Index: lemon/Makefile.am
===================================================================
--- lemon/Makefile.am	(revision 2119)
+++ lemon/Makefile.am	(revision 2126)
@@ -115,5 +115,5 @@
 	lemon/concept/bpugraph.h \
 	lemon/concept/graph.h \
-	lemon/concept/graph_component.h \
+	lemon/concept/graph_components.h \
 	lemon/concept/heap.h \
 	lemon/concept/maps.h \
Index: lemon/concept/bpugraph.h
===================================================================
--- lemon/concept/bpugraph.h	(revision 2120)
+++ lemon/concept/bpugraph.h	(revision 2126)
@@ -25,5 +25,5 @@
 #define LEMON_CONCEPT_BPUGRAPH_H
 
-#include <lemon/concept/graph_component.h>
+#include <lemon/concept/graph_components.h>
 
 #include <lemon/concept/graph.h>
Index: lemon/concept/graph.h
===================================================================
--- lemon/concept/graph.h	(revision 2121)
+++ lemon/concept/graph.h	(revision 2126)
@@ -28,5 +28,5 @@
 #include <lemon/concept/maps.h>
 #include <lemon/concept_check.h>
-#include <lemon/concept/graph_component.h>
+#include <lemon/concept/graph_components.h>
 
 namespace lemon {
Index: lemon/concept/graph_component.h
===================================================================
--- lemon/concept/graph_component.h	(revision 2121)
+++ 	(revision )
@@ -1,1720 +1,0 @@
-/* -*- C++ -*-
- *
- * This file is a part of LEMON, a generic C++ optimization library
- *
- * Copyright (C) 2003-2006
- * 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 graph components.
-
-
-#ifndef LEMON_CONCEPT_GRAPH_COMPONENT_H
-#define LEMON_CONCEPT_GRAPH_COMPONENT_H
-
-#include <lemon/bits/invalid.h>
-#include <lemon/concept/maps.h>
-
-#include <lemon/bits/alteration_notifier.h>
-
-namespace lemon {
-  namespace concept {
-
-    /// \brief Skeleton class for graph Node and Edge types
-    ///
-    /// This class describes the interface of Node and Edge (and UEdge
-    /// 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 Edge types should \em not derive from the same base class.
-    /// For Node you should instantiate it with character 'n' and for Edge
-    /// with 'e'.
-
-#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 graph class.
-    ///  
-    /// This class provides the minimal set of features needed for a graph
-    /// structure. All graph concepts have to be conform to this base
-    /// graph. It just provides types for nodes and edges and functions to
-    /// get the source and the target of the edges.
-    class BaseGraphComponent {
-    public:
-
-      typedef BaseGraphComponent Graph;
-      
-      /// \brief Node class of the graph.
-      ///
-      /// This class represents the Nodes of the graph. 
-      ///
-      typedef GraphItem<'n'> Node;
-
-      /// \brief Edge class of the graph.
-      ///
-      /// This class represents the Edges of the graph. 
-      ///
-      typedef GraphItem<'e'> Edge;
-
-      /// \brief Gives back the target node of an edge.
-      ///
-      /// Gives back the target node of an edge.
-      ///
-      Node target(const Edge&) const { return INVALID;}
-
-      /// \brief Gives back the source node of an edge.
-      ///
-      /// Gives back the source node of an edge.
-      ///
-      Node source(const Edge&) const { return INVALID;}
-
-      /// \brief Gives back the opposite node on the given edge.
-      ///
-      /// Gives back the opposite node on the given edge.
-      Node oppositeNode(const Node&, const Edge&) const {
-        return INVALID;
-      }
-
-      template <typename _Graph>
-      struct Constraints {
-	typedef typename _Graph::Node Node;
-	typedef typename _Graph::Edge Edge;
-      
-	void constraints() {
-	  checkConcept<GraphItem<'n'>, Node>();
-	  checkConcept<GraphItem<'e'>, Edge>();
-	  {
-	    Node n;
-	    Edge e(INVALID);
-	    n = graph.source(e);
-	    n = graph.target(e);
-            n = graph.oppositeNode(n, e);
-	  }      
-	}
-      
-	const _Graph& graph;
-      };
-    };
-
-    /// \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, edges and undirected edges and functions to get the
-    /// source and the target of the edges and undirected edges,
-    /// conversion from edges to undirected edges and function to get
-    /// both direction of the undirected edges.
-    class BaseUGraphComponent : public BaseGraphComponent {
-    public:
-      typedef BaseGraphComponent::Node Node;
-      typedef BaseGraphComponent::Edge Edge;
-      /// \brief Undirected edge class of the graph.
-      ///
-      /// This class represents the undirected edges of the graph.
-      /// The undirected graphs can be used as a directed graph which
-      /// for each edge contains the opposite edge too so the graph is
-      /// bidirected. The undirected edge represents two opposite
-      /// directed edges.
-      class UEdge : 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.
-        UEdge() {}
-        /// \brief Copy constructor.
-        ///
-        /// Copy constructor.
-        ///
-        UEdge(const UEdge &) : Parent() {}
-        /// \brief Invalid constructor \& conversion.
-        ///
-        /// This constructor initializes the item to be invalid.
-        /// \sa Invalid for more details.
-        UEdge(Invalid) {}
-        /// \brief Converter from edge to undirected edge.
-        ///
-        /// Besides the core graph item functionality each edge should
-        /// be convertible to the represented undirected edge. 
-        UEdge(const Edge&) {}
-      };
-
-      /// \brief Returns the direction of the edge.
-      ///
-      /// Returns the direction of the edge. Each edge represents an
-      /// undirected edge with a direction. It gives back the
-      /// direction.
-      bool direction(const Edge&) const { return true; }
-
-      /// \brief Returns the directed edge.
-      ///
-      /// Returns the directed edge from its direction and the
-      /// represented undirected edge.
-      Edge direct(const UEdge&, bool) const { return INVALID;} 
-
-      /// \brief Returns the directed edge.
-      ///
-      /// Returns the directed edge from its source and the
-      /// represented undirected edge.
-      Edge direct(const UEdge&, const Node&) const { return INVALID;} 
-
-      /// \brief Returns the opposite edge.
-      ///
-      /// Returns the opposite edge. It is the edge representing the
-      /// same undirected edge and has opposite direction.
-      Edge oppositeEdge(const Edge&) const { return INVALID;}
-
-      /// \brief Gives back the target node of an undirected edge.
-      ///
-      /// Gives back the target node of an undirected edge. The name
-      /// target is a little confusing because the undirected edge
-      /// does not have target but it just means that one of the end 
-      /// node.
-      Node target(const UEdge&) const { return INVALID;}
-
-      /// \brief Gives back the source node of an undirected edge.
-      ///
-      /// Gives back the source node of an undirected edge. The name
-      /// source is a little confusing because the undirected edge
-      /// does not have source but it just means that one of the end 
-      /// node.
-      Node source(const UEdge&) const { return INVALID;}
-      
-      template <typename _Graph>
-      struct Constraints {
-	typedef typename _Graph::Node Node;
-	typedef typename _Graph::Edge Edge;
-	typedef typename _Graph::UEdge UEdge;
-      
-	void constraints() {
-          checkConcept<BaseGraphComponent, _Graph>();
-	  checkConcept<GraphItem<'u'>, UEdge>();
-	  {
-	    Node n;
-	    UEdge ue(INVALID);
-            Edge e;
-	    n = graph.source(ue);
-	    n = graph.target(ue);
-            e = graph.direct(ue, true);
-            e = graph.direct(ue, n);
-            e = graph.oppositeEdge(e);
-            ue = e;
-            bool d = graph.direction(e);
-            ignore_unused_variable_warning(d);
-	  }      
-	}
-      
-	const _Graph& graph;
-      };
-
-    };
-
-    /// \brief An empty iterable base graph class.
-    ///  
-    /// This class provides beside the core graph features
-    /// core iterable interface for the graph structure.
-    /// Most of the base graphs should be conform to this concept.
-    template <typename _Base = BaseGraphComponent>
-    class BaseIterableGraphComponent : public _Base {
-    public:
-
-      typedef _Base Base; 
-      typedef typename Base::Node Node;
-      typedef typename Base::Edge Edge;
-
-      /// \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 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 point to the given
-      /// node.
-      ///
-      /// Gives back the first of the edges point to the given node.
-      ///     
-      void firstIn(Edge&, const Node&) const {}
-
-      /// \brief Gives back the next of the edges points to the given
-      /// node.
-      ///
-      /// Gives back the next of the edges points to the given node.
-      ///
-      void nextIn(Edge&) const {}
-
-      /// \brief Gives back the first of the edges start from the
-      /// given node.
-      ///      
-      /// Gives back the first of the edges start from the given node.
-      ///     
-      void firstOut(Edge&, const Node&) const {}
-
-      /// \brief Gives back the next of the edges start from the given
-      /// node.
-      ///
-      /// Gives back the next of the edges start from the given node.
-      ///     
-      void nextOut(Edge&) const {}
-
-
-      template <typename _Graph>
-      struct Constraints {
-      
-	void constraints() {
-	  checkConcept< BaseGraphComponent, _Graph >();
-	  typename _Graph::Node node;      
-	  typename _Graph::Edge edge;
-	  {
-	    graph.first(node);
-	    graph.next(node);
-	  }
-	  {
-	    graph.first(edge);
-	    graph.next(edge);
-	  }
-	  {
-	    graph.firstIn(edge, node);
-	    graph.nextIn(edge);
-	  }
-	  {
-	    graph.firstOut(edge, node);
-	    graph.nextOut(edge);
-	  }
-	}
-
-	const _Graph& graph;
-      };
-    };
-
-    /// \brief An empty iterable base undirected graph class.
-    ///  
-    /// This class provides beside the core undirceted graph features
-    /// core iterable interface for the undirected graph structure.
-    /// Most of the base undirected graphs should be conform to this
-    /// concept.
-    template <typename _Base = BaseUGraphComponent>
-    class BaseIterableUGraphComponent 
-      : public BaseIterableGraphComponent<_Base> {
-    public:
-
-      typedef _Base Base; 
-      typedef typename Base::UEdge UEdge;
-      typedef typename Base::Node Node;
-
-      using BaseIterableGraphComponent<_Base>::first;
-      using BaseIterableGraphComponent<_Base>::next;
-
-      /// \brief Gives back the first undirected edge in the iterating
-      /// order.
-      ///
-      /// Gives back the first undirected edge in the iterating order.
-      ///     
-      void first(UEdge&) const {}
-
-      /// \brief Gives back the next undirected edge in the iterating
-      /// order.
-      ///
-      /// Gives back the next undirected edge in the iterating order.
-      ///     
-      void next(UEdge&) const {}
-
-
-      /// \brief Gives back the first of the undirected edges from the
-      /// given node.
-      ///
-      /// Gives back the first of the undirected edges from the given
-      /// node. The bool parameter gives back that direction which
-      /// gives a good direction of the uedge so the source of the
-      /// directed edge is the given node.
-      void firstInc(UEdge&, bool&, const Node&) const {}
-
-      /// \brief Gives back the next of the undirected edges from the
-      /// given node.
-      ///
-      /// Gives back the next of the undirected edges from the given
-      /// node. The bool parameter should be used as the \c firstInc()
-      /// use it.
-      void nextInc(UEdge&, bool&) const {}
-
-      template <typename _Graph>
-      struct Constraints {
-      
-	void constraints() {
-	  checkConcept<Base, _Graph >();
-	  checkConcept<BaseIterableGraphComponent<Base>, _Graph>();
-	  typename _Graph::Node node;
-	  typename _Graph::UEdge uedge;
-          bool dir;
-	  {
-	    graph.first(uedge);
-	    graph.next(uedge);
-	  }
-	  {
-	    graph.firstInc(uedge, dir, node);
-	    graph.nextInc(uedge, dir);
-	  }
-	}
-
-	const _Graph& graph;
-      };
-    };
-
-    /// \brief An empty idable base graph class.
-    ///  
-    /// This class provides beside the core graph features
-    /// core id functions for the graph structure.
-    /// The most of the base graphs should be conform to this concept.
-    /// The id's are unique and immutable.
-    template <typename _Base = BaseGraphComponent>
-    class IDableGraphComponent : public _Base {
-    public:
-
-      typedef _Base Base;
-      typedef typename Base::Node Node;
-      typedef typename Base::Edge Edge;
-
-      /// \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 graph 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 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 edge 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
-      /// 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
-      /// 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< BaseGraphComponent, _Graph >();
-	  typename _Graph::Node node;
-	  int nid = graph.id(node);
-	  nid = graph.id(node);
-	  node = graph.nodeFromId(nid);
-	  typename _Graph::Edge edge;
-	  int eid = graph.id(edge);
-	  eid = graph.id(edge);
-	  edge = graph.edgeFromId(eid);
-
-	  nid = graph.maxNodeId();
-	  ignore_unused_variable_warning(nid);
-	  eid = graph.maxEdgeId();
-	  ignore_unused_variable_warning(eid);
-	}
-
-	const _Graph& graph;
-      };
-    };
-
-    /// \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 = BaseUGraphComponent>
-    class IDableUGraphComponent : public IDableGraphComponent<_Base> {
-    public:
-
-      typedef _Base Base;
-      typedef typename Base::UEdge UEdge;
-
-      using IDableGraphComponent<_Base>::id;
-
-      /// \brief Gives back an unique integer id for the UEdge. 
-      ///
-      /// Gives back an unique integer id for the UEdge. 
-      ///
-      int id(const UEdge&) const { return -1;}
-
-      /// \brief Gives back the undirected edge by the unique id.
-      ///
-      /// Gives back the undirected edge by the unique id.  If the
-      /// graph does not contain edge with the given id then the
-      /// result of the function is undetermined.
-      UEdge uEdgeFromId(int) const { return INVALID;}
-
-      /// \brief Gives back an integer greater or equal to the maximum
-      /// UEdge id.
-      ///
-      /// Gives back an integer greater or equal to the maximum UEdge
-      /// id.
-      int maxUEdgeId() const { return -1;}
-
-      template <typename _Graph>
-      struct Constraints {
-
-	void constraints() {
-	  checkConcept<Base, _Graph >();
-	  checkConcept<IDableGraphComponent<Base>, _Graph >();
-	  typename _Graph::UEdge uedge;
-	  int ueid = graph.id(uedge);
-	  ueid = graph.id(uedge);
-	  uedge = graph.uEdgeFromId(ueid);
-	  ueid = graph.maxUEdgeId();
-	  ignore_unused_variable_warning(ueid);
-	}
-
-	const _Graph& graph;
-      };
-    };
-
-    /// \brief An empty extendable base graph class.
-    ///
-    /// This class provides beside the core graph features
-    /// core graph extend interface for the graph structure.
-    /// The most of the base graphs should be conform to this concept.
-    template <typename _Base = BaseGraphComponent>
-    class BaseExtendableGraphComponent : public _Base {
-    public:
-
-      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 edge connects the given two nodes.
-      ///
-      /// Adds a new edge connects the the given two nodes.
-      Edge addEdge(const Node&, const Node&) {
-	return INVALID;
-      }
-
-      template <typename _Graph>
-      struct Constraints {
-	void constraints() {
-	  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 extendable base undirected graph class.
-    ///
-    /// This class provides beside the core undirected graph features
-    /// core undircted graph extend interface for the graph structure.
-    /// The most of the base graphs should be conform to this concept.
-    template <typename _Base = BaseUGraphComponent>
-    class BaseExtendableUGraphComponent : public _Base {
-    public:
-
-      typedef typename _Base::Node Node;
-      typedef typename _Base::UEdge UEdge;
-
-      /// \brief Adds a new node to the graph.
-      ///
-      /// Adds a new node to the graph.
-      ///
-      Node addNode() {
-	return INVALID;
-      }
-    
-      /// \brief Adds a new edge connects the given two nodes.
-      ///
-      /// Adds a new edge connects the the given two nodes.
-      UEdge addEdge(const Node&, const Node&) {
-	return INVALID;
-      }
-
-      template <typename _Graph>
-      struct Constraints {
-	void constraints() {
-	  typename _Graph::Node node_a, node_b;
-	  node_a = graph.addNode();
-	  node_b = graph.addNode();
-	  typename _Graph::UEdge uedge;
-	  uedge = graph.addUEdge(node_a, node_b);
-	}
-
-	_Graph& graph;
-      };
-    };
-
-    /// \brief An empty erasable base graph class.
-    ///  
-    /// This class provides beside the core graph features
-    /// core erase functions for the graph structure.
-    /// The most of the base graphs should be conform to this concept.
-    template <typename _Base = BaseGraphComponent>
-    class BaseErasableGraphComponent : 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 not
-      /// erase edges connecting to the Node.
-      void erase(const Node&) {}    
-
-      /// \brief Erase an edge from the graph.
-      ///
-      /// Erase an edge from the graph.
-      ///
-      void erase(const Edge&) {}
-
-      template <typename _Graph>
-      struct Constraints {
-	void constraints() {
-	  typename _Graph::Node node;
-	  graph.erase(node);
-	  typename _Graph::Edge edge;
-	  graph.erase(edge);
-	}
-
-	_Graph& graph;
-      };
-    };
-
-    /// \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.
-    template <typename _Base = BaseUGraphComponent>
-    class BaseErasableUGraphComponent : public _Base {
-    public:
-
-      typedef _Base Base;
-      typedef typename Base::Node Node;
-      typedef typename Base::UEdge UEdge;
-
-      /// \brief Erase a node from the graph.
-      ///
-      /// Erase a node from the graph. This function should not
-      /// erase edges connecting to the Node.
-      void erase(const Node&) {}    
-
-      /// \brief Erase an edge from the graph.
-      ///
-      /// Erase an edge from the graph.
-      ///
-      void erase(const UEdge&) {}
-
-      template <typename _Graph>
-      struct Constraints {
-	void constraints() {
-	  typename _Graph::Node node;
-	  graph.erase(node);
-	  typename _Graph::Edge edge;
-	  graph.erase(edge);
-	}
-
-	_Graph& graph;
-      };
-    };
-
-    /// \brief An empty clearable base graph class.
-    ///
-    /// This class provides beside the core graph features
-    /// core clear functions for the graph structure.
-    /// The most of the base graphs should be conform to this concept.
-    template <typename _Base = BaseGraphComponent>
-    class BaseClearableGraphComponent : public _Base {
-    public:
-
-      /// \brief Erase all the nodes and edges from the graph.
-      ///
-      /// Erase all the nodes and edges from the graph.
-      ///
-      void clear() {}    
-
-      template <typename _Graph>
-      struct Constraints {
-	void constraints() {
-	  graph.clear();
-	}
-
-	_Graph graph;
-      };
-    };
-
-    /// \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 most of the base graphs should be conform to this concept.
-    template <typename _Base = BaseUGraphComponent>
-    class BaseClearableUGraphComponent : public _Base {
-    public:
-
-      /// \brief Erase all the nodes and undirected edges from the graph.
-      ///
-      /// Erase all the nodes and undirected edges from the graph.
-      ///
-      void clear() {}    
-
-      template <typename _Graph>
-      struct Constraints {
-	void constraints() {
-	  graph.clear();
-	}
-
-	_Graph graph;
-      };
-    };
-
-
-    /// \brief Skeleton class for graph NodeIt and EdgeIt
-    ///
-    /// Skeleton class for graph NodeIt and EdgeIt.
-    ///
-    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 InEdgeIt and OutEdgeIt
-    ///
-    /// \note Because InEdgeIt and OutEdgeIt may not inherit from the same
-    /// base class, the _selector is a additional template parameter. For 
-    /// InEdgeIt you should instantiate it with character 'i' and for 
-    /// OutEdgeIt with 'o'.
-    template <typename _Graph,
-	      typename _Item = typename _Graph::Edge,
-              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 edge incoming into or outgoing 
-      /// from the node.
-      ///
-      /// Sets the iterator to the first edge 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 edge;
-	_Base node;
-	_Graph graph;
-	_GraphIncIt it;
-      };
-    };
-
-
-    /// \brief An empty iterable graph class.
-    ///
-    /// This class provides beside the core graph features
-    /// iterator based iterable interface for the graph structure.
-    /// This concept is part of the GraphConcept.
-    template <typename _Base = BaseGraphComponent>
-    class IterableGraphComponent : public _Base {
-
-    public:
-    
-      typedef _Base Base;
-      typedef typename Base::Node Node;
-      typedef typename Base::Edge Edge;
-
-      typedef IterableGraphComponent Graph;
-
-
-      /// \brief This iterator goes through each node.
-      ///
-      /// This iterator goes through each node.
-      ///
-      typedef GraphItemIt<Graph, Node> NodeIt;
-
-      /// \brief This iterator goes through each node.
-      ///
-      /// This iterator goes through each node.
-      ///
-      typedef GraphItemIt<Graph, Edge> EdgeIt;
-
-      /// \brief This iterator goes trough the incoming edges of a node.
-      ///
-      /// This iterator goes trough the \e inccoming edges of a certain node
-      /// of a graph.
-      typedef GraphIncIt<Graph, Edge, Node, 'i'> InEdgeIt;
-
-      /// \brief This iterator goes trough the outgoing edges of a node.
-      ///
-      /// This iterator goes trough the \e outgoing edges of a certain node
-      /// of a graph.
-      typedef GraphIncIt<Graph, Edge, Node, 'o'> OutEdgeIt;
-
-      /// \brief The base node of the iterator.
-      ///
-      /// Gives back the base node of the iterator.
-      /// It is always the target of the pointed edge.
-      Node baseNode(const InEdgeIt&) 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 edge.
-      Node runningNode(const InEdgeIt&) 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 edge.
-      Node baseNode(const OutEdgeIt&) 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 edge.
-      Node runningNode(const OutEdgeIt&) const { return INVALID; }
-
-      /// \brief The opposite node on the given edge.
-      ///
-      /// Gives back the opposite on the given edge.
-      /// \todo It should not be here.
-      Node oppositeNode(const Node&, const Edge&) const { return INVALID; }
-
-    
-      template <typename _Graph> 
-      struct Constraints {
-	void constraints() {
-	  checkConcept<Base, _Graph>();
-	  
-	  checkConcept<GraphItemIt<_Graph, typename _Graph::Edge>,
-	    typename _Graph::EdgeIt >();
-	  checkConcept<GraphItemIt<_Graph, typename _Graph::Node>,
-	    typename _Graph::NodeIt >();
-	  checkConcept<GraphIncIt<_Graph, typename _Graph::Edge, 
-            typename _Graph::Node, 'i'>, typename _Graph::InEdgeIt>();
-	  checkConcept<GraphIncIt<_Graph, typename _Graph::Edge, 
-            typename _Graph::Node, 'o'>, typename _Graph::OutEdgeIt>();
-
-          typename _Graph::Node n;
-          typename _Graph::InEdgeIt ieit(INVALID);
-          typename _Graph::OutEdgeIt oeit(INVALID);
-          n = graph.baseNode(ieit);
-          n = graph.runningNode(ieit);
-          n = graph.baseNode(oeit);
-          n = graph.runningNode(oeit);
-          ignore_unused_variable_warning(n);
-        }
-	
-	const _Graph& graph;
-	
-      };
-    };
-
-    /// \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 GraphConcept.
-    template <typename _Base = BaseUGraphComponent>
-    class IterableUGraphComponent : public IterableGraphComponent<_Base> {
-    public:
-
-      typedef _Base Base;
-      typedef typename Base::Node Node;
-      typedef typename Base::Edge Edge;
-      typedef typename Base::UEdge UEdge;
-
-    
-      typedef IterableUGraphComponent Graph;
-      using IterableGraphComponent<_Base>::baseNode;
-      using IterableGraphComponent<_Base>::runningNode;
-
-
-      /// \brief This iterator goes through each node.
-      ///
-      /// This iterator goes through each node.
-      typedef GraphItemIt<Graph, UEdge> UEdgeIt;
-      /// \brief This iterator goes trough the incident edges of a
-      /// node.
-      ///
-      /// This iterator goes trough the incident edges of a certain
-      /// node of a graph.
-      typedef GraphIncIt<Graph, UEdge, Node, 'u'> IncEdgeIt;
-      /// \brief The base node of the iterator.
-      ///
-      /// Gives back the base node of the iterator.
-      Node baseNode(const IncEdgeIt&) const { return INVALID; }
-
-      /// \brief The running node of the iterator.
-      ///
-      /// Gives back the running node of the iterator.
-      Node runningNode(const IncEdgeIt&) const { return INVALID; }
-
-      template <typename _Graph> 
-      struct Constraints {
-	void constraints() {
-	  checkConcept<Base, _Graph>();
-	  checkConcept<IterableGraphComponent<Base>, _Graph>();
-	  
-	  checkConcept<GraphItemIt<_Graph, typename _Graph::UEdge>,
-	    typename _Graph::UEdgeIt >();
-	  checkConcept<GraphIncIt<_Graph, typename _Graph::UEdge, 
-            typename _Graph::Node, 'u'>, typename _Graph::IncEdgeIt>();
-
-          typename _Graph::Node n;
-          typename _Graph::IncEdgeIt ueit(INVALID);
-          n = graph.baseNode(ueit);
-          n = graph.runningNode(ueit);
-	}
-	
-	const _Graph& graph;
-	
-      };
-    };
-
-    /// \brief An empty alteration notifier 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 _Base {
-    public:
-
-      typedef _Base Base;
-      typedef typename Base::Node Node;
-      typedef typename Base::Edge Edge;
-
-
-      /// The node observer registry.
-      typedef AlterationNotifier<AlterableGraphComponent, Node> 
-      NodeNotifier;
-      /// The edge observer registry.
-      typedef AlterationNotifier<AlterableGraphComponent, Edge> 
-      EdgeNotifier;
-      
-      /// \brief Gives back the node alteration notifier.
-      ///
-      /// Gives back the node alteration notifier.
-      NodeNotifier& getNotifier(Node) const {
-	return NodeNotifier();
-      }
-      
-      /// \brief Gives back the edge alteration notifier.
-      ///
-      /// Gives back the edge alteration notifier.
-      EdgeNotifier& getNotifier(Edge) const {
-	return EdgeNotifier();
-      }
-
-      template <typename _Graph> 
-      struct Constraints {
-	void constraints() {
-	  checkConcept<Base, _Graph>();
-          typename _Graph::NodeNotifier& nn 
-            = graph.getNotifier(typename _Graph::Node());
-
-          typename _Graph::EdgeNotifier& en 
-            = graph.getNotifier(typename _Graph::Edge());
-          
-          ignore_unused_variable_warning(nn);
-          ignore_unused_variable_warning(en);
-	}
-	
-	const _Graph& graph;
-	
-      };
-      
-    };
-
-    /// \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 = BaseUGraphComponent>
-    class AlterableUGraphComponent : public AlterableGraphComponent<_Base> {
-    public:
-
-      typedef _Base Base;
-      typedef typename Base::UEdge UEdge;
-
-
-      /// The edge observer registry.
-      typedef AlterationNotifier<AlterableUGraphComponent, UEdge> 
-      UEdgeNotifier;
-      
-      /// \brief Gives back the edge alteration notifier.
-      ///
-      /// Gives back the edge alteration notifier.
-      UEdgeNotifier& getNotifier(UEdge) const {
-	return UEdgeNotifier();
-      }
-
-      template <typename _Graph> 
-      struct Constraints {
-	void constraints() {
-	  checkConcept<Base, _Graph>();
-          checkConcept<AlterableGraphComponent, _Graph>();
-          typename _Graph::UEdgeNotifier& uen 
-            = graph.getNotifier(typename _Graph::UEdge());
-          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, EdgeMap), that is \ref maps-page "maps" which can be used to
-    /// associate data to graph descriptors (nodes or edges).
-    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 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 _Base  {
-    public:
-
-      typedef _Base Base;
-      typedef typename Base::Node Node;
-      typedef typename Base::Edge Edge;
-
-      typedef MappableGraphComponent Graph;
-
-      /// \brief ReadWrite map of the nodes.
-      ///
-      /// ReadWrite map of the nodes.
-      ///
-      template <typename Value>
-      class NodeMap : public GraphMap<Graph, Node, Value> {
-      private:
-	NodeMap();
-      public:
-        typedef GraphMap<Graph, Node, Value> Parent;
-
-	/// \brief Construct a new map.
-	///
-	/// Construct a new map for the graph.
-	/// \todo call the right parent class constructor
-	explicit NodeMap(const Graph& graph) : Parent(graph) {}
-
-	/// \brief Construct a new map with default value.
-	///
-	/// Construct a new map for the graph and initalise the values.
-	NodeMap(const Graph& graph, const Value& value)
-          : Parent(graph, 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 edges.
-      ///
-      /// ReadWrite map of the edges.
-      ///
-      template <typename Value>
-      class EdgeMap : public GraphMap<Graph, Edge, Value> {
-      private:
-	EdgeMap();
-      public:
-        typedef GraphMap<Graph, Edge, Value> Parent;
-
-	/// \brief Construct a new map.
-	///
-	/// Construct a new map for the graph.
-	/// \todo call the right parent class constructor
-	explicit EdgeMap(const Graph& graph) : Parent(graph) {}
-
-	/// \brief Construct a new map with default value.
-	///
-	/// Construct a new map for the graph and initalise the values.
-	EdgeMap(const Graph& 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<Base, _Graph>();
-	  { // int map test
-	    typedef typename _Graph::template NodeMap<int> IntNodeMap;
-	    checkConcept<GraphMap<_Graph, typename _Graph::Node, int>, 
-	      IntNodeMap >();
-	  } { // bool map test
-	    typedef typename _Graph::template NodeMap<bool> BoolNodeMap;
-	    checkConcept<GraphMap<_Graph, typename _Graph::Node, bool>,
-	      BoolNodeMap >();
-	  } { // Dummy map test
-	    typedef typename _Graph::template NodeMap<Dummy> DummyNodeMap;
-	    checkConcept<GraphMap<_Graph, typename _Graph::Node, Dummy>,
-	      DummyNodeMap >();
-	  } 
-
-	  { // 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 mappable base graph class.
-    ///
-    /// This class provides beside the core graph features
-    /// map interface for the graph structure.
-    /// This concept is part of the UGraph concept.
-    template <typename _Base = BaseUGraphComponent>
-    class MappableUGraphComponent : public MappableGraphComponent<_Base>  {
-    public:
-
-      typedef _Base Base;
-      typedef typename Base::UEdge UEdge;
-
-      typedef MappableUGraphComponent Graph;
-
-      /// \brief ReadWrite map of the uedges.
-      ///
-      /// ReadWrite map of the uedges.
-      ///
-      template <typename Value>
-      class UEdgeMap : public GraphMap<Graph, UEdge, Value> {  
-      public:
-        typedef GraphMap<Graph, UEdge, Value> Parent;
-
-	/// \brief Construct a new map.
-	///
-	/// Construct a new map for the graph.
-	/// \todo call the right parent class constructor
-	explicit UEdgeMap(const Graph& graph) : Parent(graph) {}
-
-	/// \brief Construct a new map with default value.
-	///
-	/// Construct a new map for the graph and initalise the values.
-	UEdgeMap(const Graph& graph, const Value& value)
-          : Parent(graph, value) {}
-
-	/// \brief Copy constructor.
-	///
-	/// Copy Constructor.
-	UEdgeMap(const UEdgeMap& nm) : Parent(nm) {}
-
-	/// \brief Assign operator.
-	///
-	/// Assign operator.
-        template <typename CMap>
-        UEdgeMap& operator=(const CMap&) { 
-          checkConcept<ReadMap<UEdge, Value>, CMap>();
-          return *this;
-        }
-
-      };
-
-
-      template <typename _Graph>
-      struct Constraints {
-
-	struct Dummy {
-	  int value;
-	  Dummy() : value(0) {}
-	  Dummy(int _v) : value(_v) {}
-	};
-
-	void constraints() {
-	  checkConcept<Base, _Graph>();
-	  checkConcept<MappableGraphComponent<Base>, _Graph>();
-
-	  { // int map test
-	    typedef typename _Graph::template UEdgeMap<int> IntUEdgeMap;
-	    checkConcept<GraphMap<_Graph, typename _Graph::UEdge, int>,
-	      IntUEdgeMap >();
-	  } { // bool map test
-	    typedef typename _Graph::template UEdgeMap<bool> BoolUEdgeMap;
-	    checkConcept<GraphMap<_Graph, typename _Graph::UEdge, bool>,
-	      BoolUEdgeMap >();
-	  } { // Dummy map test
-	    typedef typename _Graph::template UEdgeMap<Dummy> DummyUEdgeMap;
-	    checkConcept<GraphMap<_Graph, typename _Graph::UEdge, Dummy>, 
-	      DummyUEdgeMap >();
-	  } 
-	}
-
-	_Graph& graph;
-      };
-    };
-
-
-    /// \brief An empty extendable graph class.
-    ///
-    /// This class provides beside the core graph features graph
-    /// extendable 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 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 edge connects the given two nodes.
-      ///
-      /// Adds a new edge connects the the given two nodes.
-      Edge addEdge(const Node&, const Node&) {
-	return INVALID;
-      }
-
-      template <typename _Graph>
-      struct Constraints {
-	void constraints() {
-	  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 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 = BaseUGraphComponent>
-    class ExtendableUGraphComponent : public _Base {
-    public:
-
-      typedef typename _Base::Node Node;
-      typedef typename _Base::UEdge UEdge;
-
-      /// \brief Adds a new node to the graph.
-      ///
-      /// Adds a new node to the graph.
-      ///
-      Node addNode() {
-	return INVALID;
-      }
-    
-      /// \brief Adds a new edge connects the given two nodes.
-      ///
-      /// Adds a new edge connects the the given two nodes.
-      UEdge addEdge(const Node&, const Node&) {
-	return INVALID;
-      }
-
-      template <typename _Graph>
-      struct Constraints {
-	void constraints() {
-	  typename _Graph::Node node_a, node_b;
-	  node_a = graph.addNode();
-	  node_b = graph.addNode();
-	  typename _Graph::UEdge uedge;
-	  uedge = graph.addUEdge(node_a, node_b);
-	}
-
-	_Graph& graph;
-      };
-    };
-
-    /// \brief An empty erasable graph class.
-    ///  
-    /// This class provides beside the core graph features core erase
-    /// functions 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 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 all edges connecting to the node.
-      void erase(const Node&) {}    
-
-      /// \brief Erase an edge from the graph.
-      ///
-      /// Erase an edge from the graph.
-      ///
-      void erase(const Edge&) {}
-
-      template <typename _Graph>
-      struct Constraints {
-	void constraints() {
-	  typename _Graph::Node node;
-	  graph.erase(node);
-	  typename _Graph::Edge edge;
-	  graph.erase(edge);
-	}
-
-	_Graph& graph;
-      };
-    };
-
-    /// \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 = BaseUGraphComponent>
-    class ErasableUGraphComponent : public _Base {
-    public:
-
-      typedef _Base Base;
-      typedef typename Base::Node Node;
-      typedef typename Base::UEdge UEdge;
-
-      /// \brief Erase a node from the graph.
-      ///
-      /// Erase a node from the graph. This function should erase
-      /// edges connecting to the node.
-      void erase(const Node&) {}    
-
-      /// \brief Erase an edge from the graph.
-      ///
-      /// Erase an edge from the graph.
-      ///
-      void erase(const UEdge&) {}
-
-      template <typename _Graph>
-      struct Constraints {
-	void constraints() {
-	  typename _Graph::Node node;
-	  graph.erase(node);
-	  typename _Graph::Edge edge;
-	  graph.erase(edge);
-	}
-
-	_Graph& graph;
-      };
-    };
-
-    /// \brief An empty clearable base graph class.
-    ///
-    /// This class provides beside the core graph features core clear
-    /// functions 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 ClearableGraphComponent : public _Base {
-    public:
-
-      /// \brief Erase all nodes and edges from the graph.
-      ///
-      /// Erase all nodes and edges from the graph.
-      ///
-      void clear() {}    
-
-      template <typename _Graph>
-      struct Constraints {
-	void constraints() {
-	  graph.clear();
-	}
-
-	_Graph graph;
-      };
-    };
-
-    /// \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 = BaseUGraphComponent>
-    class ClearableUGraphComponent : public _Base {
-    public:
-
-      /// \brief Erase all nodes and undirected edges from the graph.
-      ///
-      /// Erase all nodes and undirected edges from the graph.
-      ///
-      void clear() {}    
-
-      template <typename _Graph>
-      struct Constraints {
-	void constraints() {
-	  graph.clear();
-	}
-
-	_Graph graph;
-      };
-    };
-
-  }
-
-}
-
-#endif
Index: lemon/concept/graph_components.h
===================================================================
--- lemon/concept/graph_components.h	(revision 2126)
+++ lemon/concept/graph_components.h	(revision 2126)
@@ -0,0 +1,1720 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2006
+ * 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 the graph components.
+
+
+#ifndef LEMON_CONCEPT_GRAPH_COMPONENTS_H
+#define LEMON_CONCEPT_GRAPH_COMPONENTS_H
+
+#include <lemon/bits/invalid.h>
+#include <lemon/concept/maps.h>
+
+#include <lemon/bits/alteration_notifier.h>
+
+namespace lemon {
+  namespace concept {
+
+    /// \brief Skeleton class for graph Node and Edge types
+    ///
+    /// This class describes the interface of Node and Edge (and UEdge
+    /// 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 Edge types should \em not derive from the same base class.
+    /// For Node you should instantiate it with character 'n' and for Edge
+    /// with 'e'.
+
+#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 graph class.
+    ///  
+    /// This class provides the minimal set of features needed for a graph
+    /// structure. All graph concepts have to be conform to this base
+    /// graph. It just provides types for nodes and edges and functions to
+    /// get the source and the target of the edges.
+    class BaseGraphComponent {
+    public:
+
+      typedef BaseGraphComponent Graph;
+      
+      /// \brief Node class of the graph.
+      ///
+      /// This class represents the Nodes of the graph. 
+      ///
+      typedef GraphItem<'n'> Node;
+
+      /// \brief Edge class of the graph.
+      ///
+      /// This class represents the Edges of the graph. 
+      ///
+      typedef GraphItem<'e'> Edge;
+
+      /// \brief Gives back the target node of an edge.
+      ///
+      /// Gives back the target node of an edge.
+      ///
+      Node target(const Edge&) const { return INVALID;}
+
+      /// \brief Gives back the source node of an edge.
+      ///
+      /// Gives back the source node of an edge.
+      ///
+      Node source(const Edge&) const { return INVALID;}
+
+      /// \brief Gives back the opposite node on the given edge.
+      ///
+      /// Gives back the opposite node on the given edge.
+      Node oppositeNode(const Node&, const Edge&) const {
+        return INVALID;
+      }
+
+      template <typename _Graph>
+      struct Constraints {
+	typedef typename _Graph::Node Node;
+	typedef typename _Graph::Edge Edge;
+      
+	void constraints() {
+	  checkConcept<GraphItem<'n'>, Node>();
+	  checkConcept<GraphItem<'e'>, Edge>();
+	  {
+	    Node n;
+	    Edge e(INVALID);
+	    n = graph.source(e);
+	    n = graph.target(e);
+            n = graph.oppositeNode(n, e);
+	  }      
+	}
+      
+	const _Graph& graph;
+      };
+    };
+
+    /// \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, edges and undirected edges and functions to get the
+    /// source and the target of the edges and undirected edges,
+    /// conversion from edges to undirected edges and function to get
+    /// both direction of the undirected edges.
+    class BaseUGraphComponent : public BaseGraphComponent {
+    public:
+      typedef BaseGraphComponent::Node Node;
+      typedef BaseGraphComponent::Edge Edge;
+      /// \brief Undirected edge class of the graph.
+      ///
+      /// This class represents the undirected edges of the graph.
+      /// The undirected graphs can be used as a directed graph which
+      /// for each edge contains the opposite edge too so the graph is
+      /// bidirected. The undirected edge represents two opposite
+      /// directed edges.
+      class UEdge : 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.
+        UEdge() {}
+        /// \brief Copy constructor.
+        ///
+        /// Copy constructor.
+        ///
+        UEdge(const UEdge &) : Parent() {}
+        /// \brief Invalid constructor \& conversion.
+        ///
+        /// This constructor initializes the item to be invalid.
+        /// \sa Invalid for more details.
+        UEdge(Invalid) {}
+        /// \brief Converter from edge to undirected edge.
+        ///
+        /// Besides the core graph item functionality each edge should
+        /// be convertible to the represented undirected edge. 
+        UEdge(const Edge&) {}
+      };
+
+      /// \brief Returns the direction of the edge.
+      ///
+      /// Returns the direction of the edge. Each edge represents an
+      /// undirected edge with a direction. It gives back the
+      /// direction.
+      bool direction(const Edge&) const { return true; }
+
+      /// \brief Returns the directed edge.
+      ///
+      /// Returns the directed edge from its direction and the
+      /// represented undirected edge.
+      Edge direct(const UEdge&, bool) const { return INVALID;} 
+
+      /// \brief Returns the directed edge.
+      ///
+      /// Returns the directed edge from its source and the
+      /// represented undirected edge.
+      Edge direct(const UEdge&, const Node&) const { return INVALID;} 
+
+      /// \brief Returns the opposite edge.
+      ///
+      /// Returns the opposite edge. It is the edge representing the
+      /// same undirected edge and has opposite direction.
+      Edge oppositeEdge(const Edge&) const { return INVALID;}
+
+      /// \brief Gives back the target node of an undirected edge.
+      ///
+      /// Gives back the target node of an undirected edge. The name
+      /// target is a little confusing because the undirected edge
+      /// does not have target but it just means that one of the end 
+      /// node.
+      Node target(const UEdge&) const { return INVALID;}
+
+      /// \brief Gives back the source node of an undirected edge.
+      ///
+      /// Gives back the source node of an undirected edge. The name
+      /// source is a little confusing because the undirected edge
+      /// does not have source but it just means that one of the end 
+      /// node.
+      Node source(const UEdge&) const { return INVALID;}
+      
+      template <typename _Graph>
+      struct Constraints {
+	typedef typename _Graph::Node Node;
+	typedef typename _Graph::Edge Edge;
+	typedef typename _Graph::UEdge UEdge;
+      
+	void constraints() {
+          checkConcept<BaseGraphComponent, _Graph>();
+	  checkConcept<GraphItem<'u'>, UEdge>();
+	  {
+	    Node n;
+	    UEdge ue(INVALID);
+            Edge e;
+	    n = graph.source(ue);
+	    n = graph.target(ue);
+            e = graph.direct(ue, true);
+            e = graph.direct(ue, n);
+            e = graph.oppositeEdge(e);
+            ue = e;
+            bool d = graph.direction(e);
+            ignore_unused_variable_warning(d);
+	  }      
+	}
+      
+	const _Graph& graph;
+      };
+
+    };
+
+    /// \brief An empty iterable base graph class.
+    ///  
+    /// This class provides beside the core graph features
+    /// core iterable interface for the graph structure.
+    /// Most of the base graphs should be conform to this concept.
+    template <typename _Base = BaseGraphComponent>
+    class BaseIterableGraphComponent : public _Base {
+    public:
+
+      typedef _Base Base; 
+      typedef typename Base::Node Node;
+      typedef typename Base::Edge Edge;
+
+      /// \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 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 point to the given
+      /// node.
+      ///
+      /// Gives back the first of the edges point to the given node.
+      ///     
+      void firstIn(Edge&, const Node&) const {}
+
+      /// \brief Gives back the next of the edges points to the given
+      /// node.
+      ///
+      /// Gives back the next of the edges points to the given node.
+      ///
+      void nextIn(Edge&) const {}
+
+      /// \brief Gives back the first of the edges start from the
+      /// given node.
+      ///      
+      /// Gives back the first of the edges start from the given node.
+      ///     
+      void firstOut(Edge&, const Node&) const {}
+
+      /// \brief Gives back the next of the edges start from the given
+      /// node.
+      ///
+      /// Gives back the next of the edges start from the given node.
+      ///     
+      void nextOut(Edge&) const {}
+
+
+      template <typename _Graph>
+      struct Constraints {
+      
+	void constraints() {
+	  checkConcept< BaseGraphComponent, _Graph >();
+	  typename _Graph::Node node;      
+	  typename _Graph::Edge edge;
+	  {
+	    graph.first(node);
+	    graph.next(node);
+	  }
+	  {
+	    graph.first(edge);
+	    graph.next(edge);
+	  }
+	  {
+	    graph.firstIn(edge, node);
+	    graph.nextIn(edge);
+	  }
+	  {
+	    graph.firstOut(edge, node);
+	    graph.nextOut(edge);
+	  }
+	}
+
+	const _Graph& graph;
+      };
+    };
+
+    /// \brief An empty iterable base undirected graph class.
+    ///  
+    /// This class provides beside the core undirceted graph features
+    /// core iterable interface for the undirected graph structure.
+    /// Most of the base undirected graphs should be conform to this
+    /// concept.
+    template <typename _Base = BaseUGraphComponent>
+    class BaseIterableUGraphComponent 
+      : public BaseIterableGraphComponent<_Base> {
+    public:
+
+      typedef _Base Base; 
+      typedef typename Base::UEdge UEdge;
+      typedef typename Base::Node Node;
+
+      using BaseIterableGraphComponent<_Base>::first;
+      using BaseIterableGraphComponent<_Base>::next;
+
+      /// \brief Gives back the first undirected edge in the iterating
+      /// order.
+      ///
+      /// Gives back the first undirected edge in the iterating order.
+      ///     
+      void first(UEdge&) const {}
+
+      /// \brief Gives back the next undirected edge in the iterating
+      /// order.
+      ///
+      /// Gives back the next undirected edge in the iterating order.
+      ///     
+      void next(UEdge&) const {}
+
+
+      /// \brief Gives back the first of the undirected edges from the
+      /// given node.
+      ///
+      /// Gives back the first of the undirected edges from the given
+      /// node. The bool parameter gives back that direction which
+      /// gives a good direction of the uedge so the source of the
+      /// directed edge is the given node.
+      void firstInc(UEdge&, bool&, const Node&) const {}
+
+      /// \brief Gives back the next of the undirected edges from the
+      /// given node.
+      ///
+      /// Gives back the next of the undirected edges from the given
+      /// node. The bool parameter should be used as the \c firstInc()
+      /// use it.
+      void nextInc(UEdge&, bool&) const {}
+
+      template <typename _Graph>
+      struct Constraints {
+      
+	void constraints() {
+	  checkConcept<Base, _Graph >();
+	  checkConcept<BaseIterableGraphComponent<Base>, _Graph>();
+	  typename _Graph::Node node;
+	  typename _Graph::UEdge uedge;
+          bool dir;
+	  {
+	    graph.first(uedge);
+	    graph.next(uedge);
+	  }
+	  {
+	    graph.firstInc(uedge, dir, node);
+	    graph.nextInc(uedge, dir);
+	  }
+	}
+
+	const _Graph& graph;
+      };
+    };
+
+    /// \brief An empty idable base graph class.
+    ///  
+    /// This class provides beside the core graph features
+    /// core id functions for the graph structure.
+    /// The most of the base graphs should be conform to this concept.
+    /// The id's are unique and immutable.
+    template <typename _Base = BaseGraphComponent>
+    class IDableGraphComponent : public _Base {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::Edge Edge;
+
+      /// \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 graph 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 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 edge 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
+      /// 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
+      /// 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< BaseGraphComponent, _Graph >();
+	  typename _Graph::Node node;
+	  int nid = graph.id(node);
+	  nid = graph.id(node);
+	  node = graph.nodeFromId(nid);
+	  typename _Graph::Edge edge;
+	  int eid = graph.id(edge);
+	  eid = graph.id(edge);
+	  edge = graph.edgeFromId(eid);
+
+	  nid = graph.maxNodeId();
+	  ignore_unused_variable_warning(nid);
+	  eid = graph.maxEdgeId();
+	  ignore_unused_variable_warning(eid);
+	}
+
+	const _Graph& graph;
+      };
+    };
+
+    /// \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 = BaseUGraphComponent>
+    class IDableUGraphComponent : public IDableGraphComponent<_Base> {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::UEdge UEdge;
+
+      using IDableGraphComponent<_Base>::id;
+
+      /// \brief Gives back an unique integer id for the UEdge. 
+      ///
+      /// Gives back an unique integer id for the UEdge. 
+      ///
+      int id(const UEdge&) const { return -1;}
+
+      /// \brief Gives back the undirected edge by the unique id.
+      ///
+      /// Gives back the undirected edge by the unique id.  If the
+      /// graph does not contain edge with the given id then the
+      /// result of the function is undetermined.
+      UEdge uEdgeFromId(int) const { return INVALID;}
+
+      /// \brief Gives back an integer greater or equal to the maximum
+      /// UEdge id.
+      ///
+      /// Gives back an integer greater or equal to the maximum UEdge
+      /// id.
+      int maxUEdgeId() const { return -1;}
+
+      template <typename _Graph>
+      struct Constraints {
+
+	void constraints() {
+	  checkConcept<Base, _Graph >();
+	  checkConcept<IDableGraphComponent<Base>, _Graph >();
+	  typename _Graph::UEdge uedge;
+	  int ueid = graph.id(uedge);
+	  ueid = graph.id(uedge);
+	  uedge = graph.uEdgeFromId(ueid);
+	  ueid = graph.maxUEdgeId();
+	  ignore_unused_variable_warning(ueid);
+	}
+
+	const _Graph& graph;
+      };
+    };
+
+    /// \brief An empty extendable base graph class.
+    ///
+    /// This class provides beside the core graph features
+    /// core graph extend interface for the graph structure.
+    /// The most of the base graphs should be conform to this concept.
+    template <typename _Base = BaseGraphComponent>
+    class BaseExtendableGraphComponent : public _Base {
+    public:
+
+      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 edge connects the given two nodes.
+      ///
+      /// Adds a new edge connects the the given two nodes.
+      Edge addEdge(const Node&, const Node&) {
+	return INVALID;
+      }
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+	  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 extendable base undirected graph class.
+    ///
+    /// This class provides beside the core undirected graph features
+    /// core undircted graph extend interface for the graph structure.
+    /// The most of the base graphs should be conform to this concept.
+    template <typename _Base = BaseUGraphComponent>
+    class BaseExtendableUGraphComponent : public _Base {
+    public:
+
+      typedef typename _Base::Node Node;
+      typedef typename _Base::UEdge UEdge;
+
+      /// \brief Adds a new node to the graph.
+      ///
+      /// Adds a new node to the graph.
+      ///
+      Node addNode() {
+	return INVALID;
+      }
+    
+      /// \brief Adds a new edge connects the given two nodes.
+      ///
+      /// Adds a new edge connects the the given two nodes.
+      UEdge addEdge(const Node&, const Node&) {
+	return INVALID;
+      }
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+	  typename _Graph::Node node_a, node_b;
+	  node_a = graph.addNode();
+	  node_b = graph.addNode();
+	  typename _Graph::UEdge uedge;
+	  uedge = graph.addUEdge(node_a, node_b);
+	}
+
+	_Graph& graph;
+      };
+    };
+
+    /// \brief An empty erasable base graph class.
+    ///  
+    /// This class provides beside the core graph features
+    /// core erase functions for the graph structure.
+    /// The most of the base graphs should be conform to this concept.
+    template <typename _Base = BaseGraphComponent>
+    class BaseErasableGraphComponent : 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 not
+      /// erase edges connecting to the Node.
+      void erase(const Node&) {}    
+
+      /// \brief Erase an edge from the graph.
+      ///
+      /// Erase an edge from the graph.
+      ///
+      void erase(const Edge&) {}
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+	  typename _Graph::Node node;
+	  graph.erase(node);
+	  typename _Graph::Edge edge;
+	  graph.erase(edge);
+	}
+
+	_Graph& graph;
+      };
+    };
+
+    /// \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.
+    template <typename _Base = BaseUGraphComponent>
+    class BaseErasableUGraphComponent : public _Base {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::UEdge UEdge;
+
+      /// \brief Erase a node from the graph.
+      ///
+      /// Erase a node from the graph. This function should not
+      /// erase edges connecting to the Node.
+      void erase(const Node&) {}    
+
+      /// \brief Erase an edge from the graph.
+      ///
+      /// Erase an edge from the graph.
+      ///
+      void erase(const UEdge&) {}
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+	  typename _Graph::Node node;
+	  graph.erase(node);
+	  typename _Graph::Edge edge;
+	  graph.erase(edge);
+	}
+
+	_Graph& graph;
+      };
+    };
+
+    /// \brief An empty clearable base graph class.
+    ///
+    /// This class provides beside the core graph features
+    /// core clear functions for the graph structure.
+    /// The most of the base graphs should be conform to this concept.
+    template <typename _Base = BaseGraphComponent>
+    class BaseClearableGraphComponent : public _Base {
+    public:
+
+      /// \brief Erase all the nodes and edges from the graph.
+      ///
+      /// Erase all the nodes and edges from the graph.
+      ///
+      void clear() {}    
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+	  graph.clear();
+	}
+
+	_Graph graph;
+      };
+    };
+
+    /// \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 most of the base graphs should be conform to this concept.
+    template <typename _Base = BaseUGraphComponent>
+    class BaseClearableUGraphComponent : public _Base {
+    public:
+
+      /// \brief Erase all the nodes and undirected edges from the graph.
+      ///
+      /// Erase all the nodes and undirected edges from the graph.
+      ///
+      void clear() {}    
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+	  graph.clear();
+	}
+
+	_Graph graph;
+      };
+    };
+
+
+    /// \brief Skeleton class for graph NodeIt and EdgeIt
+    ///
+    /// Skeleton class for graph NodeIt and EdgeIt.
+    ///
+    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 InEdgeIt and OutEdgeIt
+    ///
+    /// \note Because InEdgeIt and OutEdgeIt may not inherit from the same
+    /// base class, the _selector is a additional template parameter. For 
+    /// InEdgeIt you should instantiate it with character 'i' and for 
+    /// OutEdgeIt with 'o'.
+    template <typename _Graph,
+	      typename _Item = typename _Graph::Edge,
+              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 edge incoming into or outgoing 
+      /// from the node.
+      ///
+      /// Sets the iterator to the first edge 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 edge;
+	_Base node;
+	_Graph graph;
+	_GraphIncIt it;
+      };
+    };
+
+
+    /// \brief An empty iterable graph class.
+    ///
+    /// This class provides beside the core graph features
+    /// iterator based iterable interface for the graph structure.
+    /// This concept is part of the GraphConcept.
+    template <typename _Base = BaseGraphComponent>
+    class IterableGraphComponent : public _Base {
+
+    public:
+    
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::Edge Edge;
+
+      typedef IterableGraphComponent Graph;
+
+
+      /// \brief This iterator goes through each node.
+      ///
+      /// This iterator goes through each node.
+      ///
+      typedef GraphItemIt<Graph, Node> NodeIt;
+
+      /// \brief This iterator goes through each node.
+      ///
+      /// This iterator goes through each node.
+      ///
+      typedef GraphItemIt<Graph, Edge> EdgeIt;
+
+      /// \brief This iterator goes trough the incoming edges of a node.
+      ///
+      /// This iterator goes trough the \e inccoming edges of a certain node
+      /// of a graph.
+      typedef GraphIncIt<Graph, Edge, Node, 'i'> InEdgeIt;
+
+      /// \brief This iterator goes trough the outgoing edges of a node.
+      ///
+      /// This iterator goes trough the \e outgoing edges of a certain node
+      /// of a graph.
+      typedef GraphIncIt<Graph, Edge, Node, 'o'> OutEdgeIt;
+
+      /// \brief The base node of the iterator.
+      ///
+      /// Gives back the base node of the iterator.
+      /// It is always the target of the pointed edge.
+      Node baseNode(const InEdgeIt&) 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 edge.
+      Node runningNode(const InEdgeIt&) 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 edge.
+      Node baseNode(const OutEdgeIt&) 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 edge.
+      Node runningNode(const OutEdgeIt&) const { return INVALID; }
+
+      /// \brief The opposite node on the given edge.
+      ///
+      /// Gives back the opposite on the given edge.
+      /// \todo It should not be here.
+      Node oppositeNode(const Node&, const Edge&) const { return INVALID; }
+
+    
+      template <typename _Graph> 
+      struct Constraints {
+	void constraints() {
+	  checkConcept<Base, _Graph>();
+	  
+	  checkConcept<GraphItemIt<_Graph, typename _Graph::Edge>,
+	    typename _Graph::EdgeIt >();
+	  checkConcept<GraphItemIt<_Graph, typename _Graph::Node>,
+	    typename _Graph::NodeIt >();
+	  checkConcept<GraphIncIt<_Graph, typename _Graph::Edge, 
+            typename _Graph::Node, 'i'>, typename _Graph::InEdgeIt>();
+	  checkConcept<GraphIncIt<_Graph, typename _Graph::Edge, 
+            typename _Graph::Node, 'o'>, typename _Graph::OutEdgeIt>();
+
+          typename _Graph::Node n;
+          typename _Graph::InEdgeIt ieit(INVALID);
+          typename _Graph::OutEdgeIt oeit(INVALID);
+          n = graph.baseNode(ieit);
+          n = graph.runningNode(ieit);
+          n = graph.baseNode(oeit);
+          n = graph.runningNode(oeit);
+          ignore_unused_variable_warning(n);
+        }
+	
+	const _Graph& graph;
+	
+      };
+    };
+
+    /// \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 GraphConcept.
+    template <typename _Base = BaseUGraphComponent>
+    class IterableUGraphComponent : public IterableGraphComponent<_Base> {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::Edge Edge;
+      typedef typename Base::UEdge UEdge;
+
+    
+      typedef IterableUGraphComponent Graph;
+      using IterableGraphComponent<_Base>::baseNode;
+      using IterableGraphComponent<_Base>::runningNode;
+
+
+      /// \brief This iterator goes through each node.
+      ///
+      /// This iterator goes through each node.
+      typedef GraphItemIt<Graph, UEdge> UEdgeIt;
+      /// \brief This iterator goes trough the incident edges of a
+      /// node.
+      ///
+      /// This iterator goes trough the incident edges of a certain
+      /// node of a graph.
+      typedef GraphIncIt<Graph, UEdge, Node, 'u'> IncEdgeIt;
+      /// \brief The base node of the iterator.
+      ///
+      /// Gives back the base node of the iterator.
+      Node baseNode(const IncEdgeIt&) const { return INVALID; }
+
+      /// \brief The running node of the iterator.
+      ///
+      /// Gives back the running node of the iterator.
+      Node runningNode(const IncEdgeIt&) const { return INVALID; }
+
+      template <typename _Graph> 
+      struct Constraints {
+	void constraints() {
+	  checkConcept<Base, _Graph>();
+	  checkConcept<IterableGraphComponent<Base>, _Graph>();
+	  
+	  checkConcept<GraphItemIt<_Graph, typename _Graph::UEdge>,
+	    typename _Graph::UEdgeIt >();
+	  checkConcept<GraphIncIt<_Graph, typename _Graph::UEdge, 
+            typename _Graph::Node, 'u'>, typename _Graph::IncEdgeIt>();
+
+          typename _Graph::Node n;
+          typename _Graph::IncEdgeIt ueit(INVALID);
+          n = graph.baseNode(ueit);
+          n = graph.runningNode(ueit);
+	}
+	
+	const _Graph& graph;
+	
+      };
+    };
+
+    /// \brief An empty alteration notifier 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 _Base {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::Edge Edge;
+
+
+      /// The node observer registry.
+      typedef AlterationNotifier<AlterableGraphComponent, Node> 
+      NodeNotifier;
+      /// The edge observer registry.
+      typedef AlterationNotifier<AlterableGraphComponent, Edge> 
+      EdgeNotifier;
+      
+      /// \brief Gives back the node alteration notifier.
+      ///
+      /// Gives back the node alteration notifier.
+      NodeNotifier& getNotifier(Node) const {
+	return NodeNotifier();
+      }
+      
+      /// \brief Gives back the edge alteration notifier.
+      ///
+      /// Gives back the edge alteration notifier.
+      EdgeNotifier& getNotifier(Edge) const {
+	return EdgeNotifier();
+      }
+
+      template <typename _Graph> 
+      struct Constraints {
+	void constraints() {
+	  checkConcept<Base, _Graph>();
+          typename _Graph::NodeNotifier& nn 
+            = graph.getNotifier(typename _Graph::Node());
+
+          typename _Graph::EdgeNotifier& en 
+            = graph.getNotifier(typename _Graph::Edge());
+          
+          ignore_unused_variable_warning(nn);
+          ignore_unused_variable_warning(en);
+	}
+	
+	const _Graph& graph;
+	
+      };
+      
+    };
+
+    /// \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 = BaseUGraphComponent>
+    class AlterableUGraphComponent : public AlterableGraphComponent<_Base> {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::UEdge UEdge;
+
+
+      /// The edge observer registry.
+      typedef AlterationNotifier<AlterableUGraphComponent, UEdge> 
+      UEdgeNotifier;
+      
+      /// \brief Gives back the edge alteration notifier.
+      ///
+      /// Gives back the edge alteration notifier.
+      UEdgeNotifier& getNotifier(UEdge) const {
+	return UEdgeNotifier();
+      }
+
+      template <typename _Graph> 
+      struct Constraints {
+	void constraints() {
+	  checkConcept<Base, _Graph>();
+          checkConcept<AlterableGraphComponent, _Graph>();
+          typename _Graph::UEdgeNotifier& uen 
+            = graph.getNotifier(typename _Graph::UEdge());
+          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, EdgeMap), that is \ref maps-page "maps" which can be used to
+    /// associate data to graph descriptors (nodes or edges).
+    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 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 _Base  {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::Edge Edge;
+
+      typedef MappableGraphComponent Graph;
+
+      /// \brief ReadWrite map of the nodes.
+      ///
+      /// ReadWrite map of the nodes.
+      ///
+      template <typename Value>
+      class NodeMap : public GraphMap<Graph, Node, Value> {
+      private:
+	NodeMap();
+      public:
+        typedef GraphMap<Graph, Node, Value> Parent;
+
+	/// \brief Construct a new map.
+	///
+	/// Construct a new map for the graph.
+	/// \todo call the right parent class constructor
+	explicit NodeMap(const Graph& graph) : Parent(graph) {}
+
+	/// \brief Construct a new map with default value.
+	///
+	/// Construct a new map for the graph and initalise the values.
+	NodeMap(const Graph& graph, const Value& value)
+          : Parent(graph, 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 edges.
+      ///
+      /// ReadWrite map of the edges.
+      ///
+      template <typename Value>
+      class EdgeMap : public GraphMap<Graph, Edge, Value> {
+      private:
+	EdgeMap();
+      public:
+        typedef GraphMap<Graph, Edge, Value> Parent;
+
+	/// \brief Construct a new map.
+	///
+	/// Construct a new map for the graph.
+	/// \todo call the right parent class constructor
+	explicit EdgeMap(const Graph& graph) : Parent(graph) {}
+
+	/// \brief Construct a new map with default value.
+	///
+	/// Construct a new map for the graph and initalise the values.
+	EdgeMap(const Graph& 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<Base, _Graph>();
+	  { // int map test
+	    typedef typename _Graph::template NodeMap<int> IntNodeMap;
+	    checkConcept<GraphMap<_Graph, typename _Graph::Node, int>, 
+	      IntNodeMap >();
+	  } { // bool map test
+	    typedef typename _Graph::template NodeMap<bool> BoolNodeMap;
+	    checkConcept<GraphMap<_Graph, typename _Graph::Node, bool>,
+	      BoolNodeMap >();
+	  } { // Dummy map test
+	    typedef typename _Graph::template NodeMap<Dummy> DummyNodeMap;
+	    checkConcept<GraphMap<_Graph, typename _Graph::Node, Dummy>,
+	      DummyNodeMap >();
+	  } 
+
+	  { // 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 mappable base graph class.
+    ///
+    /// This class provides beside the core graph features
+    /// map interface for the graph structure.
+    /// This concept is part of the UGraph concept.
+    template <typename _Base = BaseUGraphComponent>
+    class MappableUGraphComponent : public MappableGraphComponent<_Base>  {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::UEdge UEdge;
+
+      typedef MappableUGraphComponent Graph;
+
+      /// \brief ReadWrite map of the uedges.
+      ///
+      /// ReadWrite map of the uedges.
+      ///
+      template <typename Value>
+      class UEdgeMap : public GraphMap<Graph, UEdge, Value> {  
+      public:
+        typedef GraphMap<Graph, UEdge, Value> Parent;
+
+	/// \brief Construct a new map.
+	///
+	/// Construct a new map for the graph.
+	/// \todo call the right parent class constructor
+	explicit UEdgeMap(const Graph& graph) : Parent(graph) {}
+
+	/// \brief Construct a new map with default value.
+	///
+	/// Construct a new map for the graph and initalise the values.
+	UEdgeMap(const Graph& graph, const Value& value)
+          : Parent(graph, value) {}
+
+	/// \brief Copy constructor.
+	///
+	/// Copy Constructor.
+	UEdgeMap(const UEdgeMap& nm) : Parent(nm) {}
+
+	/// \brief Assign operator.
+	///
+	/// Assign operator.
+        template <typename CMap>
+        UEdgeMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<UEdge, Value>, CMap>();
+          return *this;
+        }
+
+      };
+
+
+      template <typename _Graph>
+      struct Constraints {
+
+	struct Dummy {
+	  int value;
+	  Dummy() : value(0) {}
+	  Dummy(int _v) : value(_v) {}
+	};
+
+	void constraints() {
+	  checkConcept<Base, _Graph>();
+	  checkConcept<MappableGraphComponent<Base>, _Graph>();
+
+	  { // int map test
+	    typedef typename _Graph::template UEdgeMap<int> IntUEdgeMap;
+	    checkConcept<GraphMap<_Graph, typename _Graph::UEdge, int>,
+	      IntUEdgeMap >();
+	  } { // bool map test
+	    typedef typename _Graph::template UEdgeMap<bool> BoolUEdgeMap;
+	    checkConcept<GraphMap<_Graph, typename _Graph::UEdge, bool>,
+	      BoolUEdgeMap >();
+	  } { // Dummy map test
+	    typedef typename _Graph::template UEdgeMap<Dummy> DummyUEdgeMap;
+	    checkConcept<GraphMap<_Graph, typename _Graph::UEdge, Dummy>, 
+	      DummyUEdgeMap >();
+	  } 
+	}
+
+	_Graph& graph;
+      };
+    };
+
+
+    /// \brief An empty extendable graph class.
+    ///
+    /// This class provides beside the core graph features graph
+    /// extendable 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 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 edge connects the given two nodes.
+      ///
+      /// Adds a new edge connects the the given two nodes.
+      Edge addEdge(const Node&, const Node&) {
+	return INVALID;
+      }
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+	  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 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 = BaseUGraphComponent>
+    class ExtendableUGraphComponent : public _Base {
+    public:
+
+      typedef typename _Base::Node Node;
+      typedef typename _Base::UEdge UEdge;
+
+      /// \brief Adds a new node to the graph.
+      ///
+      /// Adds a new node to the graph.
+      ///
+      Node addNode() {
+	return INVALID;
+      }
+    
+      /// \brief Adds a new edge connects the given two nodes.
+      ///
+      /// Adds a new edge connects the the given two nodes.
+      UEdge addEdge(const Node&, const Node&) {
+	return INVALID;
+      }
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+	  typename _Graph::Node node_a, node_b;
+	  node_a = graph.addNode();
+	  node_b = graph.addNode();
+	  typename _Graph::UEdge uedge;
+	  uedge = graph.addUEdge(node_a, node_b);
+	}
+
+	_Graph& graph;
+      };
+    };
+
+    /// \brief An empty erasable graph class.
+    ///  
+    /// This class provides beside the core graph features core erase
+    /// functions 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 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 all edges connecting to the node.
+      void erase(const Node&) {}    
+
+      /// \brief Erase an edge from the graph.
+      ///
+      /// Erase an edge from the graph.
+      ///
+      void erase(const Edge&) {}
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+	  typename _Graph::Node node;
+	  graph.erase(node);
+	  typename _Graph::Edge edge;
+	  graph.erase(edge);
+	}
+
+	_Graph& graph;
+      };
+    };
+
+    /// \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 = BaseUGraphComponent>
+    class ErasableUGraphComponent : public _Base {
+    public:
+
+      typedef _Base Base;
+      typedef typename Base::Node Node;
+      typedef typename Base::UEdge UEdge;
+
+      /// \brief Erase a node from the graph.
+      ///
+      /// Erase a node from the graph. This function should erase
+      /// edges connecting to the node.
+      void erase(const Node&) {}    
+
+      /// \brief Erase an edge from the graph.
+      ///
+      /// Erase an edge from the graph.
+      ///
+      void erase(const UEdge&) {}
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+	  typename _Graph::Node node;
+	  graph.erase(node);
+	  typename _Graph::Edge edge;
+	  graph.erase(edge);
+	}
+
+	_Graph& graph;
+      };
+    };
+
+    /// \brief An empty clearable base graph class.
+    ///
+    /// This class provides beside the core graph features core clear
+    /// functions 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 ClearableGraphComponent : public _Base {
+    public:
+
+      /// \brief Erase all nodes and edges from the graph.
+      ///
+      /// Erase all nodes and edges from the graph.
+      ///
+      void clear() {}    
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+	  graph.clear();
+	}
+
+	_Graph graph;
+      };
+    };
+
+    /// \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 = BaseUGraphComponent>
+    class ClearableUGraphComponent : public _Base {
+    public:
+
+      /// \brief Erase all nodes and undirected edges from the graph.
+      ///
+      /// Erase all nodes and undirected edges from the graph.
+      ///
+      void clear() {}    
+
+      template <typename _Graph>
+      struct Constraints {
+	void constraints() {
+	  graph.clear();
+	}
+
+	_Graph graph;
+      };
+    };
+
+  }
+
+}
+
+#endif
Index: lemon/concept/ugraph.h
===================================================================
--- lemon/concept/ugraph.h	(revision 2121)
+++ lemon/concept/ugraph.h	(revision 2126)
@@ -25,5 +25,5 @@
 #define LEMON_CONCEPT_UGRAPH_H
 
-#include <lemon/concept/graph_component.h>
+#include <lemon/concept/graph_components.h>
 #include <lemon/concept/graph.h>
 #include <lemon/bits/utility.h>
