/* -*- C++ -*-

  *

  * lemon/concept/ugraph_component.h - Part of LEMON, a generic

  * C++ optimization library

  *

  * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi

  * Kutatocsoport (Egervary Research Group on Combinatorial Optimization,

  * EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 ///\ingroup graph_concepts

 ///\file

 ///\brief Undirected graphs and components of.

 #ifndef LEMON_CONCEPT_UNDIR_GRAPH_H

 #define LEMON_CONCEPT_UNDIR_GRAPH_H

 #include <lemon/concept/graph_component.h>

 #include <lemon/concept/graph.h>

 #include <lemon/utility.h>

 namespace lemon {

   namespace concept {

 //     /// 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>

       struct Constraints {

 	struct Dummy {

 	  int value;

 	  Dummy() : value(0) {}

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

 	};

 	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 >();

 	}

       };

     };

     struct ExtendableUGraphConcept {

       template <typename Graph>

       struct Constraints {

 	void constraints() {

 	  node_a = graph.addNode();

 	  uedge = graph.addEdge(node_a, node_b);

 	}

 	typename Graph::Node node_a, node_b;

 	typename Graph::UEdge uedge;

 	Graph graph;

       };

     };

     struct ErasableUGraphConcept {

       template <typename Graph>

       struct Constraints {

 	void constraints() {

 	  graph.erase(n);

 	  graph.erase(e);

 	}

 	Graph graph;

 	typename Graph::Node n;

 	typename Graph::UEdge e;

       };

     };

     /// \addtogroup graph_concepts

     /// @{

     /// Class describing the concept of Undirected Graphs.

     /// This class describes the common interface of all Undirected

     /// Graphs.

     ///

     /// As all concept describing classes it provides only interface

     /// without any sensible implementation. So any algorithm for

     /// undirected graph should compile with this class, but it will not

     /// run properly, of couse.

     ///

     /// In LEMON undirected graphs also fulfill the concept of directed

     /// graphs (\ref lemon::concept::StaticGraph "Graph Concept"). For

     /// explanation of this and more see also the page \ref ugraphs,

     /// a tutorial about undirected graphs.

     ///

     /// You can assume that all undirected graph can be handled

     /// as a static directed graph. This way it is fully conform

     /// to the StaticGraph concept.

     class UGraph {

     public:

       ///\e

       ///\todo undocumented

       ///

       typedef True UTag;

       /// \brief The base type of node iterators, 

       /// or in other words, the trivial node iterator.

       ///

       /// This is the base type of each node iterator,

       /// thus each kind of node iterator converts to this.

       /// More precisely each kind of node iterator should be inherited 

       /// from the trivial node iterator.

       class Node {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         Node() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         Node(const Node&) { }

         /// Invalid constructor \& conversion.

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

         /// \sa Invalid for more details.

         Node(Invalid) { }

         /// Equality operator

         /// Two iterators are equal if and only if they point to the

         /// same object or both are invalid.

         bool operator==(Node) const { return true; }

         /// Inequality operator

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

         ///

         bool operator!=(Node) const { return true; }

 	/// Artificial ordering operator.

 	/// To allow the use of graph descriptors as key type in std::map or

 	/// similar associative container we require this.

 	///

 	/// \note This operator only have to define some strict ordering of

 	/// the items; this order has nothing to do with the iteration

 	/// ordering of the items.

 	///

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

 	bool operator<(Node) const { return false; }

       };

       /// This iterator goes through each node.

       /// This iterator goes through each node.

       /// Its usage is quite simple, for example you can count the number

       /// of nodes in graph \c g of type \c Graph like this:

       /// \code

       /// int count=0;

       /// for (Graph::NodeIt n(g); n!=INVALID; ++n) ++count;

       /// \endcode

       class NodeIt : public Node {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         NodeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         NodeIt(const NodeIt& n) : Node(n) { }

         /// Invalid constructor \& conversion.

         /// Initialize the iterator to be invalid.

         /// \sa Invalid for more details.

         NodeIt(Invalid) { }

         /// Sets the iterator to the first node.

         /// Sets the iterator to the first node of \c g.

         ///

         NodeIt(const UGraph&) { }

         /// Node -> NodeIt conversion.

         /// Sets the iterator to the node of \c the graph pointed by 

 	/// the trivial iterator.

         /// This feature necessitates that each time we 

         /// iterate the edge-set, the iteration order is the same.

         NodeIt(const UGraph&, const Node&) { }

         /// Next node.

         /// Assign the iterator to the next node.

         ///

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

       };

       /// The base type of the undirected edge iterators.

       /// The base type of the undirected edge iterators.

       ///

       class UEdge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         UEdge() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         UEdge(const UEdge&) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         UEdge(Invalid) { }

         /// Equality operator

         /// Two iterators are equal if and only if they point to the

         /// same object or both are invalid.

         bool operator==(UEdge) const { return true; }

         /// Inequality operator

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

         ///

         bool operator!=(UEdge) const { return true; }

 	/// Artificial ordering operator.

 	/// To allow the use of graph descriptors as key type in std::map or

 	/// similar associative container we require this.

 	///

 	/// \note This operator only have to define some strict ordering of

 	/// the items; this order has nothing to do with the iteration

 	/// ordering of the items.

 	///

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

 	bool operator<(UEdge) const { return false; }

       };

       /// This iterator goes through each undirected edge.

       /// This iterator goes through each undirected edge of a graph.

       /// Its usage is quite simple, for example you can count the number

       /// of undirected edges in a graph \c g of type \c Graph as follows:

       /// \code

       /// int count=0;

       /// for(Graph::UEdgeIt e(g); e!=INVALID; ++e) ++count;

       /// \endcode

       class UEdgeIt : public UEdge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         UEdgeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         UEdgeIt(const UEdgeIt& e) : UEdge(e) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         UEdgeIt(Invalid) { }

         /// This constructor sets the iterator to the first undirected edge.

         /// This constructor sets the iterator to the first undirected edge.

         UEdgeIt(const UGraph&) { }

         /// UEdge -> UEdgeIt conversion

         /// Sets the iterator to the value of the trivial iterator.

         /// This feature necessitates that each time we

         /// iterate the undirected edge-set, the iteration order is the 

 	/// same.

         UEdgeIt(const UGraph&, const UEdge&) { } 

         /// Next undirected edge

         /// Assign the iterator to the next undirected edge.

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

       };

       /// \brief This iterator goes trough the incident undirected 

       /// edges of a node.

       ///

       /// This iterator goes trough the incident undirected edges

       /// of a certain node

       /// of a graph.

       /// Its usage is quite simple, for example you can compute the

       /// degree (i.e. count the number

       /// of incident edges of a node \c n

       /// in graph \c g of type \c Graph as follows.

       /// \code

       /// int count=0;

       /// for(Graph::IncEdgeIt e(g, n); e!=INVALID; ++e) ++count;

       /// \endcode

       class IncEdgeIt : public UEdge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         IncEdgeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         IncEdgeIt(const IncEdgeIt& e) : UEdge(e) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         IncEdgeIt(Invalid) { }

         /// This constructor sets the iterator to first incident edge.

         /// This constructor set the iterator to the first incident edge of

         /// the node.

         IncEdgeIt(const UGraph&, const Node&) { }

         /// UEdge -> IncEdgeIt conversion

         /// Sets the iterator to the value of the trivial iterator \c e.

         /// This feature necessitates that each time we 

         /// iterate the edge-set, the iteration order is the same.

         IncEdgeIt(const UGraph&, const UEdge&) { }

         /// Next incident edge

         /// Assign the iterator to the next incident edge

 	/// of the corresponding node.

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

       };

       /// The directed edge type.

       /// The directed edge type. It can be converted to the

       /// undirected edge.

       class Edge : public UEdge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         Edge() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         Edge(const Edge& e) : UEdge(e) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         Edge(Invalid) { }

         /// Equality operator

         /// Two iterators are equal if and only if they point to the

         /// same object or both are invalid.

         bool operator==(Edge) const { return true; }

         /// Inequality operator

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

         ///

         bool operator!=(Edge) const { return true; }

 	/// Artificial ordering operator.

 	/// To allow the use of graph descriptors as key type in std::map or

 	/// similar associative container we require this.

 	///

 	/// \note This operator only have to define some strict ordering of

 	/// the items; this order has nothing to do with the iteration

 	/// ordering of the items.

 	///

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

 	bool operator<(Edge) const { return false; }

       }; 

       /// This iterator goes through each directed edge.

       /// This iterator goes through each edge of a graph.

       /// Its usage is quite simple, for example you can count the number

       /// of edges in a graph \c g of type \c Graph as follows:

       /// \code

       /// int count=0;

       /// for(Graph::EdgeIt e(g); e!=INVALID; ++e) ++count;

       /// \endcode

       class EdgeIt : public Edge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         EdgeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         EdgeIt(const EdgeIt& e) : Edge(e) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         EdgeIt(Invalid) { }

         /// This constructor sets the iterator to the first edge.

         /// This constructor sets the iterator to the first edge of \c g.

         ///@param g the graph

         EdgeIt(const UGraph &g) { ignore_unused_variable_warning(g); }

         /// Edge -> EdgeIt conversion

         /// Sets the iterator to the value of the trivial iterator \c e.

         /// This feature necessitates that each time we 

         /// iterate the edge-set, the iteration order is the same.

         EdgeIt(const UGraph&, const Edge&) { } 

         ///Next edge

         /// Assign the iterator to the next edge.

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

       };

       /// This iterator goes trough the outgoing directed edges of a node.

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

       /// of a graph.

       /// Its usage is quite simple, for example you can count the number

       /// of outgoing edges of a node \c n

       /// in graph \c g of type \c Graph as follows.

       /// \code

       /// int count=0;

       /// for (Graph::OutEdgeIt e(g, n); e!=INVALID; ++e) ++count;

       /// \endcode

       class OutEdgeIt : public Edge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         OutEdgeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         OutEdgeIt(const OutEdgeIt& e) : Edge(e) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         OutEdgeIt(Invalid) { }

         /// This constructor sets the iterator to the first outgoing edge.

         /// This constructor sets the iterator to the first outgoing edge of

         /// the node.

         ///@param n the node

         ///@param g the graph

         OutEdgeIt(const UGraph& n, const Node& g) {

 	  ignore_unused_variable_warning(n);

 	  ignore_unused_variable_warning(g);

 	}

         /// Edge -> OutEdgeIt conversion

         /// Sets the iterator to the value of the trivial iterator.

 	/// This feature necessitates that each time we 

         /// iterate the edge-set, the iteration order is the same.

         OutEdgeIt(const UGraph&, const Edge&) { }

         ///Next outgoing edge

         /// Assign the iterator to the next 

         /// outgoing edge of the corresponding node.

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

       };

       /// This iterator goes trough the incoming directed edges of a node.

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

       /// of a graph.

       /// Its usage is quite simple, for example you can count the number

       /// of outgoing edges of a node \c n

       /// in graph \c g of type \c Graph as follows.

       /// \code

       /// int count=0;

       /// for(Graph::InEdgeIt e(g, n); e!=INVALID; ++e) ++count;

       /// \endcode

       class InEdgeIt : public Edge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         InEdgeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         InEdgeIt(const InEdgeIt& e) : Edge(e) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         InEdgeIt(Invalid) { }

         /// This constructor sets the iterator to first incoming edge.

         /// This constructor set the iterator to the first incoming edge of

         /// the node.

         ///@param n the node

         ///@param g the graph

         InEdgeIt(const UGraph& g, const Node& n) { 

 	  ignore_unused_variable_warning(n);

 	  ignore_unused_variable_warning(g);

 	}

         /// Edge -> InEdgeIt conversion

         /// Sets the iterator to the value of the trivial iterator \c e.

         /// This feature necessitates that each time we 

         /// iterate the edge-set, the iteration order is the same.

         InEdgeIt(const UGraph&, const Edge&) { }

         /// Next incoming edge

         /// Assign the iterator to the next inedge of the corresponding node.

         ///

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

       };

       /// \brief Read write map of the nodes to type \c T.

       /// 

       /// ReadWrite map of the nodes to type \c T.

       /// \sa Reference

       /// \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 >

       {

       public:

         ///\e

         NodeMap(const UGraph&) { }

         ///\e

         NodeMap(const UGraph&, T) { }

         ///Copy constructor

         NodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }

         ///Assignment operator

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

         // \todo fix this concept

       };

       /// \brief Read write map of the directed edges to type \c T.

       ///

       /// Reference map of the directed edges to type \c T.

       /// \sa Reference

       /// \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>

       {

       public:

         ///\e

         EdgeMap(const UGraph&) { }

         ///\e

         EdgeMap(const UGraph&, T) { }

         ///Copy constructor

         EdgeMap(const EdgeMap& em) : ReadWriteMap<Edge,T>(em) { }

         ///Assignment operator

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

         // \todo fix this concept    

       };

       /// Read write map of the undirected edges to type \c T.

       /// Reference map of the edges to type \c T.

       /// \sa Reference

       /// \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>

       {

       public:

         ///\e

         UEdgeMap(const UGraph&) { }

         ///\e

         UEdgeMap(const UGraph&, T) { }

         ///Copy constructor

         UEdgeMap(const UEdgeMap& em) : ReadWriteMap<UEdge,T>(em) {}

         ///Assignment operator

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

         // \todo fix this concept    

       };

       /// \brief Direct the given undirected edge.

       ///

       /// Direct the given undirected edge. The returned edge source

       /// will be the given edge.

       Edge direct(const UEdge&, const Node&) const {

 	return INVALID;

       }

       /// \brief Direct the given undirected edge.

       ///

       /// Direct the given undirected edge. The returned edge source

       /// will be the source of the undirected edge if the given bool

       /// is true.

       Edge direct(const UEdge&, bool) const {

 	return INVALID;

       }

       /// \brief Returns true if the edge has default orientation.

       ///

       /// Returns whether the given directed edge is same orientation as

       /// the corresponding undirected edge.

       bool direction(Edge) const { return true; }

       /// \brief Returns the opposite directed edge.

       ///

       /// Returns the opposite directed edge.

       Edge oppositeEdge(Edge) const { return INVALID; }

       /// \brief Opposite node on an edge

       ///

       /// \return the opposite of the given Node on the given Edge

       Node oppositeNode(Node, UEdge) const { return INVALID; }

       /// \brief First node of the undirected edge.

       ///

       /// \return the first node of the given UEdge.

       ///

       /// Naturally uectected edges don't have direction and thus

       /// don't have source and target node. But we use these two methods

       /// to query the two endnodes of the edge. The direction of the edge

       /// which arises this way is called the inherent direction of the

       /// undirected edge, and is used to define the "default" direction

       /// of the directed versions of the edges.

       /// \sa direction

       Node source(UEdge) const { return INVALID; }

       /// \brief Second node of the undirected edge.

       Node target(UEdge) const { return INVALID; }

       /// \brief Source node of the directed edge.

       Node source(Edge) const { return INVALID; }

       /// \brief Target node of the directed edge.

       Node target(Edge) const { return INVALID; }

 //       /// \brief First node of the graph

 //       ///

 //       /// \note This method is part of so called \ref

 //       /// developpers_interface "Developpers' interface", so it shouldn't

 //       /// be used in an end-user program.

       void first(Node&) const {}

 //       /// \brief Next node of the graph

 //       ///

 //       /// \note This method is part of so called \ref

 //       /// developpers_interface "Developpers' interface", so it shouldn't

 //       /// be used in an end-user program.

       void next(Node&) const {}

 //       /// \brief First undirected edge of the graph

 //       ///

 //       /// \note This method is part of so called \ref

 //       /// developpers_interface "Developpers' interface", so it shouldn't

 //       /// be used in an end-user program.

       void first(UEdge&) const {}

 //       /// \brief Next undirected edge of the graph

 //       ///

 //       /// \note This method is part of so called \ref

 //       /// developpers_interface "Developpers' interface", so it shouldn't

 //       /// be used in an end-user program.

       void next(UEdge&) const {}

 //       /// \brief First directed edge of the graph

 //       ///

 //       /// \note This method is part of so called \ref

 //       /// developpers_interface "Developpers' interface", so it shouldn't

 //       /// be used in an end-user program.

       void first(Edge&) const {}

 //       /// \brief Next directed edge of the graph

 //       ///

 //       /// \note This method is part of so called \ref

 //       /// developpers_interface "Developpers' interface", so it shouldn't

 //       /// be used in an end-user program.

       void next(Edge&) const {}

 //       /// \brief First outgoing edge from a given node

 //       ///

 //       /// \note This method is part of so called \ref

 //       /// developpers_interface "Developpers' interface", so it shouldn't

 //       /// be used in an end-user program.

       void firstOut(Edge&, Node) const {}

 //       /// \brief Next outgoing edge to a node

 //       ///

 //       /// \note This method is part of so called \ref

 //       /// developpers_interface "Developpers' interface", so it shouldn't

 //       /// be used in an end-user program.

       void nextOut(Edge&) const {}

 //       /// \brief First incoming edge to a given node

 //       ///

 //       /// \note This method is part of so called \ref

 //       /// developpers_interface "Developpers' interface", so it shouldn't

 //       /// be used in an end-user program.

       void firstIn(Edge&, Node) const {}

 //       /// \brief Next incoming edge to a node

 //       ///

 //       /// \note This method is part of so called \ref

 //       /// developpers_interface "Developpers' interface", so it shouldn't

 //       /// be used in an end-user program.

       void nextIn(Edge&) const {}

       /// \brief Base node of the iterator

       ///

       /// Returns the base node (the source in this case) of the iterator

       Node baseNode(OutEdgeIt e) const {

 	return source(e);

       }

       /// \brief Running node of the iterator

       ///

       /// Returns the running node (the target in this case) of the

       /// iterator

       Node runningNode(OutEdgeIt e) const {

 	return target(e);

       }

       /// \brief Base node of the iterator

       ///

       /// Returns the base node (the target in this case) of the iterator

       Node baseNode(InEdgeIt e) const {

 	return target(e);

       }

       /// \brief Running node of the iterator

       ///

       /// Returns the running node (the source in this case) of the

       /// iterator

       Node runningNode(InEdgeIt e) const {

 	return source(e);

       }

       /// \brief Base node of the iterator

       ///

       /// Returns the base node of the iterator

       Node baseNode(IncEdgeIt) const {

 	return INVALID;

       }

       /// \brief Running node of the iterator

       ///

       /// Returns the running node of the iterator

       Node runningNode(IncEdgeIt) const {

 	return INVALID;

       }

       template <typename Graph>

       struct Constraints {

 	void constraints() {

 	  checkConcept<BaseIterableUGraphConcept, Graph>();

 	  checkConcept<IterableUGraphConcept, Graph>();

 	  checkConcept<MappableUGraphConcept, Graph>();

 	}

       };

     };

     /// \brief An empty non-static undirected graph class.

     ///    

     /// This class provides everything that \ref UGraph does.

     /// Additionally it enables building graphs from scratch.

     class ExtendableUGraph : public UGraph {

     public:

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

       ///

       /// Add a new node to the graph.

       /// \return the new node.

       Node addNode();

       /// \brief Add a new undirected edge to the graph.

       ///

       /// Add a new undirected edge to the graph.

       /// \return the new edge.

       UEdge addEdge(const Node& from, const Node& to);

       /// \brief Resets the graph.

       ///

       /// This function deletes all undirected edges and nodes of the graph.

       /// It also frees the memory allocated to store them.

       void clear() { }

       template <typename Graph>

       struct Constraints {

 	void constraints() {

 	  checkConcept<BaseIterableUGraphConcept, Graph>();

 	  checkConcept<IterableUGraphConcept, Graph>();

 	  checkConcept<MappableUGraphConcept, Graph>();

 	  checkConcept<UGraph, Graph>();

 	  checkConcept<ExtendableUGraphConcept, Graph>();

 	  checkConcept<ClearableGraphComponent, Graph>();

 	}

       };

     };

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

     ///

     /// This class is an extension of \ref ExtendableUGraph. It makes it

     /// possible to erase undirected edges or nodes.

     class ErasableUGraph : public ExtendableUGraph {

     public:

       /// \brief Deletes a node.

       ///

       /// Deletes a node.

       ///

       void erase(Node) { }

       /// \brief Deletes an undirected edge.

       ///

       /// Deletes an undirected edge.

       ///

       void erase(UEdge) { }

       template <typename Graph>

       struct Constraints {

 	void constraints() {

 	  checkConcept<ExtendableUGraph, Graph>();

 	  checkConcept<ErasableUGraphConcept, Graph>();

 	}

       };

     };

     /// @}

   }

 }

 #endif