Changeset 2121:09a07a851506 in lemon-0.x

Timestamp:

07/10/06 21:04:17 (19 years ago)

Author:

Balazs Dezso

Branch:

default

Phase:

public

Convert:

svn:c9d7d8f5-90d6-0310-b91f-818b3a526b0e/lemon/trunk@2834

Message:

Modifications in the Graph Component concepts

Files:

• lemon/concept/graph.h (modified) (5 diffs)
• lemon/concept/graph_component.h (modified) (29 diffs)
• lemon/concept/ugraph.h (modified) (7 diffs)
• test/graph_test.cc (modified) (1 diff)
• test/ugraph_test.cc (modified) (1 diff)

lemon/concept/graph.h

@@ -33 +33 @@
   namespace concept {
 
-    
-    /**************** The full-featured graph concepts ****************/
-
-
-    // \brief Modular static graph class.
-    //     
-    // It should be the same as the \c Graph class.
-    class _Graph 
-      :  virtual public BaseGraphComponent,
-         public IterableGraphComponent, public MappableGraphComponent {
-    public:
-
-      typedef BaseGraphComponent::Node Node;
-      typedef BaseGraphComponent::Edge Edge;
-
-      template <typename _Graph>
-      struct Constraints {
-        void constraints() {
-          checkConcept<IterableGraphComponent, _Graph>();
-          checkConcept<MappableGraphComponent, _Graph>();
-        }
-      };
-    };
-
     /// \addtogroup graph_concepts
     /// @{
@@ -411 +387 @@
       /// \warning Making maps that can handle bool type (NodeMap<bool>)
       /// needs some extra attention!
-      /// \todo Wrong documentation
       template<class T> 
-      class NodeMap : public ReadWriteMap< Node, T >
-      {
+      class NodeMap : public ReadWriteMap< Node, T > {
       public:
 
@@ -425 +399 @@
         NodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }
         ///Assignment operator
-        NodeMap& operator=(const NodeMap&) { return *this; }
-        // \todo fix this concept
+        template <typename CMap>
+        NodeMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<Node, T>, CMap>();
+          return *this; 
+        }
       };
 
@@ -435 +412 @@
       /// \warning Making maps that can handle bool type (EdgeMap<bool>)
       /// needs some extra attention!
-      /// \todo Wrong documentation
       template<class T> 
-      class EdgeMap : public ReadWriteMap<Edge,T>
-      {
+      class EdgeMap : public ReadWriteMap<Edge,T> {
       public:
 
@@ -448 +423 @@
         EdgeMap(const EdgeMap& em) : ReadWriteMap<Edge,T>(em) { }
         ///Assignment operator
-        EdgeMap& operator=(const EdgeMap&) { return *this; }
-        // \todo fix this concept    
+        template <typename CMap>
+        EdgeMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<Edge, T>, CMap>();
+          return *this; 
+        }
       };
 
       template <typename RGraph>
-      struct Constraints : public _Graph::Constraints<RGraph> {};
+      struct Constraints {
+        void constraints() {
+          checkConcept<BaseIterableGraphComponent<>, Graph>();
+          checkConcept<IterableGraphComponent<>, Graph>();
+          checkConcept<MappableGraphComponent<>, Graph>();
+        }
+      };
 
     };

lemon/concept/graph_component.h

@@ -33 +33 @@
   namespace concept {
 
-    /****************   Graph iterator concepts   ****************/
-
-    /// Skeleton class for graph Node and Edge types
-
+    /// \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.
@@ -51 +49 @@
     class GraphItem {
     public:
-      /// Default constructor.
-      
+      /// \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.
-      
-      /// Copy constructor.
-      ///
-      GraphItem(GraphItem const&) {}
-      /// Invalid constructor \& conversion.
-
+      ///
+      GraphItem(const GraphItem &) {}
+      /// \brief Invalid constructor \& conversion.
+      ///
       /// This constructor initializes the item to be invalid.
       /// \sa Invalid for more details.
       GraphItem(Invalid) {}
-      /// Assign operator for nodes.
-
+      /// \brief Assign operator for nodes.
+      ///
       /// The nodes are assignable. 
       ///
       GraphItem& operator=(GraphItem const&) { return *this; }
-      /// Equality operator.
-      
+      /// \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; }
-      /// Inequality operator.
-        
+      /// \brief Inequality operator.
+      ///
       /// \sa operator==(const Node& n)
       ///
       bool operator!=(GraphItem) const { return false; }
 
-      /// Artificial ordering operator.
-
+      /// \brief Artificial ordering operator.
+      ///
       /// To allow the use of graph descriptors as key type in std::map or
       /// similar associative container we require this.
@@ -91 +89 @@
       /// the items; this order has nothing to do with the iteration
       /// ordering of the items.
-      ///
-      /// \bug This is a technical requirement. Do we really need this?
       bool operator<(GraphItem) const { return false; }
 
@@ -108 +104 @@
           b = (ia == ib) && (ia != ib);
           b = (ia == INVALID) && (ib != INVALID);
-          //      b = (ia < ib);
+          b = (ia < ib);
         }
 
@@ -116 +112 @@
     };
 
-    /// A type describing the concept of graph node
-
-    /// This is an instantiation of \ref GraphItem which can be used as a
-    /// Node subtype in graph skeleton definitions
-    typedef GraphItem<'n'> GraphNode;
-
-    /// A type describing the concept of graph edge
-
-    /// This is an instantiation of \ref GraphItem which can be used as a
-    /// Edge subtype in graph skeleton definitions
-    typedef GraphItem<'e'> GraphEdge;
-
-
-    /**************** Basic features of graphs ****************/
-
-    /// An empty base graph class.
-  
+    /// \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.
-    ///
-    /// \bug This is not true. The minimal graph concept is the
-    /// BaseIterableGraphComponent.
-
+    /// graph. It just provides types for nodes and edges and functions to
+    /// get the source and the target of the edges.
     class BaseGraphComponent {
     public:
@@ -145 +123 @@
       typedef BaseGraphComponent Graph;
       
-      /// Node class of the graph.
-
+      /// \brief Node class of the graph.
+      ///
       /// This class represents the Nodes of the graph. 
       ///
       typedef GraphItem<'n'> Node;
 
-      /// Edge class of the graph.
-
+      /// \brief Edge class of the graph.
+      ///
       /// This class represents the Edges of the graph. 
       ///
       typedef GraphItem<'e'> Edge;
 
-      ///Gives back the target node of an edge.
-
-      ///Gives back the target node of an 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;}
 
-      ///Gives back the source node of an edge.
-
-      ///Gives back the source node of an edge.
+      /// \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>
@@ -183 +167 @@
             n = graph.source(e);
             n = graph.target(e);
+            n = graph.oppositeNode(n, e);
           }      
         }
@@ -190 +175 @@
     };
 
-    /// An empty iterable base graph class.
-  
+    /// \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.
-
-    class BaseIterableGraphComponent : virtual public BaseGraphComponent {
-    public:
-
-      typedef BaseGraphComponent::Node Node;
-      typedef BaseGraphComponent::Edge Edge;
-
-      /// Gives back the first Node in the iterating order.
-      
-      /// Gives back the first Node in the iterating order.
+    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 {}
 
-      /// Gives back the next Node in the iterating order.
-      
-      /// Gives back the next Node in the iterating order.
+      /// \brief Gives back the next node in the iterating order.
+      ///
+      /// Gives back the next node in the iterating order.
       ///     
       void next(Node&) const {}
 
-      /// Gives back the first Edge in the iterating order.
-      
-      /// Gives back the first Edge in the iterating order.
+      /// \brief Gives back the first edge in the iterating order.
+      ///
+      /// Gives back the first edge in the iterating order.
       ///     
       void first(Edge&) const {}
-      /// Gives back the next Edge in the iterating order.
-      
-      /// Gives back the next Edge in the iterating order.
+
+      /// \brief Gives back the next edge in the iterating order.
+      ///
+      /// Gives back the next edge in the iterating order.
       ///     
       void next(Edge&) const {}
 
 
-      /// Gives back the first of the Edges point to the given Node.
-      
-      /// Gives back the first of the Edges point to the given Node.
+      /// \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 {}
 
-      /// Gives back the next of the Edges points to the given Node.
-
-
-      /// Gives back the next of the Edges points to the given Node.
+      /// \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 {}
 
-      /// Gives back the first of the Edges start from the given Node.
-      
-      /// Gives back the first of the Edges start from the given Node.
+      /// \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 {}
 
-      /// Gives back the next of the Edges start from the given Node.
-      
-      /// Gives back the next of the Edges start from the given Node.
+      /// \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 {}
@@ -281 +387 @@
     };
 
-    /// An empty idable base graph class.
-  
+    /// \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.
-    class IDableGraphComponent : virtual public BaseGraphComponent {
-    public:
-
-      typedef BaseGraphComponent::Node Node;
-      typedef BaseGraphComponent::Edge Edge;
-
-      /// Gives back an unique integer id for the Node. 
-
+    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. 
       ///
@@ -304 +485 @@
       /// If the graph does not contain node with the given id
       /// then the result of the function is undetermined. 
-      Node fromId(int , Node) const { return INVALID;}
+      Node nodeFromId(int) const { return INVALID;}
 
       /// \brief Gives back an unique integer id for the Edge. 
@@ -317 +498 @@
       /// If the graph does not contain edge with the given id
       /// then the result of the function is undetermined. 
-      Edge fromId(int, Edge) const { return INVALID;}
+      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>
@@ -327 +522 @@
           int nid = graph.id(node);
           nid = graph.id(node);
-          node = graph.fromId(nid, Node());
+          node = graph.nodeFromId(nid);
           typename _Graph::Edge edge;
           int eid = graph.id(edge);
           eid = graph.id(edge);
-          edge = graph.fromId(eid, Edge());
+          edge = graph.edgeFromId(eid);
+
+          nid = graph.maxNodeId();
+          ignore_unused_variable_warning(nid);
+          eid = graph.maxEdgeId();
+          ignore_unused_variable_warning(eid);
         }
 
@@ -338 +538 @@
     };
 
-
-    /// An empty max-idable base graph class.
-  
-    /// This class provides beside the core graph features
-    /// core max 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.
-    class MaxIDableGraphComponent : virtual public BaseGraphComponent {
-    public:
-
-      /// 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 maxId(Node = INVALID) const { return -1;}
-
-      /// 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 maxId(Edge = INVALID) const { return -1;}
-
-      template <typename _Graph>
-      struct Constraints {
-
-        void constraints() {
-          checkConcept<BaseGraphComponent, _Graph>();
-          int nid = graph.maxId(typename _Graph::Node());
-          ignore_unused_variable_warning(nid);
-          int eid = graph.maxId(typename _Graph::Edge());
-          ignore_unused_variable_warning(eid);
-        }
-      
+    /// \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;
       };
     };
 
-    /// An empty extendable base graph class.
-  
+    /// \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.
-    class BaseExtendableGraphComponent : virtual public BaseGraphComponent {
-    public:
-
-      typedef BaseGraphComponent::Node Node;
-      typedef BaseGraphComponent::Edge Edge;
-
-      /// Adds a new Node to the graph.
-
-      /// Adds a new Node to the graph.
+    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() {
@@ -394 +611 @@
       }
     
-      /// Adds a new Edge connects the two Nodes to the graph.
-
-      /// Adds a new Edge connects the two Nodes to the graph.
-      ///
+      /// \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;
@@ -405 +621 @@
       struct Constraints {
         void constraints() {
-          checkConcept<BaseGraphComponent, _Graph >();
           typename _Graph::Node node_a, node_b;
           node_a = graph.addNode();
@@ -417 +632 @@
     };
 
-    /// An empty erasable base graph class.
-  
+    /// \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.
-    class BaseErasableGraphComponent : virtual public BaseGraphComponent {
-    public:
-
-      typedef BaseGraphComponent::Node Node;
-      typedef BaseGraphComponent::Edge Edge;
-
-      /// Erase a Node from the graph.
-      
-      /// Erase a Node from the graph. This function should not
+    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&) {}    
 
-      /// Erase an Edge from the graph.
-
-      /// Erase an Edge from the graph.
+      /// \brief Erase an edge from the graph.
+      ///
+      /// Erase an edge from the graph.
       ///
       void erase(const Edge&) {}
@@ -443 +701 @@
       struct Constraints {
         void constraints() {
-          checkConcept<BaseGraphComponent, _Graph>();
           typename _Graph::Node node;
           graph.erase(node);
@@ -454 +711 @@
     };
 
-    /// An empty clearable base graph class.
-  
+    /// \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.
-    class BaseClearableGraphComponent : virtual public BaseGraphComponent {
-    public:
-
-      /// Erase all the Nodes and Edges from the graph.
-
-      /// Erase all the Nodes and Edges from the graph.
+    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() {}    
@@ -471 +766 @@
       struct Constraints {
         void constraints() {
-          checkConcept<BaseGraphComponent, _Graph>();
           graph.clear();
         }
@@ -479 +773 @@
     };
 
-
-    /// Skeleton class for graph NodeIt and EdgeIt
-
+    /// \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 GraphIterator : public _Item {
-    public:
-      /// \todo Don't we need the Item type as typedef?
-
-      /// Default constructor.
-      
+    class GraphItemIt : public _Item {
+    public:
+      /// \brief Default constructor.
+      ///
       /// @warning The default constructor sets the iterator
       /// to an undefined value.
-      GraphIterator() {}
+      GraphItemIt() {}
+      /// \brief Copy constructor.
+      ///
       /// Copy constructor.
-      
-      /// Copy constructor.
-      ///
-      GraphIterator(GraphIterator const&) {}
-      /// Sets the iterator to the first item.
-      
+      ///
+      GraphItemIt(const GraphItemIt& ) {}
+      /// \brief Sets the iterator to the first item.
+      ///
       /// Sets the iterator to the first item of \c the graph.
       ///
-      explicit GraphIterator(const _Graph&) {}
-      /// Invalid constructor \& conversion.
-
+      explicit GraphItemIt(const _Graph&) {}
+      /// \brief Invalid constructor \& conversion.
+      ///
       /// This constructor initializes the item to be invalid.
       /// \sa Invalid for more details.
-      GraphIterator(Invalid) {}
-      /// Assign operator for items.
-
+      GraphItemIt(Invalid) {}
+      /// \brief Assign operator for items.
+      ///
       /// The items are assignable. 
       ///
-      GraphIterator& operator=(GraphIterator const&) { return *this; }      
-      /// Next item.
-
+      GraphItemIt& operator=(const GraphItemIt&) { return *this; }      
+      /// \brief Next item.
+      /// 
       /// Assign the iterator to the next item.
       ///
-      GraphIterator& operator++() { return *this; }
-      //        Node operator*() const { return INVALID; }
-      /// Equality operator
-
+      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 GraphIterator&) const { return true;}
-      /// Inequality operator
-        
+      bool operator==(const GraphItemIt&) const { return true;}
+      /// \brief Inequality operator
+      ///       
       /// \sa operator==(Node n)
       ///
-      bool operator!=(const GraphIterator&) const { return true;}
+      bool operator!=(const GraphItemIt&) const { return true;}
       
-      template<typename _GraphIterator>
-      struct Constraints {
-        void constraints() {
-          //      checkConcept< Item, _GraphIterator >();
-          _GraphIterator it1(g);
-        
-          /// \todo Do we need NodeIt(Node) kind of constructor?
-          //    _GraphIterator it2(bj);
-          _GraphIterator it2;
+      template<typename _GraphItemIt>
+      struct Constraints {
+        void constraints() {
+          _GraphItemIt it1(g);  
+          _GraphItemIt it2;
 
           it2 = ++it1;
           ++it2 = it1;
           ++(++it1);
-          /// \bug This should be: is_base_and_derived<BaseItem, _GraphIterator>
+
           _Item bi = it1;
           bi = it2;
@@ -552 +864 @@
     };
 
-    /// Skeleton class for graph InEdgeIt and OutEdgeIt
-
+    /// \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'.
-    /// \todo Is this a good name for this concept?
-    template <typename Graph,
-              typename Edge = typename Graph::Edge,
+    template <typename _Graph,
+              typename _Item = typename _Graph::Edge,
+              typename _Base = typename _Graph::Node, 
               char _selector = '0'>
-    class GraphIncIterator : public Edge {
-    public:
-      /// Default constructor.
-      
+    class GraphIncIt : public _Item {
+    public:
+      /// \brief Default constructor.
+      ///
       /// @warning The default constructor sets the iterator
       /// to an undefined value.
-      GraphIncIterator() {}
+      GraphIncIt() {}
+      /// \brief Copy constructor.
+      ///
       /// Copy constructor.
-      
-      /// Copy constructor.
-      ///
-      GraphIncIterator(GraphIncIterator const& gi) :Edge(gi) {}
+      ///
+      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.
-      
-      /// Sets the iterator to the first edge incoming into or outgoing 
-      /// from the node.
-      ///
-      explicit GraphIncIterator(const Graph&, const typename Graph::Node&) {}
-      /// Invalid constructor \& conversion.
-
+      ///
+      explicit GraphIncIt(const _Graph&, const _Base&) {}
+      /// \brief Invalid constructor \& conversion.
+      ///
       /// This constructor initializes the item to be invalid.
       /// \sa Invalid for more details.
-      GraphIncIterator(Invalid) {}
-      /// Assign operator for nodes.
-
-      /// The nodes are assignable. 
-      ///
-      GraphIncIterator& operator=(GraphIncIterator const&) { return *this; }      
-      /// Next edge.
-
-      /// Assign the iterator to the next node.
-      ///
-      GraphIncIterator& operator++() { return *this; }
-
-      //        Node operator*() const { return INVALID; }
-
-      /// Equality operator
-
+      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 GraphIncIterator&) const { return true;}
-
-      /// Inequality operator
-        
+      bool operator==(const GraphIncIt&) const { return true;}
+
+      /// \brief Inequality operator
+      ///
       /// \sa operator==(Node n)
       ///
-      bool operator!=(const GraphIncIterator&) const { return true;}
-
-      template <typename _GraphIncIterator>
-      struct Constraints {
-        typedef typename Graph::Node Node;
-        void constraints() {
-          checkConcept<GraphItem<'e'>, _GraphIncIterator>();
-          _GraphIncIterator it1(graph, node);
-          /// \todo Do we need OutEdgeIt(Edge) kind of constructor?
-          //    _GraphIncIterator it2(edge);
-          _GraphIncIterator it2;
+      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);
-          Edge e = it1;
+          _Item e = it1;
           e = it2;
 
-          const_constraits();
-        }
-
-        void const_constraits() {
-          Node n = graph.baseNode(it);
-          n = graph.runningNode(it);
-        }
-
-        Edge edge;
-        Node node;
-        Graph graph;
-        _GraphIncIterator it;
-      };
-    };
-
-
-    /// An empty iterable base graph class.
-  
+        }
+
+        _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.
-    class IterableGraphComponent : virtual public BaseGraphComponent {
+    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;
 
-      typedef BaseGraphComponent::Node Node;
-      typedef BaseGraphComponent::Edge Edge;
-
+
+      /// \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 GraphIterator<Graph, Node> NodeIt;
-      /// This iterator goes through each node.
-
-      /// This iterator goes through each node.
-      ///
-      typedef GraphIterator<Graph, Edge> EdgeIt;
-      /// This iterator goes trough the incoming edges of a 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 GraphIncIterator<Graph, Edge, 'i'> InEdgeIt;
-      /// This iterator goes trough the outgoing edges of a node.
-
+      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 GraphIncIterator<Graph, Edge, 'o'> OutEdgeIt;
+      typedef GraphIncIt<Graph, Edge, Node, 'o'> OutEdgeIt;
 
       /// \brief The base node of the iterator.
@@ -712 +1019 @@
       struct Constraints {
         void constraints() {
-          checkConcept< BaseGraphComponent, _Graph>();
+          checkConcept<Base, _Graph>();
           
-          checkConcept<GraphIterator<_Graph, typename _Graph::Edge>,
+          checkConcept<GraphItemIt<_Graph, typename _Graph::Edge>,
             typename _Graph::EdgeIt >();
-          checkConcept<GraphIterator<_Graph, typename _Graph::Node>,
+          checkConcept<GraphItemIt<_Graph, typename _Graph::Node>,
             typename _Graph::NodeIt >();
-          checkConcept<GraphIncIterator<_Graph>, typename _Graph::InEdgeIt>();
-          checkConcept<GraphIncIterator<_Graph>, typename _Graph::OutEdgeIt>();
-
-          typename _Graph::Node n(INVALID);
-          typename _Graph::Edge e(INVALID);
-          n = graph.oppositeNode(n, e);
-        }
+          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;
@@ -731 +1045 @@
     };
 
-    /// An empty alteration notifier base graph class.
-  
-    /// This class provides beside the core graph features
-    /// alteration notifier interface for the graph structure.
-    /// This is an observer-notifier pattern. More Obsevers can
-    /// be registered into the notifier and whenever an alteration
-    /// occured in the graph all the observers will notified about it.
-    class AlterableGraphComponent : virtual public BaseIterableGraphComponent {
-    public:
-
+    /// \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;
-      /// The node observer registry.
-      typedef AlterationNotifier<AlterableGraphComponent, Node> 
-      NodeNotifier;
-      
-      /// \brief Gives back the edge alteration notifier.
-      ///
-      /// Gives back the edge alteration notifier.
-      EdgeNotifier getNotifier(Edge) const {
-        return EdgeNotifier();
-      }
       
       /// \brief Gives back the node alteration notifier.
       ///
       /// Gives back the node alteration notifier.
-      NodeNotifier getNotifier(Node) const {
+      NodeNotifier& getNotifier(Node) const {
         return NodeNotifier();
       }
       
-    };
-
-
-    /// Class describing the concept of graph maps
-
+      /// \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> {
-    protected:      
-      GraphMap() {}
-    public:
+    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.
       ///
@@ -782 +1234 @@
       ///
       /// Construct a new map for the graph and initalise the values.
-      GraphMap(const Graph&, const _Value&) {}
+      GraphMap(const Graph&, const Value&) {}
       /// \brief Copy constructor.
       ///
       /// Copy Constructor.
-      GraphMap(const GraphMap& gm) :ReadWriteMap<Item, _Value>(gm) {}
+      GraphMap(const GraphMap&) : Parent() {}
       
       /// \brief Assign operator.
       ///
-      /// Assign operator.
-      GraphMap& operator=(const GraphMap&) { return *this;}
+      /// 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<Item, _Value>, _Map >();
+          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. Do we need it?
-          _Map b=c;
+          // Copy constructor.
+          _Map b(c);
+          
+          ReadMap<Key, Value> cmap;
+          b = cmap;
 
           ignore_unused_variable_warning(a2);
+          ignore_unused_variable_warning(b);
         }
 
@@ -814 +1276 @@
     };
 
-    /// An empty mappable base graph class.
-  
+    /// \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 GraphConcept.
-    class MappableGraphComponent : virtual public BaseGraphComponent {
-    public:
+    /// 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;
 
-      typedef BaseGraphComponent::Node Node;
-      typedef BaseGraphComponent::Edge Edge;
-
+      /// \brief ReadWrite map of the nodes.
+      ///
       /// ReadWrite map of the nodes.
-    
-      /// ReadWrite map of the nodes.
-      ///
-      template <typename _Value>
-      class NodeMap : public GraphMap<Graph, Node, _Value> {
+      ///
+      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&) {}
+        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&, const _Value&) {}
+        NodeMap(const Graph& graph, const Value& value)
+          : Parent(graph, value) {}
+
         /// \brief Copy constructor.
         ///
         /// Copy Constructor.
-        NodeMap(const NodeMap& nm) : GraphMap<Graph, Node, _Value>(nm) {}
+        NodeMap(const NodeMap& nm) : Parent(nm) {}
 
         /// \brief Assign operator.
         ///
         /// Assign operator.
-        NodeMap& operator=(const NodeMap&) { return *this;}
-
-      };
-
+        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.
-    
-      /// ReadWrite map of the edges.
-      ///
-      template <typename _Value>
-      class EdgeMap : public GraphMap<Graph, Edge, _Value> {
+      ///
+      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&) {}
+        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&, const _Value&) {}
+        EdgeMap(const Graph& graph, const Value& value)
+          : Parent(graph, value) {}
+
         /// \brief Copy constructor.
         ///
         /// Copy Constructor.
-        EdgeMap(const EdgeMap& em) :GraphMap<Graph, Edge, _Value>(em) {}
+        EdgeMap(const EdgeMap& nm) : Parent(nm) {}
 
         /// \brief Assign operator.
         ///
         /// Assign operator.
-        EdgeMap& operator=(const EdgeMap&) { return *this;}
-
-      };
-
-      template <typename _Graph>
-      struct Constraints {
-
-        struct Type {
+        template <typename CMap>
+        EdgeMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<Edge, Value>, CMap>();
+          return *this;
+        }
+
+      };
+
+
+      template <typename _Graph>
+      struct Constraints {
+
+        struct Dummy {
           int value;
-          Type() : value(0) {}
-          Type(int _v) : value(_v) {}
+          Dummy() : value(0) {}
+          Dummy(int _v) : value(_v) {}
         };
 
         void constraints() {
-          checkConcept<BaseGraphComponent, _Graph>();
+          checkConcept<Base, _Graph>();
           { // int map test
             typedef typename _Graph::template NodeMap<int> IntNodeMap;
@@ -906 +1389 @@
             checkConcept<GraphMap<_Graph, typename _Graph::Node, bool>,
               BoolNodeMap >();
-          } { // Type map test
-            typedef typename _Graph::template NodeMap<Type> TypeNodeMap;
-            checkConcept<GraphMap<_Graph, typename _Graph::Node, Type>,
-              TypeNodeMap >();
+          } { // Dummy map test
+            typedef typename _Graph::template NodeMap<Dummy> DummyNodeMap;
+            checkConcept<GraphMap<_Graph, typename _Graph::Node, Dummy>,
+              DummyNodeMap >();
           } 
 
@@ -920 +1403 @@
             checkConcept<GraphMap<_Graph, typename _Graph::Edge, bool>,
               BoolEdgeMap >();
-          } { // Type map test
-            typedef typename _Graph::template EdgeMap<Type> TypeEdgeMap;
-            checkConcept<GraphMap<_Graph, typename _Graph::Edge, Type>, 
-              TypeEdgeMap >();
+          } { // Dummy map test
+            typedef typename _Graph::template EdgeMap<Dummy> DummyEdgeMap;
+            checkConcept<GraphMap<_Graph, typename _Graph::Edge, Dummy>, 
+              DummyEdgeMap >();
           } 
         }
@@ -931 +1414 @@
     };
 
-
-//     /// Skeleton class which describes an edge with direction in \ref
-//     /// UGraph "undirected graph".
-    template <typename UGraph>
-    class UGraphEdge : public UGraph::UEdge {
-      typedef typename UGraph::UEdge UEdge;
-      typedef typename UGraph::Node Node;
-    public:
-
-      /// \e
-      UGraphEdge() {}
-
-      /// \e
-      UGraphEdge(const UGraphEdge& e) : UGraph::UEdge(e) {}
-
-      /// \e
-      UGraphEdge(Invalid) {}
-
-      /// \brief Directed edge from undirected edge and a source node.
-      ///
-      /// Constructs a directed edge from undirected edge and a source node.
-      ///
-      /// \note You have to specify the graph for this constructor.
-      UGraphEdge(const UGraph &g,
-                     UEdge u_edge, Node n) {
-        ignore_unused_variable_warning(u_edge);
-        ignore_unused_variable_warning(g);
-        ignore_unused_variable_warning(n);
-      }
-
-      /// \e
-      UGraphEdge& operator=(UGraphEdge) { return *this; }
-
-      /// \e
-      bool operator==(UGraphEdge) const { return true; }
-      /// \e
-      bool operator!=(UGraphEdge) const { return false; }
-
-      /// \e
-      bool operator<(UGraphEdge) const { return false; }
-
-      template <typename Edge>
-      struct Constraints {
-        void constraints() {
-          const_constraints();
-        }
-        void const_constraints() const {
-          /// \bug This should be is_base_and_derived ...
-          UEdge ue = e;
-          ue = e;
-
-          Edge e_with_source(graph,ue,n);
-          ignore_unused_variable_warning(e_with_source);
-        }
-        Edge e;
-        UEdge ue;
-        UGraph graph;
-        Node n;
-      };
-    };
-    
-
-    struct BaseIterableUGraphConcept {
-
-      template <typename Graph>
-      struct Constraints {
-
-        typedef typename Graph::UEdge UEdge;
-        typedef typename Graph::Edge Edge;
-        typedef typename Graph::Node Node;
-
-        void constraints() {
-          checkConcept<BaseIterableGraphComponent, Graph>();
-          checkConcept<GraphItem<>, UEdge>();
-          //checkConcept<UGraphEdge<Graph>, Edge>();
-
-          graph.first(ue);
-          graph.next(ue);
-
-          const_constraints();
-        }
-        void const_constraints() {
-          Node n;
-          n = graph.target(ue);
-          n = graph.source(ue);
-          n = graph.oppositeNode(n0, ue);
-
-          bool b;
-          b = graph.direction(e);
-          Edge e = graph.direct(UEdge(), true);
-          e = graph.direct(UEdge(), n);
- 
-          ignore_unused_variable_warning(b);
-        }
-
-        Graph graph;
-        Edge e;
-        Node n0;
-        UEdge ue;
-      };
-
-    };
-
-
-    struct IterableUGraphConcept {
-
-      template <typename Graph>
-      struct Constraints {
-        void constraints() {
-          /// \todo we don't need the iterable component to be base iterable
-          /// Don't we really???
-          //checkConcept< BaseIterableUGraphConcept, Graph > ();
-
-          checkConcept<IterableGraphComponent, Graph> ();
-
-          typedef typename Graph::UEdge UEdge;
-          typedef typename Graph::UEdgeIt UEdgeIt;
-          typedef typename Graph::IncEdgeIt IncEdgeIt;
-
-          checkConcept<GraphIterator<Graph, UEdge>, UEdgeIt>();
-          checkConcept<GraphIncIterator<Graph, UEdge>, IncEdgeIt>();
-        }
-      };
-
-    };
-
-    struct MappableUGraphConcept {
-
-      template <typename 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 {
 
@@ -1069 +1476 @@
 
         void constraints() {
-          checkConcept<MappableGraphComponent, Graph>();
-
-          typedef typename Graph::template UEdgeMap<int> IntMap;
-          checkConcept<GraphMap<Graph, typename Graph::UEdge, int>,
-            IntMap >();
-
-          typedef typename Graph::template UEdgeMap<bool> BoolMap;
-          checkConcept<GraphMap<Graph, typename Graph::UEdge, bool>,
-            BoolMap >();
-
-          typedef typename Graph::template UEdgeMap<Dummy> DummyMap;
-          checkConcept<GraphMap<Graph, typename Graph::UEdge, Dummy>,
-            DummyMap >();
-        }
-      };
-
+          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;
+      };
     };
 

lemon/concept/ugraph.h

@@ -490 +490 @@
       /// \warning Making maps that can handle bool type (NodeMap<bool>)
       /// needs some extra attention!
-      /// \todo Wrong documentation
       template<class T> 
       class NodeMap : public ReadWriteMap< Node, T >
@@ -504 +503 @@
         NodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }
         ///Assignment operator
-        NodeMap& operator=(const NodeMap&) { return *this; }
-        // \todo fix this concept
+        template <typename CMap>
+        NodeMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<Node, T>, CMap>();
+          return *this; 
+        }
       };
 
@@ -514 +516 @@
       /// \warning Making maps that can handle bool type (EdgeMap<bool>)
       /// needs some extra attention!
-      /// \todo Wrong documentation
       template<class T> 
       class EdgeMap : public ReadWriteMap<Edge,T>
@@ -527 +528 @@
         EdgeMap(const EdgeMap& em) : ReadWriteMap<Edge,T>(em) { }
         ///Assignment operator
-        EdgeMap& operator=(const EdgeMap&) { return *this; }
-        // \todo fix this concept    
+        template <typename CMap>
+        EdgeMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<Edge, T>, CMap>();
+          return *this; 
+        }
       };
 
@@ -537 +541 @@
       /// \warning Making maps that can handle bool type (UEdgeMap<bool>)
       /// needs some extra attention!
-      /// \todo Wrong documentation
       template<class T> 
       class UEdgeMap : public ReadWriteMap<UEdge,T>
@@ -550 +553 @@
         UEdgeMap(const UEdgeMap& em) : ReadWriteMap<UEdge,T>(em) {}
         ///Assignment operator
-        UEdgeMap &operator=(const UEdgeMap&) { return *this; }
-        // \todo fix this concept    
+        template <typename CMap>
+        UEdgeMap& operator=(const CMap&) { 
+          checkConcept<ReadMap<UEdge, T>, CMap>();
+          return *this; 
+        }
       };
 
@@ -673 +679 @@
       struct Constraints {
         void constraints() {
-          checkConcept<BaseIterableUGraphConcept, Graph>();
-          checkConcept<IterableUGraphConcept, Graph>();
-          checkConcept<MappableUGraphConcept, Graph>();
+          checkConcept<BaseIterableUGraphComponent<>, Graph>();
+          checkConcept<IterableUGraphComponent<>, Graph>();
+          checkConcept<MappableUGraphComponent<>, Graph>();
         }
       };

test/graph_test.cc

@@ -39 +39 @@
     checkConcept<BaseGraphComponent, BaseGraphComponent >();
 
-    checkConcept<BaseIterableGraphComponent, BaseIterableGraphComponent >();
+    checkConcept<BaseIterableGraphComponent<>, 
+      BaseIterableGraphComponent<> >();
 
-    checkConcept<IDableGraphComponent, IDableGraphComponent >();
-    checkConcept<MaxIDableGraphComponent, MaxIDableGraphComponent >();
+    checkConcept<IDableGraphComponent<>, 
+      IDableGraphComponent<> >();
 
-    checkConcept<IterableGraphComponent, IterableGraphComponent >();
+    checkConcept<IterableGraphComponent<>, 
+      IterableGraphComponent<> >();
 
-    checkConcept<MappableGraphComponent, MappableGraphComponent >();
+    checkConcept<MappableGraphComponent<>, 
+      MappableGraphComponent<> >();
 
   }
   { // checking skeleton graphs
-    checkConcept<Graph, Graph >();
+    checkConcept<Graph, Graph>();
   }
   { // checking list graph
     checkConcept<Graph, ListGraph >();
+    checkConcept<AlterableGraphComponent<>, ListGraph>();
+    checkConcept<ExtendableGraphComponent<>, ListGraph>();
+    checkConcept<ClearableGraphComponent<>, ListGraph>();
+    checkConcept<ErasableGraphComponent<>, ListGraph>();
 
     checkGraph<ListGraph>();

test/ugraph_test.cc

@@ -33 +33 @@
 
 void check_concepts() {
-  checkConcept<UGraph, ListUGraph>();
-
-  checkConcept<UGraph, SmartUGraph>();
-
-  checkConcept<UGraph, FullUGraph>();
-
-  checkConcept<UGraph, UGraph>();
-
-  checkConcept<UGraph, GridUGraph>();
+
+  { // checking graph components
+    checkConcept<BaseUGraphComponent, BaseUGraphComponent >();
+
+    checkConcept<BaseIterableUGraphComponent<>, 
+      BaseIterableUGraphComponent<> >();
+
+    checkConcept<IDableUGraphComponent<>, 
+      IDableUGraphComponent<> >();
+
+    checkConcept<IterableUGraphComponent<>, 
+      IterableUGraphComponent<> >();
+
+    checkConcept<MappableUGraphComponent<>, 
+      MappableUGraphComponent<> >();
+
+  }
+  {
+    checkConcept<UGraph, ListUGraph>();
+    
+    checkConcept<UGraph, SmartUGraph>();
+    
+    checkConcept<UGraph, FullUGraph>();
+    
+    checkConcept<UGraph, UGraph>();
+    
+    checkConcept<UGraph, GridUGraph>();
+  }
 }