/* -*- C++ -*-

 * src/lemon/skeletons/graph.h - Part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Combinatorial Optimization Research Group, 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.

 *

 */

#ifndef LEMON_SKELETON_GRAPH_H

#define LEMON_SKELETON_GRAPH_H

///\ingroup skeletons

///\file

///\brief Declaration of Graph.

#include <lemon/invalid.h>

#include <lemon/skeletons/maps.h>

#include <lemon/concept_check.h>

#include <lemon/skeletons/graph_component.h>

namespace lemon {

  namespace skeleton {

    /// \addtogroup skeletons

    /// @{

//     /// An empty static graph class.

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

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

//     /// behind the interface.

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

//     /// run properly, of course.

//     ///

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

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

//     /// 

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

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

//     /// like @ref ListGraph or

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

//     ///

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

//     /// be nice.

//     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 {

    public:

      BaseGraphItem() {}

      BaseGraphItem(Invalid) {}

      // We explicitely list these:

      BaseGraphItem(BaseGraphItem const&) {}

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

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

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

      // Technical requirement. Do we really need this?

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

    };

    /// A minimal GraphBase concept

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

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

    class GraphBase {

    public:

      GraphBase() {}

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

      class Node : public BaseGraphItem {};

      class Edge : public BaseGraphItem {};

      // Graph operation

      void firstNode(Node &n) const { }

      void firstEdge(Edge &e) const { }

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

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

      void nextNode(Node &n) const { }

      void nextEdge(Edge &e) const { }

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

      // 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;

	i1 = i3;

	if( i1 == i3 ) {

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

	    return;

	}

      }

    };

    class StaticGraph 

      :  virtual public BaseGraphComponent, public IterableGraphComponent, public MappableGraphComponent {

    public:

      typedef BaseGraphComponent::Node Node;

      typedef BaseGraphComponent::Edge Edge;

    };

    template <typename Graph>

    struct StaticGraphConcept {

      void constraints() {

	function_requires<BaseGraphComponentConcept<Graph> >();

	function_requires<IterableGraphComponentConcept<Graph> >();

	function_requires<MappableGraphComponentConcept<Graph> >();

      }

      Graph& graph;

    };

    class ExtendableGraph 

      :  virtual public BaseGraphComponent, public StaticGraph, public ExtendableGraphComponent, public ClearableGraphComponent {

    public:

      typedef BaseGraphComponent::Node Node;

      typedef BaseGraphComponent::Edge Edge;

    };

    template <typename Graph>

    struct ExtendableGraphConcept {

      void constraints() {

	function_requires<StaticGraphConcept<Graph> >();

	function_requires<ExtendableGraphComponentConcept<Graph> >();

	function_requires<ClearableGraphComponentConcept<Graph> >();

      }

      Graph& graph;

    };

    class ErasableGraph 

      :  virtual public BaseGraphComponent, public ExtendableGraph, public ErasableGraphComponent {

    public:

      typedef BaseGraphComponent::Node Node;

      typedef BaseGraphComponent::Edge Edge;

    };

    template <typename Graph>

    struct ErasableGraphConcept {

      void constraints() {

	function_requires<ExtendableGraphConcept<Graph> >();

	function_requires<ErasableGraphComponentConcept<Graph> >();

      }

      Graph& graph;

    };

    // @}

  } //namespace skeleton  

} //namespace lemon

#endif // LEMON_SKELETON_GRAPH_H