diff --git a/lemon/concepts/graph.h b/lemon/concepts/graph.h
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+/* -*- 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