/* -*- C++ -*-

  * lemon/concept/graph_component.h - Part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2005 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/invalid.h>

 #include <lemon/concept/maps.h>

 #include <lemon/bits/alteration_notifier.h>

 namespace lemon {

   namespace concept {

     /// \addtogroup graph_concepts

     /// @{

     /****************   Graph iterator concepts   ****************/

     /// Skeleton class for graph Node and Edge types

     /// This class describes the interface of Node and Edge (and UndirEdge

     /// 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:

       /// 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() {}

       /// Copy constructor.

       /// Copy constructor.

       ///

       GraphItem(GraphItem const&) {}

       /// Invalid constructor \& conversion.

       /// This constructor initializes the item to be invalid.

       /// \sa Invalid for more details.

       GraphItem(Invalid) {}

       /// Assign operator for nodes.

       /// The nodes are assignable. 

       ///

       GraphItem& operator=(GraphItem const&) { return *this; }

       /// 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.

       /// \sa operator==(const Node& n)

       ///

       bool operator!=(GraphItem) const { return false; }

       /// 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.

       ///

       /// \bug This is a technical requirement. Do we really need this?

       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;

       };

     };

     /// 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.

     /// 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.

     class BaseGraphComponent {

     public:

       typedef BaseGraphComponent Graph;

       /// Node class of the graph.

       /// This class represents the Nodes of the graph. 

       ///

       typedef GraphItem<'n'> Node;

       /// 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.

       ///

       Node target(const Edge&) const { return INVALID;}

       ///Gives back the source node of an edge.

       ///Gives back the source node of an edge.

       ///

       Node source(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;

 	    n = graph.source(e);

 	    n = graph.target(e);

 	  }      

 	}

 	const _Graph& graph;

       };

     };

     /// 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.

       ///     

       void first(Node&) const {}

       /// 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.

       ///     

       void first(Edge&) const {}

       /// 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.

       ///     

       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.

       ///

       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.

       ///     

       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.

       ///     

       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;

       };

     };

     /// 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. 

       /// 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 fromId(int , Node) 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 fromId(int, Edge) const { return INVALID;}

       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.fromId(nid, Node());

 	  typename _Graph::Edge edge;

 	  int eid = graph.id(edge);

 	  eid = graph.id(edge);

 	  edge = graph.fromId(eid, Edge());

 	}

 	const _Graph& graph;

       };

     };

     /// 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);

 	}

 	const _Graph& graph;

       };

     };

     /// 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.

       ///

       Node addNode() {

 	return INVALID;

       }

       /// Adds a new Edge connects the two Nodes to the graph.

       /// Adds a new Edge connects the two Nodes to the graph.

       ///

       Edge addEdge(const Node&, const Node&) {

 	return INVALID;

       }

       template <typename _Graph>

       struct Constraints {

 	void constraints() {

 	  checkConcept<BaseGraphComponent, _Graph >();

 	  typename _Graph::Node node_a, node_b;

 	  node_a = graph.addNode();

 	  node_b = graph.addNode();

 	  typename _Graph::Edge edge;

 	  edge = graph.addEdge(node_a, node_b);

 	}

 	_Graph& graph;

       };

     };

     /// 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

       /// erase edges connecting to the Node.

       void erase(const Node&) {}    

       /// Erase an Edge from the graph.

       /// Erase an Edge from the graph.

       ///

       void erase(const Edge&) {}

       template <typename _Graph>

       struct Constraints {

 	void constraints() {

 	  checkConcept<BaseGraphComponent, _Graph>();

 	  typename _Graph::Node node;

 	  graph.erase(node);

 	  typename _Graph::Edge edge;

 	  graph.erase(edge);

 	}

 	_Graph& graph;

       };

     };

     /// 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 ClearableGraphComponent : virtual public BaseGraphComponent {

     public:

       /// 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() {

 	  checkConcept<BaseGraphComponent, _Graph>();

 	  graph.clear();

 	}

 	_Graph graph;

       };

     };

     /// 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.

       /// @warning The default constructor sets the iterator

       /// to an undefined value.

       GraphIterator() {}

       /// Copy constructor.

       /// Copy constructor.

       ///

       GraphIterator(GraphIterator const&) {}

       /// 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.

       /// This constructor initializes the item to be invalid.

       /// \sa Invalid for more details.

       GraphIterator(Invalid) {}

       /// Assign operator for items.

       /// The items are assignable. 

       ///

       GraphIterator& operator=(GraphIterator const&) { return *this; }      

       /// Next item.

       /// Assign the iterator to the next item.

       ///

       GraphIterator& operator++() { return *this; }

       //	Node operator*() const { return INVALID; }

       /// 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

       /// \sa operator==(Node n)

       ///

       bool operator!=(const GraphIterator&) 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;

 	  it2 = ++it1;

 	  ++it2 = it1;

 	  ++(++it1);

 	  /// \bug This should be: is_base_and_derived<BaseItem, _GraphIterator>

 	  _Item bi = it1;

 	  bi = it2;

 	}

 	_Graph& g;

       };

     };

     /// 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,

 	      char _selector = '0'>

     class GraphIncIterator : public Edge {

     public:

       /// Default constructor.

       /// @warning The default constructor sets the iterator

       /// to an undefined value.

       GraphIncIterator() {}

       /// Copy constructor.

       /// Copy constructor.

       ///

       GraphIncIterator(GraphIncIterator const& gi) :Edge(gi) {}

       /// 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.

       /// 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

       /// 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

       /// \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;

 	  it2 = ++it1;

 	  ++it2 = it1;

 	  ++(++it1);

 	  Edge 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.

     /// This class provides beside the core graph features

     /// iterator based iterable interface for the graph structure.

     /// This concept is part of the StaticGraphConcept.

     class IterableGraphComponent : virtual public BaseGraphComponent {

     public:

       typedef IterableGraphComponent Graph;

       typedef BaseGraphComponent::Node Node;

       typedef BaseGraphComponent::Edge Edge;

       /// 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.

       /// 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.

       /// This iterator goes trough the \e outgoing edges of a certain node

       /// of a graph.

       typedef GraphIncIterator<Graph, Edge, 'o'> OutEdgeIt;

     };

     template <typename _Graph> 

     struct Constraints {

       void constraints() {

   	checkConcept< BaseGraphComponent, _Graph>();

 	checkConcept<GraphIterator<_Graph, typename _Graph::Edge>,

 	  typename _Graph::EdgeIt >();

 	checkConcept<GraphIterator<_Graph, typename _Graph::Node>,

 	  typename _Graph::NodeIt >();

 	checkConcept<GraphIncIterator<_Graph>, typename _Graph::InEdgeIt >();

 	checkConcept<GraphIncIterator<_Graph>, typename _Graph::OutEdgeIt >();

       }

     };

     /// 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 BaseGraphComponent {

     public:

       /// The edge observer registry.

       typedef AlterationNotifier<Edge> EdgeNotifier;

       /// The node observer registry.

       typedef AlterationNotifier<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 {

 	return NodeNotifier();

       }

     };

     /// Class describing the concept of graph maps

     /// This class describes the common interface of the graph maps

     /// (NodeMap, EdgeMap), that is \ref maps-pages "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:

       /// \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& gm) :ReadWriteMap<Item, _Value>(gm) {}

       /// \brief Assign operator.

       ///

       /// Assign operator.

       GraphMap& operator=(const GraphMap&) { return *this;}

       template<typename _Map>

       struct Constraints {

 	void constraints() {

 	  checkConcept<ReadWriteMap<Item, _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 operator. Do we need it?

 	  a=b;

 	  ignore_unused_variable_warning(a2);

 	}

 	const _Map &c;

 	const Graph &g;

 	const typename GraphMap::Value &t;

       };

     };

     /// 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 StaticGraphConcept.

     class MappableGraphComponent : virtual public BaseGraphComponent {

     public:

       typedef MappableGraphComponent Graph;

       typedef BaseGraphComponent::Node Node;

       typedef BaseGraphComponent::Edge Edge;

       /// ReadWrite map of the nodes.

       /// ReadWrite map of the nodes.

       ///

       template <typename _Value>

       class NodeMap : public GraphMap<Graph, Node, _Value> {

       private:

 	NodeMap();

       public:

 	/// \brief Construct a new map.

 	///

 	/// Construct a new map for the graph.

 	/// \todo call the right parent class constructor

 	explicit NodeMap(const 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&) {}

 	/// \brief Copy constructor.

 	///

 	/// Copy Constructor.

 	NodeMap(const NodeMap& nm) : GraphMap<Graph, Node, _Value>(nm) {}

 	/// \brief Assign operator.

 	///

 	/// Assign operator.

 	NodeMap& operator=(const NodeMap&) { return *this;}

       };

       /// ReadWrite map of the edges.

       /// ReadWrite map of the edges.

       ///

       template <typename _Value>

       class EdgeMap : public GraphMap<Graph, Edge, _Value> {

       private:

 	EdgeMap();

       public:

 	/// \brief Construct a new map.

 	///

 	/// Construct a new map for the graph.

 	/// \todo call the right parent class constructor

 	explicit EdgeMap(const 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&) {}

 	/// \brief Copy constructor.

 	///

 	/// Copy Constructor.

 	EdgeMap(const EdgeMap& em) :GraphMap<Graph, Edge, _Value>(em) {}

 	/// \brief Assign operator.

 	///

 	/// Assign operator.

 	EdgeMap& operator=(const EdgeMap&) { return *this;}

       };

       template <typename _Graph>

       struct Constraints {

 	struct Type {

 	  int value;

 	  Type() : value(0) {}

 	  Type(int _v) : value(_v) {}

 	};

 	void constraints() {

 	  checkConcept<BaseGraphComponent, _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 >();

 	  } { // Type map test

 	    typedef typename _Graph::template NodeMap<Type> TypeNodeMap;

 	    checkConcept<GraphMap<_Graph, typename _Graph::Node, Type>,

 	      TypeNodeMap >();

 	  } 

 	  { // 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 >();

 	  } { // Type map test

 	    typedef typename _Graph::template EdgeMap<Type> TypeEdgeMap;

 	    checkConcept<GraphMap<_Graph, typename _Graph::Edge, Type>, 

 	      TypeEdgeMap >();

 	  } 

 	}

 	_Graph& graph;

       };

     };

     /// \brief An empty extendable extended graph class.

     ///

     /// This class provides beside the core graph features

     /// item addition interface for the graph structure.

     /// The difference between this class and the 

     /// \c BaseExtendableGraphComponent is that it should

     /// notify the item alteration observers.

     class ExtendableGraphComponent : virtual public BaseGraphComponent {

     public:

       typedef ExtendableGraphComponent Graph;

       typedef BaseGraphComponent::Node Node;

       typedef BaseGraphComponent::Edge Edge;

       /// \brief Add a node to the graph.

       ///

       /// Add a node to the graph and notify the observers.

       Node addNode() {

 	return INVALID;

       }

       /// \brief Add an edge to the graph.

       ///

       /// Add an edge to the graph and notify the observers.

       Edge addEdge(const Node&, const Node&) {

 	return INVALID;

       }

       template <typename _Graph>

       struct Constraints {

 	void constraints() {

 	  checkConcept<BaseGraphComponent, _Graph >();

 	  typename _Graph::Node node_a, node_b;

 	  node_a = graph.addNode();

 	  node_b = graph.addNode();

 	  typename _Graph::Edge edge;

 	  edge = graph.addEdge(node_a, node_b);      

 	}

 	_Graph& graph;

       };

     };

     /// \brief An empty erasable extended graph class.

     ///

     /// This class provides beside the core graph features

     /// item erase interface for the graph structure.

     /// The difference between this class and the 

     /// \c BaseErasableGraphComponent is that it should

     /// notify the item alteration observers.

     class ErasableGraphComponent : virtual public BaseGraphComponent {

     public:

       typedef ErasableGraphComponent Graph;

       typedef BaseGraphComponent::Node Node;

       typedef BaseGraphComponent::Edge Edge;

       /// \brief Erase the Node and notify the node alteration observers.

       ///

       ///  Erase the Node and notify the node alteration observers.

       void erase(const Node&) {}    

       /// \brief Erase the Edge and notify the edge alteration observers.

       ///

       ///  Erase the Edge and notify the edge alteration observers.

       void erase(const Edge&) {}

       template <typename _Graph>

       struct Constraints {

 	void constraints() {

 	  checkConcept<BaseGraphComponent, _Graph >();

 	  typename _Graph::Node node;

 	  graph.erase(node);

 	  typename _Graph::Edge edge;

 	  graph.erase(edge);      

 	}

 	_Graph& graph;

       };

     };

     /// @}

   }

 }

 #endif