source: lemon-0.x/src/lemon/concept/graph.h @ 959:c80ef5912903

/* -*- C++ -*-
 * src/lemon/concept/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_CONCEPT_GRAPH_H
#define LEMON_CONCEPT_GRAPH_H

///\ingroup concept
///\file
///\brief Declaration of Graph.

#include <lemon/invalid.h>
#include <lemon/concept/maps.h>
#include <lemon/concept_check.h>
#include <lemon/concept/graph_component.h>

namespace lemon {
  namespace concept {
    
    /// \addtogroup concept
    /// @{

//     /// 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 concept
//       ///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 concept
//       ///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::concept::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::concept::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::concept::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 concept  
} //namespace lemon



#endif // LEMON_CONCEPT_GRAPH_H