/// An empty static graph class.

 //     /// An empty static graph class.

     /// This class provides all the common features of a graph structure,

 //     /// This class provides all the common features of a graph structure,

     /// however completely without implementations and real data structures

 //     /// however completely without implementations and real data structures

     /// behind the interface.

 //     /// behind the interface.

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

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

     /// run properly, of course.

 //     /// run properly, of course.

     ///

 //     ///

     /// It can be used for checking the interface compatibility,

 //     /// It can be used for checking the interface compatibility,

     /// or it can serve as a skeleton of a new graph structure.

 //     /// or it can serve as a skeleton of a new graph structure.

     /// 

 //     /// 

     /// Also, you will find here the full documentation of a certain graph

 //     /// Also, you will find here the full documentation of a certain graph

     /// feature, the documentation of a real graph imlementation

 //     /// feature, the documentation of a real graph imlementation

     /// like @ref ListGraph or

 //     /// like @ref ListGraph or

     /// @ref SmartGraph will just refer to this structure.

 //     /// @ref SmartGraph will just refer to this structure.

     ///

 //     ///

     /// \todo A pages describing the concept of concept description would

 //     /// \todo A pages describing the concept of concept description would

     /// be nice.

 //     /// be nice.

     class StaticGraph

 //     class StaticGraph

     {

 //     {

 //     public:

 //       /// Defalult constructor.

 //       /// Defalult constructor.

 //       ///

 //       StaticGraph() { }

 //       ///Copy consructor.

 // //       ///\todo It is not clear, what we expect from a copy constructor.

 // //       ///E.g. How to assign the nodes/edges to each other? What about maps?

 // //       StaticGraph(const StaticGraph& g) { }

 //       /// 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; }

 //  	///Comparison operator.

 // 	///This is a strict ordering between the nodes.

 // 	///

 // 	///This ordering can be different from the order in which NodeIt

 // 	///goes through the nodes.

 // 	///\todo Possibly we don't need it.

 // 	bool operator<(Node) const { return true; }

 //       };

 //       /// 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&) { }

 // 	/// 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 StaticGraph& g) { }

 // 	/// Node -> NodeIt conversion.

 // 	/// Sets the iterator to the node of \c g pointed by the trivial 

 // 	/// iterator n.

 // 	/// This feature necessitates that each time we 

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

 // 	NodeIt(const StaticGraph& g, const Node& n) { }

 // 	/// Next node.

 // 	/// Assign the iterator to the next node.

 // 	///

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

 //       };

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

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

 //       ///

 //       class Edge {

 //       public:

 // 	/// Default constructor

 // 	/// @warning The default constructor sets the iterator

 // 	/// to an undefined value.

 // 	Edge() { }

 // 	/// Copy constructor.

 // 	/// Copy constructor.

 // 	///

 // 	Edge(const Edge&) { }

 // 	/// Initialize the iterator to be invalid.

 // 	/// Initialize the iterator to be invalid.

 // 	///

 // 	Edge(Invalid) { }

 // 	/// Equality operator

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

 // 	/// same object or both are invalid.

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

 // 	/// Inequality operator

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

 // 	///

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

 //  	///Comparison operator.

 // 	///This is a strict ordering between the nodes.

 // 	///

 // 	///This ordering can be different from the order in which NodeIt

 // 	///goes through the nodes.

 // 	///\todo Possibly we don't need it.

 //  	bool operator<(Edge) const { return true; }

 //       };

 //       /// 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.

 //       /// 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&) { }

 // 	/// Initialize the iterator to be invalid.

 // 	/// Initialize the iterator to be invalid.

 // 	///

 // 	OutEdgeIt(Invalid) { }

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

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

 // 	/// node

 // 	///@param n the node

 // 	///@param g the graph

 // 	OutEdgeIt(const StaticGraph& g, const Node& n) { }

 // 	/// Edge -> OutEdgeIt 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.

 // 	OutEdgeIt(const StaticGraph& g, const Edge& e) { }

 // 	///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 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&) { }

 // 	/// 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

 // 	/// node

 // 	///@param n the node

 // 	///@param g the graph

 // 	InEdgeIt(const StaticGraph& g, const Node& n) { }

 // 	/// 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 StaticGraph& g, const Edge& n) { }

 // 	/// Next incoming edge

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

 // 	///

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

 //       };

 //       /// This iterator goes through each edge.

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

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

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

 //       /// \code

 //       /// int count=0;

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

 //       /// \endcode

 //       class EdgeIt : public Edge {

 //       public:

 // 	/// Default constructor

 // 	/// @warning The default constructor sets the iterator

 // 	/// to an undefined value.

 // 	EdgeIt() { }

 // 	/// Copy constructor.

 // 	/// Copy constructor.

 // 	///

 // 	EdgeIt(const EdgeIt&) { }

 // 	/// Initialize the iterator to be invalid.

 // 	/// Initialize the iterator to be invalid.

 // 	///

 // 	EdgeIt(Invalid) { }

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

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

 // 	/// node

 // 	///@param g the graph

 // 	EdgeIt(const StaticGraph& 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 StaticGraph&, const Edge&) { } 

 //     	///Next edge

 // 	/// Assign the iterator to the next 

 // 	/// edge of the corresponding node.

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

 //       };

 //       /// First node of the graph.

 //       /// \retval i the first node.

 //       /// \return the first node.

 //       ///

 //       NodeIt& first(NodeIt& i) const { return i; }

 //       /// The first incoming edge.

 //       /// The first incoming edge.

 //       ///

 //       InEdgeIt& first(InEdgeIt &i, Node) const { return i; }

 //       /// The first outgoing edge.

 //       /// The first outgoing edge.

 //       ///

 //       OutEdgeIt& first(OutEdgeIt& i, Node) const { return i; }

 //       /// The first edge of the Graph.

 //       /// The first edge of the Graph.

 //       ///

 //       EdgeIt& first(EdgeIt& i) const { return i; }

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

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

 //       ///

 //       Node head(Edge) const { return INVALID; }

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

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

 //       ///

 //       Node tail(Edge) const { return INVALID; }

 //       ///Gives back the \e id of a node.

 //       ///\warning Not all graph structures provide this feature.

 //       ///

 //       ///\todo Should each graph provide \c id?

 //       int id(const Node&) const { return 0; }

 //       ///Gives back the \e id of an edge.

 //       ///\warning Not all graph structures provide this feature.

 //       ///

 //       ///\todo Should each graph provide \c id?

 //       int id(const Edge&) const { return 0; }

 //       ///\e

 //       ///\todo Should it be in the concept?

 //       ///

 //       int nodeNum() const { return 0; }

 //       ///\e

 //       ///\todo Should it be in the concept?

 //       ///

 //       int edgeNum() const { return 0; }

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

 //       /// \ingroup skeletons

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

 //       /// \sa Reference

 //       /// \warning Making maps that can handle bool type (NodeMap<bool>)

 //       /// needs some extra attention!

 //       template<class T> class NodeMap : public ReferenceMap< Node, T >

 //       {

 //       public:

 // 	///\e

 // 	NodeMap(const StaticGraph&) { }

 // 	///\e

 // 	NodeMap(const StaticGraph&, T) { }

 // 	///Copy constructor

 // 	template<typename TT> NodeMap(const NodeMap<TT>&) { }

 // 	///Assignment operator

 // 	template<typename TT> NodeMap& operator=(const NodeMap<TT>&)

 // 	{ return *this; }

 //       };

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

 //       /// \ingroup skeletons

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

 //       /// \sa Reference

 //       /// \warning Making maps that can handle bool type (EdgeMap<bool>)

 //       /// needs some extra attention!

 //       template<class T> class EdgeMap

 // 	: public ReferenceMap<Edge,T>

 //       {

 //       public:

 // 	///\e

 // 	EdgeMap(const StaticGraph&) { }

 // 	///\e

 // 	EdgeMap(const StaticGraph&, T) { }

 // 	///Copy constructor

 // 	template<typename TT> EdgeMap(const EdgeMap<TT>&) { }

 // 	///Assignment operator

 // 	template<typename TT> EdgeMap &operator=(const EdgeMap<TT>&)

 // 	{ return *this; }

 //       };

 //     };

 //     struct DummyType {

 //       int value;

 //       DummyType() {}

 //       DummyType(int p) : value(p) {}

 //       DummyType& operator=(int p) { value = p; return *this;}

 //     };

 //     ///\brief Checks whether \c G meets the

 //     ///\ref lemon::skeleton::StaticGraph "StaticGraph" concept

 //     template<class Graph> void checkCompileStaticGraph(Graph &G) 

 //     {

 //       typedef typename Graph::Node Node;

 //       typedef typename Graph::NodeIt NodeIt;

 //       typedef typename Graph::Edge Edge;

 //       typedef typename Graph::EdgeIt EdgeIt;

 //       typedef typename Graph::InEdgeIt InEdgeIt;

 //       typedef typename Graph::OutEdgeIt OutEdgeIt;

 //       {

 // 	Node i; Node j(i); Node k(INVALID);

 // 	i=j;

 // 	bool b; b=true;

 // 	b=(i==INVALID); b=(i!=INVALID);

 // 	b=(i==j); b=(i!=j); b=(i<j);

 //       }

 //       {

 // 	NodeIt i; NodeIt j(i); NodeIt k(INVALID); NodeIt l(G);

 // 	i=j;

 // 	j=G.first(i);

 // 	j=++i;

 // 	bool b; b=true;

 // 	b=(i==INVALID); b=(i!=INVALID);

 // 	Node n(i);

 // 	n=i;

 // 	b=(i==j); b=(i!=j); b=(i<j);

 // 	//Node ->NodeIt conversion

 // 	NodeIt ni(G,n);

 //       }

 //       {

 // 	Edge i; Edge j(i); Edge k(INVALID);

 // 	i=j;

 // 	bool b; b=true;

 // 	b=(i==INVALID); b=(i!=INVALID);

 // 	b=(i==j); b=(i!=j); b=(i<j);

 //       }

 //       {

 // 	EdgeIt i; EdgeIt j(i); EdgeIt k(INVALID); EdgeIt l(G);

 // 	i=j;

 // 	j=G.first(i);

 // 	j=++i;

 // 	bool b; b=true;

 // 	b=(i==INVALID); b=(i!=INVALID);

 // 	Edge e(i);

 // 	e=i;

 // 	b=(i==j); b=(i!=j); b=(i<j);

 // 	//Edge ->EdgeIt conversion

 // 	EdgeIt ei(G,e);

 //       }

 //       {

 // 	Node n;

 // 	InEdgeIt i; InEdgeIt j(i); InEdgeIt k(INVALID); InEdgeIt l(G,n);

 // 	i=j;

 // 	j=G.first(i,n);

 // 	j=++i;

 // 	bool b; b=true;

 // 	b=(i==INVALID); b=(i!=INVALID);

 // 	Edge e(i);

 // 	e=i;

 // 	b=(i==j); b=(i!=j); b=(i<j);

 // 	//Edge ->InEdgeIt conversion

 // 	InEdgeIt ei(G,e);

 //       }

 //       {

 // 	Node n;

 // 	OutEdgeIt i; OutEdgeIt j(i); OutEdgeIt k(INVALID); OutEdgeIt l(G,n);

 // 	i=j;

 // 	j=G.first(i,n);

 // 	j=++i;

 // 	bool b; b=true;

 // 	b=(i==INVALID); b=(i!=INVALID);

 // 	Edge e(i);

 // 	e=i;

 // 	b=(i==j); b=(i!=j); b=(i<j);

 // 	//Edge ->OutEdgeIt conversion

 // 	OutEdgeIt ei(G,e);

 //       }

 //       {

 // 	Node n,m;

 // 	n=m=INVALID;

 // 	Edge e;

 // 	e=INVALID;

 // 	n=G.tail(e);

 // 	n=G.head(e);

 //       }

 //       // id tests

 //       { Node n; int i=G.id(n); i=i; }

 //       { Edge e; int i=G.id(e); i=i; }

 //       //NodeMap tests

 //       {

 // 	Node k;

 // 	typename Graph::template NodeMap<int> m(G);

 // 	//Const map

 // 	typename Graph::template NodeMap<int> const &cm = m;

 // 	//Inicialize with default value

 // 	typename Graph::template NodeMap<int> mdef(G,12);

 // 	//Copy

 // 	typename Graph::template NodeMap<int> mm(cm);

 // 	//Copy from another type

 // 	typename Graph::template NodeMap<double> dm(cm);

 // 	//Copy to more complex type

 // 	typename Graph::template NodeMap<DummyType> em(cm);

 // 	int v;

 // 	v=m[k]; m[k]=v; m.set(k,v);

 // 	v=cm[k];

 // 	m=cm;  

 // 	dm=cm; //Copy from another type  

 // 	em=cm; //Copy to more complex type

 // 	{

 // 	  //Check the typedef's

 // 	  typename Graph::template NodeMap<int>::ValueType val;

 // 	  val=1;

 // 	  typename Graph::template NodeMap<int>::KeyType key;

 // 	  key = typename Graph::NodeIt(G);

 // 	}

 //       }  

 //       { //bool NodeMap

 // 	Node k;

 // 	typename Graph::template NodeMap<bool> m(G);

 // 	typename Graph::template NodeMap<bool> const &cm = m;  //Const map

 // 	//Inicialize with default value

 // 	typename Graph::template NodeMap<bool> mdef(G,12);

 // 	typename Graph::template NodeMap<bool> mm(cm);   //Copy

 // 	typename Graph::template NodeMap<int> dm(cm); //Copy from another type

 // 	bool v;

 // 	v=m[k]; m[k]=v; m.set(k,v);

 // 	v=cm[k];

 // 	m=cm;  

 // 	dm=cm; //Copy from another type

 // 	m=dm; //Copy to another type

 // 	{

 // 	  //Check the typedef's

 // 	  typename Graph::template NodeMap<bool>::ValueType val;

 // 	  val=true;

 // 	  typename Graph::template NodeMap<bool>::KeyType key;

 // 	  key= typename Graph::NodeIt(G);

 // 	}

 //       }

 //       //EdgeMap tests

 //       {

 // 	Edge k;

 // 	typename Graph::template EdgeMap<int> m(G);

 // 	typename Graph::template EdgeMap<int> const &cm = m;  //Const map

 // 	//Inicialize with default value

 // 	typename Graph::template EdgeMap<int> mdef(G,12);

 // 	typename Graph::template EdgeMap<int> mm(cm);   //Copy

 // 	typename Graph::template EdgeMap<double> dm(cm);//Copy from another type

 // 	int v;

 // 	v=m[k]; m[k]=v; m.set(k,v);

 // 	v=cm[k];

 // 	m=cm;  

 // 	dm=cm; //Copy from another type

 // 	{

 // 	  //Check the typedef's

 // 	  typename Graph::template EdgeMap<int>::ValueType val;

 // 	  val=1;

 // 	  typename Graph::template EdgeMap<int>::KeyType key;

 // 	  key= typename Graph::EdgeIt(G);

 // 	}

 //       }  

 //       { //bool EdgeMap

 // 	Edge k;

 // 	typename Graph::template EdgeMap<bool> m(G);

 // 	typename Graph::template EdgeMap<bool> const &cm = m;  //Const map

 // 	//Inicialize with default value

 // 	typename Graph::template EdgeMap<bool> mdef(G,12);

 // 	typename Graph::template EdgeMap<bool> mm(cm);   //Copy

 // 	typename Graph::template EdgeMap<int> dm(cm); //Copy from another type

 // 	bool v;

 // 	v=m[k]; m[k]=v; m.set(k,v);

 // 	v=cm[k];

 // 	m=cm;  

 // 	dm=cm; //Copy from another type

 // 	m=dm; //Copy to another type

 // 	{

 // 	  //Check the typedef's

 // 	  typename Graph::template EdgeMap<bool>::ValueType val;

 // 	  val=true;

 // 	  typename Graph::template EdgeMap<bool>::KeyType key;

 // 	  key= typename Graph::EdgeIt(G);

 // 	}

 //       }

 //     }

 //     /// An empty non-static graph class.

 //     /// This class provides everything that \ref StaticGraph

 //     /// with additional functionality which enables to build a

 //     /// graph from scratch.

 //     class ExtendableGraph : public StaticGraph

 //     {

 //     public:

 //       /// Defalult constructor.

 //       /// Defalult constructor.

 //       ///

 //       ExtendableGraph() { }

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

 //       /// \return the new node.

 //       ///

 //       Node addNode() { return INVALID; }

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

 //       ///Add a new edge to the graph with tail node \c t

 //       ///and head node \c h.

 //       ///\return the new edge.

 //       Edge addEdge(Node h, Node t) { return INVALID; }

 //       /// Resets the graph.

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

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

 //       /// \todo It might belong to \ref ErasableGraph.

 //       void clear() { }

 //     };

 //     ///\brief Checks whether \c G meets the

 //     ///\ref lemon::skeleton::ExtendableGraph "ExtendableGraph" concept

 //     template<class Graph> void checkCompileExtendableGraph(Graph &G) 

 //     {

 //       checkCompileStaticGraph(G);

 //       typedef typename Graph::Node Node;

 //       typedef typename Graph::NodeIt NodeIt;

 //       typedef typename Graph::Edge Edge;

 //       typedef typename Graph::EdgeIt EdgeIt;

 //       typedef typename Graph::InEdgeIt InEdgeIt;

 //       typedef typename Graph::OutEdgeIt OutEdgeIt;

 //       Node n,m;

 //       n=G.addNode();

 //       m=G.addNode();

 //       Edge e;

 //       e=G.addEdge(n,m); 

 //       //  G.clear();

 //     }

 //     /// An empty erasable graph class.

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

 //     /// possible to erase edges or nodes.

 //     class ErasableGraph : public ExtendableGraph

 //     {

 //     public:

 //       /// Defalult constructor.

 //       /// Defalult constructor.

 //       ///

 //       ErasableGraph() { }

 //       /// Deletes a node.

 //       /// Deletes node \c n node.

 //       ///

 //       void erase(Node n) { }

 //       /// Deletes an edge.

 //       /// Deletes edge \c e edge.

 //       ///

 //       void erase(Edge e) { }

 //     };

 //     template<class Graph> void checkCompileGraphEraseEdge(Graph &G) 

 //     {

 //       typename Graph::Edge e;

 //       G.erase(e);

 //     }

 //     template<class Graph> void checkCompileGraphEraseNode(Graph &G) 

 //     {

 //       typename Graph::Node n;

 //       G.erase(n);

 //     }

 //     ///\brief Checks whether \c G meets the

 //     ///\ref lemon::skeleton::EresableGraph "EresableGraph" concept

 //     template<class Graph> void checkCompileErasableGraph(Graph &G) 

 //     {

 //       checkCompileExtendableGraph(G);

 //       checkCompileGraphEraseNode(G);

 //       checkCompileGraphEraseEdge(G);

 //     }

 //     ///Checks whether a graph has findEdge() member function.

 //     ///\todo findEdge() might be a global function.

 //     ///

 //     template<class Graph> void checkCompileGraphFindEdge(Graph &G) 

 //     {

 //       typedef typename Graph::NodeIt Node;

 //       typedef typename Graph::NodeIt NodeIt;

 //       G.findEdge(NodeIt(G),++NodeIt(G),G.findEdge(NodeIt(G),++NodeIt(G)));

 //       G.findEdge(Node(),Node(),G.findEdge(Node(),Node()));  

 //     }

     /************* New GraphBase stuff **************/

     /// \bug The nodes and edges are not allowed to inherit from the

     /// same baseclass.

     class BaseGraphItem {

       /// Defalult constructor.

       BaseGraphItem() {}

       BaseGraphItem(Invalid) {}

       /// Defalult constructor.

       ///

       // We explicitely list these:

       StaticGraph() { }

       BaseGraphItem(BaseGraphItem const&) {}

       ///Copy consructor.

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

 //       ///\todo It is not clear, what we expect from a copy constructor.

       bool operator==(BaseGraphItem) const { return false; }

 //       ///E.g. How to assign the nodes/edges to each other? What about maps?

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

 //       StaticGraph(const StaticGraph& g) { }

       // Technical requirement. Do we really need this?

       /// The base type of node iterators, 

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

       /// 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.

     /// A minimal GraphBase concept

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

       /// from the trivial node iterator.

     /// This class describes a minimal concept which can be extended to a

       class Node {

     /// full-featured graph with \ref GraphFactory.

       public:

     class GraphBase {

 	/// Default constructor

     public:

 	/// @warning The default constructor sets the iterator

       GraphBase() {}

 	/// to an undefined value.

 	Node() { }

 	/// Copy constructor.

       /// \bug Nodes and Edges are comparable each other

 	/// Copy constructor.

       class Node : public BaseGraphItem {};

 	///

       class Edge : public BaseGraphItem {};

 	Node(const Node&) { }

       // Graph operation

 	/// Invalid constructor \& conversion.

       void firstNode(Node &n) const { }

       void firstEdge(Edge &e) const { }

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

 	/// \sa Invalid for more details.

       void firstOutEdge(Edge &e, Node) const { }

 	Node(Invalid) { }

       void firstInEdge(Edge &e, Node) const { }

 	/// Equality operator

       void nextNode(Node &n) const { }

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

       void nextEdge(Edge &e) const { }

 	/// same object or both are invalid.

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

       // Question: isn't it reasonable if this methods have a Node

 	/// Inequality operator

       // parameter? Like this:

       // Edge& nextOut(Edge &e, Node) const { return e; }

       void nextOutEdge(Edge &e) const { }

       void nextInEdge(Edge &e) const { }

       Node head(Edge) const { return Node(); }

       Node tail(Edge) const { return Node(); }

       // Do we need id, nodeNum, edgeNum and co. in this basic graphbase

       // concept?

       // Maps.

       //

       // We need a special slimer concept which does not provide maps (it

       // wouldn't be strictly slimer, cause for map-factory id() & friends

       // a required...)

       template<typename T>

       class NodeMap : public GraphMap<Node, T, GraphBase> {};

       template<typename T>

       class EdgeMap : public GraphMap<Edge, T, GraphBase> {};

     };

     /**************** Concept checking classes ****************/

     template<typename BGI>

     struct BaseGraphItemConcept {

       void constraints() {

 	BGI i1;

 	BGI i2 = i1;

 	BGI i3 = INVALID;

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

 	i1 = i3;

 	///

 	if( i1 == i3 ) {

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

 	  if ( i2 != i3 && i3 < i2 )

 	    return;

  	///Comparison operator.

 	///This is a strict ordering between the nodes.

 	///

 	///This ordering can be different from the order in which NodeIt

 	///goes through the nodes.

 	///\todo Possibly we don't need it.

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

       };

       /// 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&) { }

 	/// 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 StaticGraph& g) { }

 	/// Node -> NodeIt conversion.

 	/// Sets the iterator to the node of \c g pointed by the trivial 

 	/// iterator n.

 	/// This feature necessitates that each time we 

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

 	NodeIt(const StaticGraph& g, const Node& n) { }

 	/// Next node.

 	/// Assign the iterator to the next node.

 	///

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

       };

       /// The base type of the edge iterators.

       /// The base type of the edge iterators.

       ///

       class Edge {

       public:

 	/// Default constructor

 	/// @warning The default constructor sets the iterator

 	/// to an undefined value.

 	Edge() { }

 	/// Copy constructor.

 	/// Copy constructor.

 	///

 	Edge(const Edge&) { }

 	/// Initialize the iterator to be invalid.

 	/// Initialize the iterator to be invalid.

 	///

 	Edge(Invalid) { }

 	/// Equality operator

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

 	/// same object or both are invalid.

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

 	/// Inequality operator

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

 	///

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

  	///Comparison operator.

 	///This is a strict ordering between the nodes.

 	///

 	///This ordering can be different from the order in which NodeIt

 	///goes through the nodes.

 	///\todo Possibly we don't need it.

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

       };

       /// 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.

       /// 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&) { }

 	/// Initialize the iterator to be invalid.

 	/// Initialize the iterator to be invalid.

 	///

 	OutEdgeIt(Invalid) { }

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

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

 	/// node

 	///@param n the node

 	///@param g the graph

 	OutEdgeIt(const StaticGraph& g, const Node& n) { }

 	/// Edge -> OutEdgeIt 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.

 	OutEdgeIt(const StaticGraph& g, const Edge& e) { }

 	///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 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&) { }

 	/// 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

 	/// node

 	///@param n the node

 	///@param g the graph

 	InEdgeIt(const StaticGraph& g, const Node& n) { }

 	/// 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 StaticGraph& g, const Edge& n) { }

 	/// Next incoming edge

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

 	///

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

       };

       /// This iterator goes through each edge.

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

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

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

       /// \code

       /// int count=0;

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

       /// \endcode

       class EdgeIt : public Edge {

       public:

 	/// Default constructor

 	/// @warning The default constructor sets the iterator

 	/// to an undefined value.

 	EdgeIt() { }

 	/// Copy constructor.

 	/// Copy constructor.

 	///

 	EdgeIt(const EdgeIt&) { }

 	/// Initialize the iterator to be invalid.

 	/// Initialize the iterator to be invalid.

 	///

 	EdgeIt(Invalid) { }

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

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

 	/// node

 	///@param g the graph

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

     	///Next edge

 	/// Assign the iterator to the next 

 	/// edge of the corresponding node.

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

       };

       /// First node of the graph.

       /// \retval i the first node.

       /// \return the first node.

       ///

       NodeIt& first(NodeIt& i) const { return i; }

       /// The first incoming edge.

       /// The first incoming edge.

       ///

       InEdgeIt& first(InEdgeIt &i, Node) const { return i; }

       /// The first outgoing edge.

       /// The first outgoing edge.

       ///

       OutEdgeIt& first(OutEdgeIt& i, Node) const { return i; }

       /// The first edge of the Graph.

       /// The first edge of the Graph.

       ///

       EdgeIt& first(EdgeIt& i) const { return i; }

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

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

       ///

       Node head(Edge) const { return INVALID; }

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

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

       ///

       Node tail(Edge) const { return INVALID; }

       ///Gives back the \e id of a node.

       ///\warning Not all graph structures provide this feature.

       ///

       ///\todo Should each graph provide \c id?

       int id(const Node&) const { return 0; }

       ///Gives back the \e id of an edge.

       ///\warning Not all graph structures provide this feature.

       ///

       ///\todo Should each graph provide \c id?

       int id(const Edge&) const { return 0; }

       ///\e

       ///\todo Should it be in the concept?

       ///

       int nodeNum() const { return 0; }

       ///\e

       ///\todo Should it be in the concept?

       ///

       int edgeNum() const { return 0; }

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

       /// \ingroup skeletons