigraph &) {}
+  public:
+
+    typedef ExtendedListDigraphBase Parent;
+
+    /// Constructor
+    
+    /// Constructor.
+    ///
+    ListDigraph() {}
+
+    ///Add a new node to the digraph.
+    
+    /// \return the new node.
+    ///
+    Node addNode() { return Parent::addNode(); }
+
+    ///Add a new arc to the digraph.
+    
+    ///Add a new arc to the digraph with source node \c s
+    ///and target node \c t.
+    ///\return the new arc.
+    Arc addArc(const Node& s, const Node& t) { 
+      return Parent::addArc(s, t); 
+    }
+
+    /// Changes the target of \c e to \c n
+
+    /// Changes the target of \c e to \c n
+    ///
+    ///\note The <tt>ArcIt</tt>s and <tt>OutArcIt</tt>s referencing
+    ///the changed arc remain valid. However <tt>InArcIt</tt>s are
+    ///invalidated.
+    ///\warning This functionality cannot be used together with the Snapshot
+    ///feature.
+    void changeTarget(Arc e, Node n) { 
+      Parent::changeTarget(e,n); 
+    }
+    /// Changes the source of \c e to \c n
+
+    /// Changes the source of \c e to \c n
+    ///
+    ///\note The <tt>ArcIt</tt>s and <tt>InArcIt</tt>s referencing
+    ///the changed arc remain valid. However <tt>OutArcIt</tt>s are
+    ///invalidated.
+    ///\warning This functionality cannot be used together with the Snapshot
+    ///feature.
+    void changeSource(Arc e, Node n) { 
+      Parent::changeSource(e,n);
+    }
+
+    /// Invert the direction of an arc.
+
+    ///\note The <tt>ArcIt</tt>s referencing the changed arc remain
+    ///valid. However <tt>OutArcIt</tt>s and <tt>InArcIt</tt>s are
+    ///invalidated.
+    ///\warning This functionality cannot be used together with the Snapshot
+    ///feature.
+    void reverseArc(Arc e) {
+      Node t=target(e);
+      changeTarget(e,source(e));
+      changeSource(e,t);
+    }
+
+    /// Using this it is possible to avoid the superfluous memory
+    /// allocation: if you know that the digraph you want to build will
+    /// be very large (e.g. it will contain millions of nodes and/or arcs)
+    /// then it is worth reserving space for this amount before starting
+    /// to build the digraph.
+    /// \sa reserveArc
+    void reserveNode(int n) { nodes.reserve(n); };
+
+    /// \brief Using this it is possible to avoid the superfluous memory
+    /// allocation.
+
+    /// Using this it is possible to avoid the superfluous memory
+    /// allocation: if you know that the digraph you want to build will
+    /// be very large (e.g. it will contain millions of nodes and/or arcs)
+    /// then it is worth reserving space for this amount before starting
+    /// to build the digraph.
+    /// \sa reserveNode
+    void reserveArc(int m) { arcs.reserve(m); };
+
+    ///Contract two nodes.
+
+    ///This function contracts two nodes.
+    ///
+    ///Node \p b will be removed but instead of deleting
+    ///incident arcs, they will be joined to \p a.
+    ///The last parameter \p r controls whether to remove loops. \c true
+    ///means that loops will be removed.
+    ///
+    ///\note The <tt>ArcIt</tt>s
+    ///referencing a moved arc remain
+    ///valid. However <tt>InArcIt</tt>s and <tt>OutArcIt</tt>s
+    ///may be invalidated.
+    ///\warning This functionality cannot be used together with the Snapshot
+    ///feature.
+    void contract(Node a, Node b, bool r = true) 
+    {
+      for(OutArcIt e(*this,b);e!=INVALID;) {
+	OutArcIt f=e;
+	++f;
+	if(r && target(e)==a) erase(e);
+	else changeSource(e,a);
+	e=f;
+      }
+      for(InArcIt e(*this,b);e!=INVALID;) {
+	InArcIt f=e;
+	++f;
+	if(r && source(e)==a) erase(e);
+	else changeTarget(e,a);
+	e=f;
+      }
+      erase(b);
+    }
+
+    ///Split a node.
+
+    ///This function splits a node. First a new node is added to the digraph,
+    ///then the source of each outgoing arc of \c n is moved to this new node.
+    ///If \c connect is \c true (this is the default value), then a new arc
+    ///from \c n to the newly created node is also added.
+    ///\return The newly created node.
+    ///
+    ///\note The <tt>ArcIt</tt>s referencing a moved arc remain
+    ///valid. However <tt>InArcIt</tt>s and <tt>OutArcIt</tt>s may
+    ///be invalidated.  
+    ///
+    ///\warning This functionality cannot be used together with the
+    ///Snapshot feature.  \todo It could be implemented in a bit
+    ///faster way.
+    Node split(Node n, bool connect = true) {
+      Node b = addNode();
+      for(OutArcIt e(*this,n);e!=INVALID;) {
+ 	OutArcIt f=e;
+	++f;
+	changeSource(e,b);
+	e=f;
+      }
+      if (connect) addArc(n,b);
+      return b;
+    }
+      
+    ///Split an arc.
+
+    ///This function splits an arc. First a new node \c b is added to
+    ///the digraph, then the original arc is re-targeted to \c
+    ///b. Finally an arc from \c b to the original target is added.
+    ///\return The newly created node.  
+    ///\warning This functionality
+    ///cannot be used together with the Snapshot feature.
+    Node split(Arc e) {
+      Node b = addNode();
+      addArc(b,target(e));
+      changeTarget(e,b);
+      return b;
+    }
+      
+    /// \brief Class to make a snapshot of the digraph and restore
+    /// to it later.
+    ///
+    /// Class to make a snapshot of the digraph and to restore it
+    /// later.
+    ///
+    /// The newly added nodes and arcs can be removed using the
+    /// restore() function.
+    ///
+    /// \warning Arc and node deletions cannot be restored. This
+    /// events invalidate the snapshot. 
+    class Snapshot {
+    protected:
+
+      typedef Parent::NodeNotifier NodeNotifier;
+
+      class NodeObserverProxy : public NodeNotifier::ObserverBase {
+      public:
+
+        NodeObserverProxy(Snapshot& _snapshot)
+          : snapshot(_snapshot) {}
+
+        using NodeNotifier::ObserverBase::attach;
+        using NodeNotifier::ObserverBase::detach;
+        using NodeNotifier::ObserverBase::attached;
+        
+      protected:
+        
+        virtual void add(const Node& node) {
+          snapshot.addNode(node);
+        }
+        virtual void add(const std::vector<Node>& nodes) {
+          for (int i = nodes.size() - 1; i >= 0; ++i) {
+            snapshot.addNode(nodes[i]);
+          }
+        }
+        virtual void erase(const Node& node) {
+          snapshot.eraseNode(node);
+        }
+        virtual void erase(const std::vector<Node>& nodes) {
+          for (int i = 0; i < int(nodes.size()); ++i) {
+            snapshot.eraseNode(nodes[i]);
+          }
+        }
+        virtual void build() {
+          Node node;
+          std::vector<Node> nodes;
+          for (notifier()->first(node); node != INVALID; 
+               notifier()->next(node)) {
+            nodes.push_back(node);
+          }
+          for (int i = nodes.size() - 1; i >= 0; --i) {
+            snapshot.addNode(nodes[i]);
+          }
+        }
+        virtual void clear() {
+          Node node;
+          for (notifier()->first(node); node != INVALID; 
+               notifier()->next(node)) {
+            snapshot.eraseNode(node);
+          }
+        }
+
+        Snapshot& snapshot;
+      };
+
+      class ArcObserverProxy : public ArcNotifier::ObserverBase {
+      public:
+
+        ArcObserverProxy(Snapshot& _snapshot)
+          : snapshot(_snapshot) {}
+
+        using ArcNotifier::ObserverBase::attach;
+        using ArcNotifier::ObserverBase::detach;
+        using ArcNotifier::ObserverBase::attached;
+        
+      protected:
+
+        virtual void add(const Arc& arc) {
+          snapshot.addArc(arc);
+        }
+        virtual void add(const std::vector<Arc>& arcs) {
+          for (int i = arcs.size() - 1; i >= 0; ++i) {
+            snapshot.addArc(arcs[i]);
+          }
+        }
+        virtual void erase(const Arc& arc) {
+          snapshot.eraseArc(arc);
+        }
+        virtual void erase(const std::vector<Arc>& arcs) {
+          for (int i = 0; i < int(arcs.size()); ++i) {
+            snapshot.eraseArc(arcs[i]);
+          }
+        }
+        virtual void build() {
+          Arc arc;
+          std::vector<Arc> arcs;
+          for (notifier()->first(arc); arc != INVALID; 
+               notifier()->next(arc)) {
+            arcs.push_back(arc);
+          }
+          for (int i = arcs.size() - 1; i >= 0; --i) {
+            snapshot.addArc(arcs[i]);
+          }
+        }
+        virtual void clear() {
+          Arc arc;
+          for (notifier()->first(arc); arc != INVALID; 
+               notifier()->next(arc)) {
+            snapshot.eraseArc(arc);
+          }
+        }
+
+        Snapshot& snapshot;
+      };
+      
+      ListDigraph *digraph;
+
+      NodeObserverProxy node_observer_proxy;
+      ArcObserverProxy arc_observer_proxy;
+
+      std::list<Node> added_nodes;
+      std::list<Arc> added_arcs;
+
+
+      void addNode(const Node& node) {
+        added_nodes.push_front(node);        
+      }
+      void eraseNode(const Node& node) {
+        std::list<Node>::iterator it = 
+          std::find(added_nodes.begin(), added_nodes.end(), node);
+        if (it == added_nodes.end()) {
+          clear();
+          arc_observer_proxy.detach();
+          throw NodeNotifier::ImmediateDetach();
+        } else {
+          added_nodes.erase(it);
+        }
+      }
+
+      void addArc(const Arc& arc) {
+        added_arcs.push_front(arc);        
+      }
+      void eraseArc(const Arc& arc) {
+        std::list<Arc>::iterator it = 
+          std::find(added_arcs.begin(), added_arcs.end(), arc);
+        if (it == added_arcs.end()) {
+          clear();
+          node_observer_proxy.detach(); 
+          throw ArcNotifier::ImmediateDetach();
+        } else {
+          added_arcs.erase(it);
+        }        
+      }
+
+      void attach(ListDigraph &_digraph) {
+	digraph = &_digraph;
+	node_observer_proxy.attach(digraph->notifier(Node()));
+        arc_observer_proxy.attach(digraph->notifier(Arc()));
+      }
+            
+      void detach() {
+	node_observer_proxy.detach();
+	arc_observer_proxy.detach();
+      }
+
+      bool attached() const {
+        return node_observer_proxy.attached();
+      }
+
+      void clear() {
+        added_nodes.clear();
+        added_arcs.clear();        
+      }
+
+    public:
+
+      /// \brief Default constructor.
+      ///
+      /// Default constructor.
+      /// To actually make a snapshot you must call save().
+      Snapshot() 
+        : digraph(0), node_observer_proxy(*this), 
+          arc_observer_proxy(*this) {}
+      
+      /// \brief Constructor that immediately makes a snapshot.
+      ///      
+      /// This constructor immediately makes a snapshot of the digraph.
+      /// \param _digraph The digraph we make a snapshot of.
+      Snapshot(ListDigraph &_digraph) 
+        : node_observer_proxy(*this), 
+          arc_observer_proxy(*this) {
+	attach(_digraph);
+      }
+      
+      /// \brief Make a snapshot.
+      ///
+      /// Make a snapshot of the digraph.
+      ///
+      /// This function can be called more than once. In case of a repeated
+      /// call, the previous snapshot gets lost.
+      /// \param _digraph The digraph we make the snapshot of.
+      void save(ListDigraph &_digraph) {
+        if (attached()) {
+          detach();
+          clear();
+        }
+        attach(_digraph);
+      }
+      
+      /// \brief Undo the changes until the last snapshot.
+      // 
+      /// Undo the changes until the last snapshot created by save().
+      void restore() {
+	detach();
+	for(std::list<Arc>::iterator it = added_arcs.begin(); 
+            it != added_arcs.end(); ++it) {
+	  digraph->erase(*it);
+	}
+	for(std::list<Node>::iterator it = added_nodes.begin(); 
+            it != added_nodes.end(); ++it) {
+	  digraph->erase(*it);
+	}
+        clear();
+      }
+
+      /// \brief Gives back true when the snapshot is valid.
+      ///
+      /// Gives back true when the snapshot is valid.
+      bool valid() const {
+        return attached();
+      }
+    };
+    
+  };
+
+  ///@}
+
+  class ListGraphBase {
+
+  protected:
+
+    struct NodeT {
+      int first_out;
+      int prev, next;
+    };
+ 
+    struct ArcT {
+      int target;
+      int prev_out, next_out;
+    };
+
+    std::vector<NodeT> nodes;
+
+    int first_node;
+
+    int first_free_node;
+
+    std::vector<ArcT> arcs;
+
+    int first_free_arc;
+    
+  public:
+    
+    typedef ListGraphBase Digraph;
+
+    class Node;
+    class Arc;
+    class Edge;
+    
+    class Node {
+      friend class ListGraphBase;
+    protected:
+
+      int id;
+      explicit Node(int pid) { id = pid;}
+
+    public:
+      Node() {}
+      Node (Invalid) { id = -1; }
+      bool operator==(const Node& node) const {return id == node.id;}
+      bool operator!=(const Node& node) const {return id != node.id;}
+      bool operator<(const Node& node) const {return id < node.id;}
+    };
+
+    class Edge {
+      friend class ListGraphBase;
+    protected:
+
+      int id;
+      explicit Edge(int pid) { id = pid;}
+
+    public:
+      Edge() {}
+      Edge (Invalid) { id = -1; }
+      bool operator==(const Edge& arc) const {return id == arc.id;}
+      bool operator!=(const Edge& arc) const {return id != arc.id;}
+      bool operator<(const Edge& arc) const {return id < arc.id;}
+    };
+
+    class Arc {
+      friend class ListGraphBase;
+    protected:
+
+      int id;
+      explicit Arc(int pid) { id = pid;}
+
+    public:
+      operator Edge() const { return edgeFromId(id / 2); }
+
+      Arc() {}
+      Arc (Invalid) { id = -1; }
+      bool operator==(const Arc& arc) const {return id == arc.id;}
+      bool operator!=(const Arc& arc) const {return id != arc.id;}
+      bool operator<(const Arc& arc) const {return id < arc.id;}
+    };
+
+
+
+    ListGraphBase()
+      : nodes(), first_node(-1),
+	first_free_node(-1), arcs(), first_free_arc(-1) {}
+
+    
+    int maxNodeId() const { return nodes.size()-1; } 
+    int maxEdgeId() const { return arcs.size() / 2 - 1; }
+    int maxArcId() const { return arcs.size()-1; }
+
+    Node source(Arc e) const { return Node(arcs[e.id ^ 1].target); }
+    Node target(Arc e) const { return Node(arcs[e.id].target); }
+
+    Node u(Edge e) const { return Node(arcs[2 * e.id].target); }
+    Node v(Edge e) const { return Node(arcs[2 * e.id + 1].target); }
+
+    static bool direction(Arc e) {
+      return (e.id & 1) == 1;
+    }
+
+    static Arc direct(Edge e, bool d) {
+      return Arc(e.id * 2 + (d ? 1 : 0));
+    }
+
+    void first(Node& node) const { 
+      node.id = first_node;
+    }
+
+    void next(Node& node) const {
+      node.id = nodes[node.id].next;
+    }
+
+    void first(Arc& e) const { 
+      int n = first_node;
+      while (n != -1 && nodes[n].first_out == -1) {
+        n = nodes[n].next;
+      }
+      e.id = (n == -1) ? -1 : nodes[n].first_out;
+    }
+
+    void next(Arc& e) const {
+      if (arcs[e.id].next_out != -1) {
+	e.id = arcs[e.id].next_out;
+      } else {
+	int n = nodes[arcs[e.id ^ 1].target].next;
+        while(n != -1 && nodes[n].first_out == -1) {
+          n = nodes[n].next;
+        }
+	e.id = (n == -1) ? -1 : nodes[n].first_out;
+      }      
+    }
+
+    void first(Edge& e) const { 
+      int n = first_node;
+      while (n != -1) {
+        e.id = nodes[n].first_out;
+        while ((e.id & 1) != 1) {
+          e.id = arcs[e.id].next_out;
+        }
+        if (e.id != -1) {
+          e.id /= 2;
+          return;
+        } 
+        n = nodes[n].next;
+      }
+      e.id = -1;
+    }
+
+    void next(Edge& e) const {
+      int n = arcs[e.id * 2].target;
+      e.id = arcs[(e.id * 2) | 1].next_out;
+      while ((e.id & 1) != 1) {
+        e.id = arcs[e.id].next_out;
+      }
+      if (e.id != -1) {
+        e.id /= 2;
+        return;
+      } 
+      n = nodes[n].next;
+      while (n != -1) {
+        e.id = nodes[n].first_out;
+        while ((e.id & 1) != 1) {
+          e.id = arcs[e.id].next_out;
+        }
+        if (e.id != -1) {
+          e.id /= 2;
+          return;
+        } 
+        n = nodes[n].next;
+      }
+      e.id = -1;
+    }
+
+    void firstOut(Arc &e, const Node& v) const {
+      e.id = nodes[v.id].first_out;
+    }
+    void nextOut(Arc &e) const {
+      e.id = arcs[e.id].next_out;
+    }
+
+    void firstIn(Arc &e, const Node& v) const {
+      e.id = ((nodes[v.id].first_out) ^ 1);
+      if (e.id == -2) e.id = -1;
+    }
+    void nextIn(Arc &e) const {
+      e.id = ((arcs[e.id ^ 1].next_out) ^ 1);
+      if (e.id == -2) e.id = -1;
+    }
+
+    void firstInc(Edge &e, bool& d, const Node& v) const {
+      int de = nodes[v.id].first_out;
+      if (de != -1 ) {
+        e.id = de / 2;
+        d = ((de & 1) == 1);
+      } else {
+        e.id = -1;
+        d = true;
+      }
+    }
+    void nextInc(Edge &e, bool& d) const {
+      int de = (arcs[(e.id * 2) | (d ? 1 : 0)].next_out);
+      if (de != -1 ) {
+        e.id = de / 2;
+        d = ((de & 1) == 1);
+      } else {
+        e.id = -1;
+        d = true;
+      }
+    }
+    
+    static int id(Node v) { return v.id; }
+    static int id(Arc e) { return e.id; }
+    static int id(Edge e) { return e.id; }
+
+    static Node nodeFromId(int id) { return Node(id);}
+    static Arc arcFromId(int id) { return Arc(id);}
+    static Edge edgeFromId(int id) { return Edge(id);}
+
+    Node addNode() {     
+      int n;
+      
+      if(first_free_node==-1) {
+	n = nodes.size();
+	nodes.push_back(NodeT());
+      } else {
+	n = first_free_node;
+	first_free_node = nodes[n].next;
+      }
+      
+      nodes[n].next = first_node;
+      if (first_node != -1) nodes[first_node].prev = n;
+      first_node = n;
+      nodes[n].prev = -1;
+      
+      nodes[n].first_out = -1;
+      
+      return Node(n);
+    }
+    
+    Edge addEdge(Node u, Node v) {
+      int n;      
+
+      if (first_free_arc == -1) {
+	n = arcs.size();
+	arcs.push_back(ArcT());
+	arcs.push_back(ArcT());
+      } else {
+	n = first_free_arc;
+	first_free_arc = arcs[n].next_out;
+      }
+      
+      arcs[n].target = u.id;
+      arcs[n | 1].target = v.id;
+
+      arcs[n].next_out = nodes[v.id].first_out;
+      if (nodes[v.id].first_out != -1) {
+	arcs[nodes[v.id].first_out].prev_out = n;
+      }      
+      arcs[n].prev_out = -1;
+      nodes[v.id].first_out = n;
+      
+      arcs[n | 1].next_out = nodes[u.id].first_out;
+      if (nodes[u.id].first_out != -1) {
+	arcs[nodes[u.id].first_out].prev_out = (n | 1);
+      }
+      arcs[n | 1].prev_out = -1;      
+      nodes[u.id].first_out = (n | 1);
+
+      return Edge(n / 2);
+    }
+    
+    void erase(const Node& node) {
+      int n = node.id;
+      
+      if(nodes[n].next != -1) {
+	nodes[nodes[n].next].prev = nodes[n].prev;
+      }
+      
+      if(nodes[n].prev != -1) {
+	nodes[nodes[n].prev].next = nodes[n].next;
+      } else {
+	first_node = nodes[n].next;
+      }
+      
+      nodes[n].next = first_free_node;
+      first_free_node = n;
+
+    }
+    
+    void erase(const Edge& arc) {
+      int n = arc.id * 2;
+      
+      if (arcs[n].next_out != -1) {
+	arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;
+      } 
+
+      if (arcs[n].prev_out != -1) {
+	arcs[arcs[n].prev_out].next_out = arcs[n].next_out;
+      } else {
+	nodes[arcs[n | 1].target].first_out = arcs[n].next_out;
+      }
+
+      if (arcs[n | 1].next_out != -1) {
+	arcs[arcs[n | 1].next_out].prev_out = arcs[n | 1].prev_out;
+      } 
+
+      if (arcs[n | 1].prev_out != -1) {
+	arcs[arcs[n | 1].prev_out].next_out = arcs[n | 1].next_out;
+      } else {
+	nodes[arcs[n].target].first_out = arcs[n | 1].next_out;
+      }
+      
+      arcs[n].next_out = first_free_arc;
+      first_free_arc = n;      
+
+    }
+
+    void clear() {
+      arcs.clear();
+      nodes.clear();
+      first_node = first_free_node = first_free_arc = -1;
+    }
+
+  protected:
+
+    void changeTarget(Edge e, Node n) {
+      if(arcs[2 * e.id].next_out != -1) {
+	arcs[arcs[2 * e.id].next_out].prev_out = arcs[2 * e.id].prev_out;
+      }
+      if(arcs[2 * e.id].prev_out != -1) {
+	arcs[arcs[2 * e.id].prev_out].next_out = 
+          arcs[2 * e.id].next_out;
+      } else {
+        nodes[arcs[(2 * e.id) | 1].target].first_out = 
+          arcs[2 * e.id].next_out;
+      }
+
+      if (nodes[n.id].first_out != -1) {
+	arcs[nodes[n.id].first_out].prev_out = 2 * e.id;
+      }
+      arcs[(2 * e.id) | 1].target = n.id;
+      arcs[2 * e.id].prev_out = -1;
+      arcs[2 * e.id].next_out = nodes[n.id].first_out;
+      nodes[n.id].first_out = 2 * e.id;
+    }
+
+    void changeSource(Edge e, Node n) {
+      if(arcs[(2 * e.id) | 1].next_out != -1) {
+	arcs[arcs[(2 * e.id) | 1].next_out].prev_out = 
+          arcs[(2 * e.id) | 1].prev_out;
+      }
+      if(arcs[(2 * e.id) | 1].prev_out != -1) {
+	arcs[arcs[(2 * e.id) | 1].prev_out].next_out = 
+          arcs[(2 * e.id) | 1].next_out;
+      } else {
+        nodes[arcs[2 * e.id].target].first_out = 
+          arcs[(2 * e.id) | 1].next_out;
+      }
+
+      if (nodes[n.id].first_out != -1) {
+	arcs[nodes[n.id].first_out].prev_out = ((2 * e.id) | 1);
+      }
+      arcs[2 * e.id].target = n.id;
+      arcs[(2 * e.id) | 1].prev_out = -1;
+      arcs[(2 * e.id) | 1].next_out = nodes[n.id].first_out;
+      nodes[n.id].first_out = ((2 * e.id) | 1);
+    }
+
+  };
+
+//   typedef GraphExtender<UndirDigraphExtender<ListDigraphBase> > 
+//   ExtendedListGraphBase;
+
+  typedef GraphExtender<ListGraphBase> ExtendedListGraphBase;
+
+
+
+  /// \addtogroup digraphs
+  /// @{
+
+  ///An undirected list digraph class.
+
+  ///This is a simple and fast undirected digraph implementation.
+  ///
+  ///An important extra feature of this digraph implementation is that
+  ///its maps are real \ref concepts::ReferenceMap "reference map"s.
+  ///
+  ///It conforms to the
+  ///\ref concepts::Graph "Graph concept".
+  ///
+  ///\sa concepts::Graph.
+  ///
+  class ListGraph : public ExtendedListGraphBase {
+  private:
+    ///ListGraph is \e not copy constructible. Use GraphCopy() instead.
+
+    ///ListGraph is \e not copy constructible. Use GraphCopy() instead.
+    ///
+    ListGraph(const ListGraph &) :ExtendedListGraphBase()  {};
+    ///\brief Assignment of ListGraph to another one is \e not allowed.
+    ///Use GraphCopy() instead.
+
+    ///Assignment of ListGraph to another one is \e not allowed.
+    ///Use GraphCopy() instead.
+    void operator=(const ListGraph &) {}
+  public:
+    /// Constructor
+    
+    /// Constructor.
+    ///
+    ListGraph() {}
+
+    typedef ExtendedListGraphBase Parent;
+
+    typedef Parent::OutArcIt IncArcIt;
+
+    /// \brief Add a new node to the digraph.
+    ///
+    /// \return the new node.
+    ///
+    Node addNode() { return Parent::addNode(); }
+
+    /// \brief Add a new edge to the digraph.
+    ///
+    /// Add a new arc to the digraph with source node \c s
+    /// and target node \c t.
+    /// \return the new edge.
+    Edge addEdge(const Node& s, const Node& t) { 
+      return Parent::addEdge(s, t); 
+    }
+    /// \brief Changes the source of \c e to \c n
+    ///
+    /// Changes the source of \c e to \c n
+    ///
+    ///\note The <tt>ArcIt</tt>s and <tt>InArcIt</tt>s
+    ///referencing the changed arc remain
+    ///valid. However <tt>OutArcIt</tt>s are invalidated.
+    void changeSource(Edge e, Node n) { 
+      Parent::changeSource(e,n); 
+    }    
+    /// \brief Changes the target of \c e to \c n
+    ///
+    /// Changes the target of \c e to \c n
+    ///
+    /// \note The <tt>ArcIt</tt>s referencing the changed arc remain
+    /// valid. However the other iterators may be invalidated.
+    void changeTarget(Edge e, Node n) { 
+      Parent::changeTarget(e,n); 
+    }
+    /// \brief Changes the source of \c e to \c n
+    ///
+    /// Changes the source of \c e to \c n. It changes the proper
+    /// node of the represented edge.
+    ///
+    ///\note The <tt>ArcIt</tt>s and <tt>InArcIt</tt>s
+    ///referencing the changed arc remain
+    ///valid. However <tt>OutArcIt</tt>s are invalidated.
+    void changeSource(Arc e, Node n) { 
+      if (Parent::direction(e)) {
+        Parent::changeSource(e,n);
+      } else {
+        Parent::changeTarget(e,n);
+      } 
+    }
+    /// \brief Changes the target of \c e to \c n
+    ///
+    /// Changes the target of \c e to \c n. It changes the proper
+    /// node of the represented edge.
+    ///
+    ///\note The <tt>ArcIt</tt>s and <tt>OutArcIt</tt>s
+    ///referencing the changed arc remain
+    ///valid. However <tt>InArcIt</tt>s are invalidated.
+    void changeTarget(Arc e, Node n) { 
+      if (Parent::direction(e)) {
+        Parent::changeTarget(e,n);
+      } else {
+        Parent::changeSource(e,n);
+      } 
+    }
+    /// \brief Contract two nodes.
+    ///
+    /// This function contracts two nodes.
+    ///
+    /// Node \p b will be removed but instead of deleting
+    /// its neighboring arcs, they will be joined to \p a.
+    /// The last parameter \p r controls whether to remove loops. \c true
+    /// means that loops will be removed.
+    ///
+    /// \note The <tt>ArcIt</tt>s referencing a moved arc remain
+    /// valid.
+    void contract(Node a, Node b, bool r = true) {
+      for(IncArcIt e(*this, b); e!=INVALID;) {
+	IncArcIt f = e; ++f;
+	if (r && runningNode(e) == a) {
+	  erase(e);
+	} else if (source(e) == b) {
+	  changeSource(e, a);
+	} else {
+	  changeTarget(e, a);
+	}
+	e = f;
+      }
+      erase(b);
+    }
+
+
+    /// \brief Class to make a snapshot of the digraph and restore
+    /// to it later.
+    ///
+    /// Class to make a snapshot of the digraph and to restore it
+    /// later.
+    ///
+    /// The newly added nodes and edges can be removed
+    /// using the restore() function.
+    ///
+    /// \warning Arc and node deletions cannot be restored. This
+    /// events invalidate the snapshot. 
+    class Snapshot {
+    protected:
+
+      typedef Parent::NodeNotifier NodeNotifier;
+
+      class NodeObserverProxy : public NodeNotifier::ObserverBase {
+      public:
+
+        NodeObserverProxy(Snapshot& _snapshot)
+          : snapshot(_snapshot) {}
+
+        using NodeNotifier::ObserverBase::attach;
+        using NodeNotifier::ObserverBase::detach;
+        using NodeNotifier::ObserverBase::attached;
+        
+      protected:
+        
+        virtual void add(const Node& node) {
+          snapshot.addNode(node);
+        }
+        virtual void add(const std::vector<Node>& nodes) {
+          for (int i = nodes.size() - 1; i >= 0; ++i) {
+            snapshot.addNode(nodes[i]);
+          }
+        }
+        virtual void erase(const Node& node) {
+          snapshot.eraseNode(node);
+        }
+        virtual void erase(const std::vector<Node>& nodes) {
+          for (int i = 0; i < int(nodes.size()); ++i) {
+            snapshot.eraseNode(nodes[i]);
+          }
+        }
+        virtual void build() {
+          Node node;
+          std::vector<Node> nodes;
+          for (notifier()->first(node); node != INVALID; 
+               notifier()->next(node)) {
+            nodes.push_back(node);
+          }
+          for (int i = nodes.size() - 1; i >= 0; --i) {
+            snapshot.addNode(nodes[i]);
+          }
+        }
+        virtual void clear() {
+          Node node;
+          for (notifier()->first(node); node != INVALID; 
+               notifier()->next(node)) {
+            snapshot.eraseNode(node);
+          }
+        }
+
+        Snapshot& snapshot;
+      };
+
+      class EdgeObserverProxy : public EdgeNotifier::ObserverBase {
+      public:
+
+        EdgeObserverProxy(Snapshot& _snapshot)
+          : snapshot(_snapshot) {}
+
+        using EdgeNotifier::ObserverBase::attach;
+        using EdgeNotifier::ObserverBase::detach;
+        using EdgeNotifier::ObserverBase::attached;
+        
+      protected:
+
+        virtual void add(const Edge& arc) {
+          snapshot.addEdge(arc);
+        }
+        virtual void add(const std::vector<Edge>& arcs) {
+          for (int i = arcs.size() - 1; i >= 0; ++i) {
+            snapshot.addEdge(arcs[i]);
+          }
+        }
+        virtual void erase(const Edge& arc) {
+          snapshot.eraseEdge(arc);
+        }
+        virtual void erase(const std::vector<Edge>& arcs) {
+          for (int i = 0; i < int(arcs.size()); ++i) {
+            snapshot.eraseEdge(arcs[i]);
+          }
+        }
+        virtual void build() {
+          Edge arc;
+          std::vector<Edge> arcs;
+          for (notifier()->first(arc); arc != INVALID; 
+               notifier()->next(arc)) {
+            arcs.push_back(arc);
+          }
+          for (int i = arcs.size() - 1; i >= 0; --i) {
+            snapshot.addEdge(arcs[i]);
+          }
+        }
+        virtual void clear() {
+          Edge arc;
+          for (notifier()->first(arc); arc != INVALID; 
+               notifier()->next(arc)) {
+            snapshot.eraseEdge(arc);
+          }
+        }
+
+        Snapshot& snapshot;
+      };
+      
+      ListGraph *digraph;
+
+      NodeObserverProxy node_observer_proxy;
+      EdgeObserverProxy arc_observer_proxy;
+
+      std::list<Node> added_nodes;
+      std::list<Edge> added_arcs;
+
+
+      void addNode(const Node& node) {
+        added_nodes.push_front(node);        
+      }
+      void eraseNode(const Node& node) {
+        std::list<Node>::iterator it = 
+          std::find(added_nodes.begin(), added_nodes.end(), node);
+        if (it == added_nodes.end()) {
+          clear();
+          arc_observer_proxy.detach();
+          throw NodeNotifier::ImmediateDetach();
+        } else {
+          added_nodes.erase(it);
+        }
+      }
+
+      void addEdge(const Edge& arc) {
+        added_arcs.push_front(arc);        
+      }
+      void eraseEdge(const Edge& arc) {
+        std::list<Edge>::iterator it = 
+          std::find(added_arcs.begin(), added_arcs.end(), arc);
+        if (it == added_arcs.end()) {
+          clear();
+          node_observer_proxy.detach();
+          throw EdgeNotifier::ImmediateDetach();
+        } else {
+          added_arcs.erase(it);
+        }        
+      }
+
+      void attach(ListGraph &_digraph) {
+	digraph = &_digraph;
+	node_observer_proxy.attach(digraph->notifier(Node()));
+        arc_observer_proxy.attach(digraph->notifier(Edge()));
+      }
+            
+      void detach() {
+	node_observer_proxy.detach();
+	arc_observer_proxy.detach();
+      }
+
+      bool attached() const {
+        return node_observer_proxy.attached();
+      }
+
+      void clear() {
+        added_nodes.clear();
+        added_arcs.clear();        
+      }
+
+    public:
+
+      /// \brief Default constructor.
+      ///
+      /// Default constructor.
+      /// To actually make a snapshot you must call save().
+      Snapshot() 
+        : digraph(0), node_observer_proxy(*this), 
+          arc_observer_proxy(*this) {}
+      
+      /// \brief Constructor that immediately makes a snapshot.
+      ///      
+      /// This constructor immediately makes a snapshot of the digraph.
+      /// \param _digraph The digraph we make a snapshot of.
+      Snapshot(ListGraph &_digraph) 
+        : node_observer_proxy(*this), 
+          arc_observer_proxy(*this) {
+	attach(_digraph);
+      }
+      
+      /// \brief Make a snapshot.
+      ///
+      /// Make a snapshot of the digraph.
+      ///
+      /// This function can be called more than once. In case of a repeated
+      /// call, the previous snapshot gets lost.
+      /// \param _digraph The digraph we make the snapshot of.
+      void save(ListGraph &_digraph) {
+        if (attached()) {
+          detach();
+          clear();
+        }
+        attach(_digraph);
+      }
+      
+      /// \brief Undo the changes until the last snapshot.
+      // 
+      /// Undo the changes until the last snapshot created by save().
+      void restore() {
+	detach();
+	for(std::list<Edge>::iterator it = added_arcs.begin(); 
+            it != added_arcs.end(); ++it) {
+	  digraph->erase(*it);
+	}
+	for(std::list<Node>::iterator it = added_nodes.begin(); 
+            it != added_nodes.end(); ++it) {
+	  digraph->erase(*it);
+	}
+        clear();
+      }
+
+      /// \brief Gives back true when the snapshot is valid.
+      ///
+      /// Gives back true when the snapshot is valid.
+      bool valid() const {
+        return attached();
+      }
+    };
+  };
+  
+  /// @}  
+} //namespace lemon
+  
+
+#endif
