diff -r cd72eae05bdf -r 3c00344f49c9 lemon/concepts/bpgraph.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/concepts/bpgraph.h	Wed Oct 17 19:14:07 2018 +0200
@@ -0,0 +1,1029 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2013
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+///\ingroup graph_concepts
+///\file
+///\brief The concept of undirected graphs.
+
+#ifndef LEMON_CONCEPTS_BPGRAPH_H
+#define LEMON_CONCEPTS_BPGRAPH_H
+
+#include <lemon/concepts/graph_components.h>
+#include <lemon/concepts/maps.h>
+#include <lemon/concept_check.h>
+#include <lemon/core.h>
+
+namespace lemon {
+  namespace concepts {
+
+    /// \ingroup graph_concepts
+    ///
+    /// \brief Class describing the concept of undirected bipartite graphs.
+    ///
+    /// This class describes the common interface of all undirected
+    /// bipartite graphs.
+    ///
+    /// Like all concept classes, it only provides an interface
+    /// without any sensible implementation. So any general algorithm for
+    /// undirected bipartite graphs should compile with this class,
+    /// but it will not run properly, of course.
+    /// An actual graph implementation like \ref ListBpGraph or
+    /// \ref SmartBpGraph may have additional functionality.
+    ///
+    /// The bipartite graphs also fulfill the concept of \ref Graph
+    /// "undirected graphs". Bipartite graphs provide a bipartition of
+    /// the node set, namely a red and blue set of the nodes. The
+    /// nodes can be iterated with the RedNodeIt and BlueNodeIt in the
+    /// two node sets. With RedNodeMap and BlueNodeMap values can be
+    /// assigned to the nodes in the two sets.
+    ///
+    /// The edges of the graph cannot connect two nodes of the same
+    /// set. The edges inherent orientation is from the red nodes to
+    /// the blue nodes.
+    ///
+    /// \sa Graph
+    class BpGraph {
+    private:
+      /// BpGraphs are \e not copy constructible. Use bpGraphCopy instead.
+      BpGraph(const BpGraph&) {}
+      /// \brief Assignment of a graph to another one is \e not allowed.
+      /// Use bpGraphCopy instead.
+      void operator=(const BpGraph&) {}
+
+    public:
+      /// Default constructor.
+      BpGraph() {}
+
+      /// \brief Undirected graphs should be tagged with \c UndirectedTag.
+      ///
+      /// Undirected graphs should be tagged with \c UndirectedTag.
+      ///
+      /// This tag helps the \c enable_if technics to make compile time
+      /// specializations for undirected graphs.
+      typedef True UndirectedTag;
+
+      /// The node type of the graph
+
+      /// This class identifies a node of the graph. It also serves
+      /// as a base class of the node iterators,
+      /// thus they convert to this type.
+      class Node {
+      public:
+        /// Default constructor
+
+        /// Default constructor.
+        /// \warning It sets the object to an undefined value.
+        Node() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        Node(const Node&) { }
+
+        /// %Invalid constructor \& conversion.
+
+        /// Initializes the object to be invalid.
+        /// \sa Invalid for more details.
+        Node(Invalid) { }
+        /// Equality operator
+
+        /// Equality operator.
+        ///
+        /// Two iterators are equal if and only if they point to the
+        /// same object or both are \c INVALID.
+        bool operator==(Node) const { return true; }
+
+        /// Inequality operator
+
+        /// Inequality operator.
+        bool operator!=(Node) const { return true; }
+
+        /// Artificial ordering operator.
+
+        /// Artificial ordering operator.
+        ///
+        /// \note This operator only has to define some strict ordering of
+        /// the items; this order has nothing to do with the iteration
+        /// ordering of the items.
+        bool operator<(Node) const { return false; }
+
+      };
+
+      /// Class to represent red nodes.
+
+      /// This class represents the red nodes of the graph. It does
+      /// not supposed to be used directly, because the nodes can be
+      /// represented as Node instances. This class can be used as
+      /// template parameter for special map classes.
+      class RedNode : public Node {
+      public:
+        /// Default constructor
+
+        /// Default constructor.
+        /// \warning It sets the object to an undefined value.
+        RedNode() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        RedNode(const RedNode&) : Node() { }
+
+        /// %Invalid constructor \& conversion.
+
+        /// Initializes the object to be invalid.
+        /// \sa Invalid for more details.
+        RedNode(Invalid) { }
+
+      };
+
+      /// Class to represent blue nodes.
+
+      /// This class represents the blue nodes of the graph. It does
+      /// not supposed to be used directly, because the nodes can be
+      /// represented as Node instances. This class can be used as
+      /// template parameter for special map classes.
+      class BlueNode : public Node {
+      public:
+        /// Default constructor
+
+        /// Default constructor.
+        /// \warning It sets the object to an undefined value.
+        BlueNode() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        BlueNode(const BlueNode&) : Node() { }
+
+        /// %Invalid constructor \& conversion.
+
+        /// Initializes the object to be invalid.
+        /// \sa Invalid for more details.
+        BlueNode(Invalid) { }
+
+      };
+
+      /// Iterator class for the red nodes.
+
+      /// This iterator goes through each red node of the graph.
+      /// Its usage is quite simple, for example, you can count the number
+      /// of red nodes in a graph \c g of type \c %BpGraph like this:
+      ///\code
+      /// int count=0;
+      /// for (BpGraph::RedNodeIt n(g); n!=INVALID; ++n) ++count;
+      ///\endcode
+      class RedNodeIt : public RedNode {
+      public:
+        /// Default constructor
+
+        /// Default constructor.
+        /// \warning It sets the iterator to an undefined value.
+        RedNodeIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        RedNodeIt(const RedNodeIt& n) : RedNode(n) { }
+        /// %Invalid constructor \& conversion.
+
+        /// Initializes the iterator to be invalid.
+        /// \sa Invalid for more details.
+        RedNodeIt(Invalid) { }
+        /// Sets the iterator to the first red node.
+
+        /// Sets the iterator to the first red node of the given
+        /// digraph.
+        explicit RedNodeIt(const BpGraph&) { }
+        /// Sets the iterator to the given red node.
+
+        /// Sets the iterator to the given red node of the given
+        /// digraph.
+        RedNodeIt(const BpGraph&, const RedNode&) { }
+        /// Next node.
+
+        /// Assign the iterator to the next red node.
+        ///
+        RedNodeIt& operator++() { return *this; }
+      };
+
+      /// Iterator class for the blue nodes.
+
+      /// This iterator goes through each blue node of the graph.
+      /// Its usage is quite simple, for example, you can count the number
+      /// of blue nodes in a graph \c g of type \c %BpGraph like this:
+      ///\code
+      /// int count=0;
+      /// for (BpGraph::BlueNodeIt n(g); n!=INVALID; ++n) ++count;
+      ///\endcode
+      class BlueNodeIt : public BlueNode {
+      public:
+        /// Default constructor
+
+        /// Default constructor.
+        /// \warning It sets the iterator to an undefined value.
+        BlueNodeIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        BlueNodeIt(const BlueNodeIt& n) : BlueNode(n) { }
+        /// %Invalid constructor \& conversion.
+
+        /// Initializes the iterator to be invalid.
+        /// \sa Invalid for more details.
+        BlueNodeIt(Invalid) { }
+        /// Sets the iterator to the first blue node.
+
+        /// Sets the iterator to the first blue node of the given
+        /// digraph.
+        explicit BlueNodeIt(const BpGraph&) { }
+        /// Sets the iterator to the given blue node.
+
+        /// Sets the iterator to the given blue node of the given
+        /// digraph.
+        BlueNodeIt(const BpGraph&, const BlueNode&) { }
+        /// Next node.
+
+        /// Assign the iterator to the next blue node.
+        ///
+        BlueNodeIt& operator++() { return *this; }
+      };
+
+      /// Iterator class for the nodes.
+
+      /// This iterator goes through each node of the graph.
+      /// Its usage is quite simple, for example, you can count the number
+      /// of nodes in a graph \c g of type \c %BpGraph like this:
+      ///\code
+      /// int count=0;
+      /// for (BpGraph::NodeIt n(g); n!=INVALID; ++n) ++count;
+      ///\endcode
+      class NodeIt : public Node {
+      public:
+        /// Default constructor
+
+        /// Default constructor.
+        /// \warning It sets the iterator to an undefined value.
+        NodeIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        NodeIt(const NodeIt& n) : Node(n) { }
+        /// %Invalid constructor \& conversion.
+
+        /// Initializes 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 the given digraph.
+        ///
+        explicit NodeIt(const BpGraph&) { }
+        /// Sets the iterator to the given node.
+
+        /// Sets the iterator to the given node of the given digraph.
+        ///
+        NodeIt(const BpGraph&, const Node&) { }
+        /// Next node.
+
+        /// Assign the iterator to the next node.
+        ///
+        NodeIt& operator++() { return *this; }
+      };
+
+
+      /// The edge type of the graph
+
+      /// This class identifies an edge of the graph. It also serves
+      /// as a base class of the edge iterators,
+      /// thus they will convert to this type.
+      class Edge {
+      public:
+        /// Default constructor
+
+        /// Default constructor.
+        /// \warning It sets the object to an undefined value.
+        Edge() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        Edge(const Edge&) { }
+        /// %Invalid constructor \& conversion.
+
+        /// Initializes the object to be invalid.
+        /// \sa Invalid for more details.
+        Edge(Invalid) { }
+        /// Equality operator
+
+        /// Equality operator.
+        ///
+        /// Two iterators are equal if and only if they point to the
+        /// same object or both are \c INVALID.
+        bool operator==(Edge) const { return true; }
+        /// Inequality operator
+
+        /// Inequality operator.
+        bool operator!=(Edge) const { return true; }
+
+        /// Artificial ordering operator.
+
+        /// Artificial ordering operator.
+        ///
+        /// \note This operator only has to define some strict ordering of
+        /// the edges; this order has nothing to do with the iteration
+        /// ordering of the edges.
+        bool operator<(Edge) const { return false; }
+      };
+
+      /// Iterator class for the edges.
+
+      /// This iterator goes through each edge of the graph.
+      /// Its usage is quite simple, for example, you can count the number
+      /// of edges in a graph \c g of type \c %BpGraph as follows:
+      ///\code
+      /// int count=0;
+      /// for(BpGraph::EdgeIt e(g); e!=INVALID; ++e) ++count;
+      ///\endcode
+      class EdgeIt : public Edge {
+      public:
+        /// Default constructor
+
+        /// Default constructor.
+        /// \warning It sets the iterator to an undefined value.
+        EdgeIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        EdgeIt(const EdgeIt& e) : Edge(e) { }
+        /// %Invalid constructor \& conversion.
+
+        /// Initializes the iterator to be invalid.
+        /// \sa Invalid for more details.
+        EdgeIt(Invalid) { }
+        /// Sets the iterator to the first edge.
+
+        /// Sets the iterator to the first edge of the given graph.
+        ///
+        explicit EdgeIt(const BpGraph&) { }
+        /// Sets the iterator to the given edge.
+
+        /// Sets the iterator to the given edge of the given graph.
+        ///
+        EdgeIt(const BpGraph&, const Edge&) { }
+        /// Next edge
+
+        /// Assign the iterator to the next edge.
+        ///
+        EdgeIt& operator++() { return *this; }
+      };
+
+      /// Iterator class for the incident 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. the number of incident edges) of a node \c n
+      /// in a graph \c g of type \c %BpGraph as follows.
+      ///
+      ///\code
+      /// int count=0;
+      /// for(BpGraph::IncEdgeIt e(g, n); e!=INVALID; ++e) ++count;
+      ///\endcode
+      ///
+      /// \warning Loop edges will be iterated twice.
+      class IncEdgeIt : public Edge {
+      public:
+        /// Default constructor
+
+        /// Default constructor.
+        /// \warning It sets the iterator to an undefined value.
+        IncEdgeIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        IncEdgeIt(const IncEdgeIt& e) : Edge(e) { }
+        /// %Invalid constructor \& conversion.
+
+        /// Initializes the iterator to be invalid.
+        /// \sa Invalid for more details.
+        IncEdgeIt(Invalid) { }
+        /// Sets the iterator to the first incident edge.
+
+        /// Sets the iterator to the first incident edge of the given node.
+        ///
+        IncEdgeIt(const BpGraph&, const Node&) { }
+        /// Sets the iterator to the given edge.
+
+        /// Sets the iterator to the given edge of the given graph.
+        ///
+        IncEdgeIt(const BpGraph&, const Edge&) { }
+        /// Next incident edge
+
+        /// Assign the iterator to the next incident edge
+        /// of the corresponding node.
+        IncEdgeIt& operator++() { return *this; }
+      };
+
+      /// The arc type of the graph
+
+      /// This class identifies a directed arc of the graph. It also serves
+      /// as a base class of the arc iterators,
+      /// thus they will convert to this type.
+      class Arc {
+      public:
+        /// Default constructor
+
+        /// Default constructor.
+        /// \warning It sets the object to an undefined value.
+        Arc() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        Arc(const Arc&) { }
+        /// %Invalid constructor \& conversion.
+
+        /// Initializes the object to be invalid.
+        /// \sa Invalid for more details.
+        Arc(Invalid) { }
+        /// Equality operator
+
+        /// Equality operator.
+        ///
+        /// Two iterators are equal if and only if they point to the
+        /// same object or both are \c INVALID.
+        bool operator==(Arc) const { return true; }
+        /// Inequality operator
+
+        /// Inequality operator.
+        bool operator!=(Arc) const { return true; }
+
+        /// Artificial ordering operator.
+
+        /// Artificial ordering operator.
+        ///
+        /// \note This operator only has to define some strict ordering of
+        /// the arcs; this order has nothing to do with the iteration
+        /// ordering of the arcs.
+        bool operator<(Arc) const { return false; }
+
+        /// Converison to \c Edge
+
+        /// Converison to \c Edge.
+        ///
+        operator Edge() const { return Edge(); }
+      };
+
+      /// Iterator class for the arcs.
+
+      /// This iterator goes through each directed arc of the graph.
+      /// Its usage is quite simple, for example, you can count the number
+      /// of arcs in a graph \c g of type \c %BpGraph as follows:
+      ///\code
+      /// int count=0;
+      /// for(BpGraph::ArcIt a(g); a!=INVALID; ++a) ++count;
+      ///\endcode
+      class ArcIt : public Arc {
+      public:
+        /// Default constructor
+
+        /// Default constructor.
+        /// \warning It sets the iterator to an undefined value.
+        ArcIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        ArcIt(const ArcIt& e) : Arc(e) { }
+        /// %Invalid constructor \& conversion.
+
+        /// Initializes the iterator to be invalid.
+        /// \sa Invalid for more details.
+        ArcIt(Invalid) { }
+        /// Sets the iterator to the first arc.
+
+        /// Sets the iterator to the first arc of the given graph.
+        ///
+        explicit ArcIt(const BpGraph &g)
+        {
+          ::lemon::ignore_unused_variable_warning(g);
+        }
+        /// Sets the iterator to the given arc.
+
+        /// Sets the iterator to the given arc of the given graph.
+        ///
+        ArcIt(const BpGraph&, const Arc&) { }
+        /// Next arc
+
+        /// Assign the iterator to the next arc.
+        ///
+        ArcIt& operator++() { return *this; }
+      };
+
+      /// Iterator class for the outgoing arcs of a node.
+
+      /// This iterator goes trough the \e outgoing directed arcs of a
+      /// certain node of a graph.
+      /// Its usage is quite simple, for example, you can count the number
+      /// of outgoing arcs of a node \c n
+      /// in a graph \c g of type \c %BpGraph as follows.
+      ///\code
+      /// int count=0;
+      /// for (Digraph::OutArcIt a(g, n); a!=INVALID; ++a) ++count;
+      ///\endcode
+      class OutArcIt : public Arc {
+      public:
+        /// Default constructor
+
+        /// Default constructor.
+        /// \warning It sets the iterator to an undefined value.
+        OutArcIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        OutArcIt(const OutArcIt& e) : Arc(e) { }
+        /// %Invalid constructor \& conversion.
+
+        /// Initializes the iterator to be invalid.
+        /// \sa Invalid for more details.
+        OutArcIt(Invalid) { }
+        /// Sets the iterator to the first outgoing arc.
+
+        /// Sets the iterator to the first outgoing arc of the given node.
+        ///
+        OutArcIt(const BpGraph& n, const Node& g) {
+          ::lemon::ignore_unused_variable_warning(n);
+          ::lemon::ignore_unused_variable_warning(g);
+        }
+        /// Sets the iterator to the given arc.
+
+        /// Sets the iterator to the given arc of the given graph.
+        ///
+        OutArcIt(const BpGraph&, const Arc&) { }
+        /// Next outgoing arc
+
+        /// Assign the iterator to the next
+        /// outgoing arc of the corresponding node.
+        OutArcIt& operator++() { return *this; }
+      };
+
+      /// Iterator class for the incoming arcs of a node.
+
+      /// This iterator goes trough the \e incoming directed arcs of a
+      /// certain node of a graph.
+      /// Its usage is quite simple, for example, you can count the number
+      /// of incoming arcs of a node \c n
+      /// in a graph \c g of type \c %BpGraph as follows.
+      ///\code
+      /// int count=0;
+      /// for (Digraph::InArcIt a(g, n); a!=INVALID; ++a) ++count;
+      ///\endcode
+      class InArcIt : public Arc {
+      public:
+        /// Default constructor
+
+        /// Default constructor.
+        /// \warning It sets the iterator to an undefined value.
+        InArcIt() { }
+        /// Copy constructor.
+
+        /// Copy constructor.
+        ///
+        InArcIt(const InArcIt& e) : Arc(e) { }
+        /// %Invalid constructor \& conversion.
+
+        /// Initializes the iterator to be invalid.
+        /// \sa Invalid for more details.
+        InArcIt(Invalid) { }
+        /// Sets the iterator to the first incoming arc.
+
+        /// Sets the iterator to the first incoming arc of the given node.
+        ///
+        InArcIt(const BpGraph& g, const Node& n) {
+          ::lemon::ignore_unused_variable_warning(n);
+          ::lemon::ignore_unused_variable_warning(g);
+        }
+        /// Sets the iterator to the given arc.
+
+        /// Sets the iterator to the given arc of the given graph.
+        ///
+        InArcIt(const BpGraph&, const Arc&) { }
+        /// Next incoming arc
+
+        /// Assign the iterator to the next
+        /// incoming arc of the corresponding node.
+        InArcIt& operator++() { return *this; }
+      };
+
+      /// \brief Standard graph map type for the nodes.
+      ///
+      /// Standard graph map type for the nodes.
+      /// It conforms to the ReferenceMap concept.
+      template<class T>
+      class NodeMap : public ReferenceMap<Node, T, T&, const T&>
+      {
+      public:
+
+        /// Constructor
+        explicit NodeMap(const BpGraph&) { }
+        /// Constructor with given initial value
+        NodeMap(const BpGraph&, T) { }
+
+      private:
+        ///Copy constructor
+        NodeMap(const NodeMap& nm) :
+          ReferenceMap<Node, T, T&, const T&>(nm) { }
+        ///Assignment operator
+        template <typename CMap>
+        NodeMap& operator=(const CMap&) {
+          checkConcept<ReadMap<Node, T>, CMap>();
+          return *this;
+        }
+      };
+
+      /// \brief Standard graph map type for the red nodes.
+      ///
+      /// Standard graph map type for the red nodes.
+      /// It conforms to the ReferenceMap concept.
+      template<class T>
+      class RedNodeMap : public ReferenceMap<Node, T, T&, const T&>
+      {
+      public:
+
+        /// Constructor
+        explicit RedNodeMap(const BpGraph&) { }
+        /// Constructor with given initial value
+        RedNodeMap(const BpGraph&, T) { }
+
+      private:
+        ///Copy constructor
+        RedNodeMap(const RedNodeMap& nm) :
+          ReferenceMap<Node, T, T&, const T&>(nm) { }
+        ///Assignment operator
+        template <typename CMap>
+        RedNodeMap& operator=(const CMap&) {
+          checkConcept<ReadMap<Node, T>, CMap>();
+          return *this;
+        }
+      };
+
+      /// \brief Standard graph map type for the blue nodes.
+      ///
+      /// Standard graph map type for the blue nodes.
+      /// It conforms to the ReferenceMap concept.
+      template<class T>
+      class BlueNodeMap : public ReferenceMap<Node, T, T&, const T&>
+      {
+      public:
+
+        /// Constructor
+        explicit BlueNodeMap(const BpGraph&) { }
+        /// Constructor with given initial value
+        BlueNodeMap(const BpGraph&, T) { }
+
+      private:
+        ///Copy constructor
+        BlueNodeMap(const BlueNodeMap& nm) :
+          ReferenceMap<Node, T, T&, const T&>(nm) { }
+        ///Assignment operator
+        template <typename CMap>
+        BlueNodeMap& operator=(const CMap&) {
+          checkConcept<ReadMap<Node, T>, CMap>();
+          return *this;
+        }
+      };
+
+      /// \brief Standard graph map type for the arcs.
+      ///
+      /// Standard graph map type for the arcs.
+      /// It conforms to the ReferenceMap concept.
+      template<class T>
+      class ArcMap : public ReferenceMap<Arc, T, T&, const T&>
+      {
+      public:
+
+        /// Constructor
+        explicit ArcMap(const BpGraph&) { }
+        /// Constructor with given initial value
+        ArcMap(const BpGraph&, T) { }
+
+      private:
+        ///Copy constructor
+        ArcMap(const ArcMap& em) :
+          ReferenceMap<Arc, T, T&, const T&>(em) { }
+        ///Assignment operator
+        template <typename CMap>
+        ArcMap& operator=(const CMap&) {
+          checkConcept<ReadMap<Arc, T>, CMap>();
+          return *this;
+        }
+      };
+
+      /// \brief Standard graph map type for the edges.
+      ///
+      /// Standard graph map type for the edges.
+      /// It conforms to the ReferenceMap concept.
+      template<class T>
+      class EdgeMap : public ReferenceMap<Edge, T, T&, const T&>
+      {
+      public:
+
+        /// Constructor
+        explicit EdgeMap(const BpGraph&) { }
+        /// Constructor with given initial value
+        EdgeMap(const BpGraph&, T) { }
+
+      private:
+        ///Copy constructor
+        EdgeMap(const EdgeMap& em) :
+          ReferenceMap<Edge, T, T&, const T&>(em) {}
+        ///Assignment operator
+        template <typename CMap>
+        EdgeMap& operator=(const CMap&) {
+          checkConcept<ReadMap<Edge, T>, CMap>();
+          return *this;
+        }
+      };
+
+      /// \brief Gives back %true for red nodes.
+      ///
+      /// Gives back %true for red nodes.
+      bool red(const Node&) const { return true; }
+
+      /// \brief Gives back %true for blue nodes.
+      ///
+      /// Gives back %true for blue nodes.
+      bool blue(const Node&) const { return true; }
+
+      /// \brief Converts the node to red node object.
+      ///
+      /// This function converts unsafely the node to red node
+      /// object. It should be called only if the node is from the red
+      /// partition or INVALID.
+      RedNode asRedNodeUnsafe(const Node&) const { return RedNode(); }
+
+      /// \brief Converts the node to blue node object.
+      ///
+      /// This function converts unsafely the node to blue node
+      /// object. It should be called only if the node is from the red
+      /// partition or INVALID.
+      BlueNode asBlueNodeUnsafe(const Node&) const { return BlueNode(); }
+
+      /// \brief Converts the node to red node object.
+      ///
+      /// This function converts safely the node to red node
+      /// object. If the node is not from the red partition, then it
+      /// returns INVALID.
+      RedNode asRedNode(const Node&) const { return RedNode(); }
+
+      /// \brief Converts the node to blue node object.
+      ///
+      /// This function converts unsafely the node to blue node
+      /// object. If the node is not from the blue partition, then it
+      /// returns INVALID.
+      BlueNode asBlueNode(const Node&) const { return BlueNode(); }
+
+      /// \brief Gives back the red end node of the edge.
+      ///
+      /// Gives back the red end node of the edge.
+      RedNode redNode(const Edge&) const { return RedNode(); }
+
+      /// \brief Gives back the blue end node of the edge.
+      ///
+      /// Gives back the blue end node of the edge.
+      BlueNode blueNode(const Edge&) const { return BlueNode(); }
+
+      /// \brief The first node of the edge.
+      ///
+      /// It is a synonim for the \c redNode().
+      Node u(Edge) const { return INVALID; }
+
+      /// \brief The second node of the edge.
+      ///
+      /// It is a synonim for the \c blueNode().
+      Node v(Edge) const { return INVALID; }
+
+      /// \brief The source node of the arc.
+      ///
+      /// Returns the source node of the given arc.
+      Node source(Arc) const { return INVALID; }
+
+      /// \brief The target node of the arc.
+      ///
+      /// Returns the target node of the given arc.
+      Node target(Arc) const { return INVALID; }
+
+      /// \brief The ID of the node.
+      ///
+      /// Returns the ID of the given node.
+      int id(Node) const { return -1; }
+
+      /// \brief The red ID of the node.
+      ///
+      /// Returns the red ID of the given node.
+      int id(RedNode) const { return -1; }
+
+      /// \brief The blue ID of the node.
+      ///
+      /// Returns the blue ID of the given node.
+      int id(BlueNode) const { return -1; }
+
+      /// \brief The ID of the edge.
+      ///
+      /// Returns the ID of the given edge.
+      int id(Edge) const { return -1; }
+
+      /// \brief The ID of the arc.
+      ///
+      /// Returns the ID of the given arc.
+      int id(Arc) const { return -1; }
+
+      /// \brief The node with the given ID.
+      ///
+      /// Returns the node with the given ID.
+      /// \pre The argument should be a valid node ID in the graph.
+      Node nodeFromId(int) const { return INVALID; }
+
+      /// \brief The edge with the given ID.
+      ///
+      /// Returns the edge with the given ID.
+      /// \pre The argument should be a valid edge ID in the graph.
+      Edge edgeFromId(int) const { return INVALID; }
+
+      /// \brief The arc with the given ID.
+      ///
+      /// Returns the arc with the given ID.
+      /// \pre The argument should be a valid arc ID in the graph.
+      Arc arcFromId(int) const { return INVALID; }
+
+      /// \brief An upper bound on the node IDs.
+      ///
+      /// Returns an upper bound on the node IDs.
+      int maxNodeId() const { return -1; }
+
+      /// \brief An upper bound on the red IDs.
+      ///
+      /// Returns an upper bound on the red IDs.
+      int maxRedId() const { return -1; }
+
+      /// \brief An upper bound on the blue IDs.
+      ///
+      /// Returns an upper bound on the blue IDs.
+      int maxBlueId() const { return -1; }
+
+      /// \brief An upper bound on the edge IDs.
+      ///
+      /// Returns an upper bound on the edge IDs.
+      int maxEdgeId() const { return -1; }
+
+      /// \brief An upper bound on the arc IDs.
+      ///
+      /// Returns an upper bound on the arc IDs.
+      int maxArcId() const { return -1; }
+
+      /// \brief The direction of the arc.
+      ///
+      /// Returns \c true if the given arc goes from a red node to a blue node.
+      bool direction(Arc) const { return true; }
+
+      /// \brief Direct the edge.
+      ///
+      /// Direct the given edge. The returned arc
+      /// represents the given edge and its direction comes
+      /// from the bool parameter. If it is \c true, then the source of the node
+      /// will be a red node.
+      Arc direct(Edge, bool) const {
+        return INVALID;
+      }
+
+      /// \brief Direct the edge.
+      ///
+      /// Direct the given edge. The returned arc represents the given
+      /// edge and its source node is the given node.
+      Arc direct(Edge, Node) const {
+        return INVALID;
+      }
+
+      /// \brief The oppositely directed arc.
+      ///
+      /// Returns the oppositely directed arc representing the same edge.
+      Arc oppositeArc(Arc) const { return INVALID; }
+
+      /// \brief The opposite node on the edge.
+      ///
+      /// Returns the opposite node on the given edge.
+      Node oppositeNode(Node, Edge) const { return INVALID; }
+
+      void first(Node&) const {}
+      void next(Node&) const {}
+
+      void firstRed(RedNode&) const {}
+      void nextRed(RedNode&) const {}
+
+      void firstBlue(BlueNode&) const {}
+      void nextBlue(BlueNode&) const {}
+
+      void first(Edge&) const {}
+      void next(Edge&) const {}
+
+      void first(Arc&) const {}
+      void next(Arc&) const {}
+
+      void firstOut(Arc&, Node) const {}
+      void nextOut(Arc&) const {}
+
+      void firstIn(Arc&, Node) const {}
+      void nextIn(Arc&) const {}
+
+      void firstInc(Edge &, bool &, const Node &) const {}
+      void nextInc(Edge &, bool &) const {}
+
+      // The second parameter is dummy.
+      Node fromId(int, Node) const { return INVALID; }
+      // The second parameter is dummy.
+      Edge fromId(int, Edge) const { return INVALID; }
+      // The second parameter is dummy.
+      Arc fromId(int, Arc) const { return INVALID; }
+
+      // Dummy parameter.
+      int maxId(Node) const { return -1; }
+      // Dummy parameter.
+      int maxId(RedNode) const { return -1; }
+      // Dummy parameter.
+      int maxId(BlueNode) const { return -1; }
+      // Dummy parameter.
+      int maxId(Edge) const { return -1; }
+      // Dummy parameter.
+      int maxId(Arc) const { return -1; }
+
+      /// \brief The base node of the iterator.
+      ///
+      /// Returns the base node of the given incident edge iterator.
+      Node baseNode(IncEdgeIt) const { return INVALID; }
+
+      /// \brief The running node of the iterator.
+      ///
+      /// Returns the running node of the given incident edge iterator.
+      Node runningNode(IncEdgeIt) const { return INVALID; }
+
+      /// \brief The base node of the iterator.
+      ///
+      /// Returns the base node of the given outgoing arc iterator
+      /// (i.e. the source node of the corresponding arc).
+      Node baseNode(OutArcIt) const { return INVALID; }
+
+      /// \brief The running node of the iterator.
+      ///
+      /// Returns the running node of the given outgoing arc iterator
+      /// (i.e. the target node of the corresponding arc).
+      Node runningNode(OutArcIt) const { return INVALID; }
+
+      /// \brief The base node of the iterator.
+      ///
+      /// Returns the base node of the given incoming arc iterator
+      /// (i.e. the target node of the corresponding arc).
+      Node baseNode(InArcIt) const { return INVALID; }
+
+      /// \brief The running node of the iterator.
+      ///
+      /// Returns the running node of the given incoming arc iterator
+      /// (i.e. the source node of the corresponding arc).
+      Node runningNode(InArcIt) const { return INVALID; }
+
+      template <typename _BpGraph>
+      struct Constraints {
+        void constraints() {
+          checkConcept<BaseBpGraphComponent, _BpGraph>();
+          checkConcept<IterableBpGraphComponent<>, _BpGraph>();
+          checkConcept<IDableBpGraphComponent<>, _BpGraph>();
+          checkConcept<MappableBpGraphComponent<>, _BpGraph>();
+        }
+      };
+
+    };
+
+  }
+
+}
+
+#endif