LEMON/LEMON-main Changeset - r579:d11bf7998905

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Changeset - r579:d11bf7998905

« 573:37216c

580:2313ed »

r579:d11bf7998905

Tue, 14 Apr 2009 10:33:17

[Not Reviewed]

0 comments (0 inline)

kpeter (Peter Kovacs)
kpeter@inf.elte.hu

Various improvements and fixes (mainly in the doc) (#190)

0 2 0

default

2 files changed with 441 insertions and 429 deletions:

lemon/adaptors.h

lemon/concepts/graph_components.h

438

429

↑ Collapse diff ↑

lemon/adaptors.h

Show inline comments

@@ -2099,192 +2099,195 @@
 		        } else {
 		          return _backward[a];
+		        }
+		      }
 		    protected:
 		      MapImpl _forward, _backward;
 		    };
 		  public:
 		    template <typename V>
 		    class NodeMap : public DGR::template NodeMap<V> {
 		    public:
 		      typedef V Value;
 		      typedef typename DGR::template NodeMap<Value> Parent;
 		      explicit NodeMap(const UndirectorBase<DGR>& adaptor)
 		        : Parent(*adaptor._digraph) {}
 		      NodeMap(const UndirectorBase<DGR>& adaptor, const V& value)
 		        : Parent(*adaptor._digraph, value) { }
 		    private:
 		      NodeMap& operator=(const NodeMap& cmap) {
 		        return operator=<NodeMap>(cmap);
+		      }
 		      template <typename CMap>
 		      NodeMap& operator=(const CMap& cmap) {
 		        Parent::operator=(cmap);
 		        return *this;
+		      }
 		    };
 		    template <typename V>
 		    class ArcMap
 		      : public SubMapExtender<UndirectorBase<DGR>, ArcMapBase<V> >
+		    {
 		    public:
 		      typedef V Value;
 		      typedef SubMapExtender<Adaptor, ArcMapBase<V> > Parent;
 		      explicit ArcMap(const UndirectorBase<DGR>& adaptor)
 		        : Parent(adaptor) {}
 		      ArcMap(const UndirectorBase<DGR>& adaptor, const V& value)
 		        : Parent(adaptor, value) {}
 		    private:
 		      ArcMap& operator=(const ArcMap& cmap) {
 		        return operator=<ArcMap>(cmap);
+		      }
 		      template <typename CMap>
 		      ArcMap& operator=(const CMap& cmap) {
 		        Parent::operator=(cmap);
 		        return *this;
+		      }
 		    };
 		    template <typename V>
 		    class EdgeMap : public Digraph::template ArcMap<V> {
 		    public:
 		      typedef V Value;
 		      typedef typename Digraph::template ArcMap<V> Parent;
 		      explicit EdgeMap(const UndirectorBase<DGR>& adaptor)
 		        : Parent(*adaptor._digraph) {}
 		      EdgeMap(const UndirectorBase<DGR>& adaptor, const V& value)
 		        : Parent(*adaptor._digraph, value) {}
 		    private:
 		      EdgeMap& operator=(const EdgeMap& cmap) {
 		        return operator=<EdgeMap>(cmap);
+		      }
 		      template <typename CMap>
 		      EdgeMap& operator=(const CMap& cmap) {
 		        Parent::operator=(cmap);
 		        return *this;
+		      }
 		    };
 		    typedef typename ItemSetTraits<DGR, Node>::ItemNotifier NodeNotifier;
 		    NodeNotifier& notifier(Node) const { return _digraph->notifier(Node()); }
 		    typedef typename ItemSetTraits<DGR, Edge>::ItemNotifier EdgeNotifier;
 		    EdgeNotifier& notifier(Edge) const { return _digraph->notifier(Edge()); }
 		    typedef EdgeNotifier ArcNotifier;
 		    ArcNotifier& notifier(Arc) const { return _digraph->notifier(Edge()); }
 		  protected:
 		    UndirectorBase() : _digraph(0) {}
 		    DGR* _digraph;
 		    void initialize(DGR& digraph) {
 		      _digraph = &digraph;
+		    }
 		  };
 		  /// \ingroup graph_adaptors
 		  ///
 		  /// \brief Adaptor class for viewing a digraph as an undirected graph.
 		  ///
 		  /// Undirector adaptor can be used for viewing a digraph as an undirected
 		  /// graph. All arcs of the underlying digraph are showed in the
 		  /// adaptor as an edge (and also as a pair of arcs, of course).
 		  /// This adaptor conforms to the \ref concepts::Graph "Graph" concept.
 		  ///
 		  /// The adapted digraph can also be modified through this adaptor
 		  /// by adding or removing nodes or edges, unless the \c GR template
 		  /// parameter is set to be \c const.
 		  ///
 		  /// \tparam DGR The type of the adapted digraph.
 		  /// It must conform to the \ref concepts::Digraph "Digraph" concept.
 		  /// It can also be specified to be \c const.
 		  ///
 		  /// \note The \c Node type of this adaptor and the adapted digraph are
 		  /// convertible to each other, moreover the \c Edge type of the adaptor
 		  /// and the \c Arc type of the adapted digraph are also convertible to
 		  /// each other.
 		  /// (Thus the \c Arc type of the adaptor is convertible to the \c Arc type
 		  /// of the adapted digraph.)
 		  template<typename DGR>
 		#ifdef DOXYGEN
 		  class Undirector {
 		#else
 		  class Undirector :
 		    public GraphAdaptorExtender<UndirectorBase<DGR> > {
 		#endif
 		  public:
 		    /// The type of the adapted digraph.
 		    typedef DGR Digraph;
 		    typedef GraphAdaptorExtender<UndirectorBase<DGR> > Parent;
 		  protected:
 		    Undirector() { }
 		  public:
 		    /// \brief Constructor
 		    ///
 		    /// Creates an undirected graph from the given digraph.
 		    Undirector(DGR& digraph) {
 		      initialize(digraph);
+		    }
 		    /// \brief Arc map combined from two original arc maps
 		    ///
 		    /// This map adaptor class adapts two arc maps of the underlying
 		    /// digraph to get an arc map of the undirected graph.
 		    /// Its value type is inherited from the first arc map type (\c FW).
 		    /// \tparam FW The type of the "foward" arc map.
 		    /// \tparam BK The type of the "backward" arc map.
 		    template <typename FW, typename BK>
 		    class CombinedArcMap {
 		    public:
 		      /// The key type of the map
 		      typedef typename Parent::Arc Key;
 		      /// The value type of the map
 		      typedef typename FW::Value Value;
 		      typedef typename MapTraits<FW>::ReferenceMapTag ReferenceMapTag;
 		      typedef typename MapTraits<FW>::ReturnValue ReturnValue;
 		      typedef typename MapTraits<FW>::ConstReturnValue ConstReturnValue;
 		      typedef typename MapTraits<FW>::ReturnValue Reference;
 		      typedef typename MapTraits<FW>::ConstReturnValue ConstReference;
 		      /// Constructor
 		      CombinedArcMap(FW& forward, BK& backward)
 		        : _forward(&forward), _backward(&backward) {}
 		      /// Sets the value associated with the given key.
 		      void set(const Key& e, const Value& a) {
 		        if (Parent::direction(e)) {
 		          _forward->set(e, a);
 		        } else {
 		          _backward->set(e, a);
+		        }
+		      }
 		      /// Returns the value associated with the given key.
 		      ConstReturnValue operator[](const Key& e) const {

lemon/concepts/graph_components.h

Show inline comments

 		/* -*- mode: C++; indent-tabs-mode: nil; -*-
+		 *
 		 * This file is a part of LEMON, a generic C++ optimization library.
+		 *
 		 * Copyright (C) 2003-2009
 		 * 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 graph components.
 		#ifndef LEMON_CONCEPTS_GRAPH_COMPONENTS_H
 		#define LEMON_CONCEPTS_GRAPH_COMPONENTS_H
 		#include <lemon/core.h>
 		#include <lemon/concepts/maps.h>
 		#include <lemon/bits/alteration_notifier.h>
 		namespace lemon {
 		  namespace concepts {
-		    /// \brief Skeleton class for graph Node and Arc types
+		    /// \brief Concept class for \c Node, \c Arc and \c Edge types.
 		    ///
 		    /// This class describes the interface of Node and Arc (and Edge
 		    /// in undirected graphs) subtypes of graph types.
 		    /// This class describes the concept of \c Node, \c Arc and \c Edge
 		    /// subtypes of digraph and graph types.
 		    ///
 		    /// \note This class is a template class so that we can use it to
 		    /// create graph skeleton classes. The reason for this is than Node
 		    /// and Arc types should \em not derive from the same base class.
 		    /// For Node you should instantiate it with character 'n' and for Arc
 		    /// with 'a'.
+		    /// create graph skeleton classes. The reason for this is that \c Node
 		    /// and \c Arc (or \c Edge) types should \e not derive from the same
 		    /// base class. For \c Node you should instantiate it with character
 		    /// \c 'n', for \c Arc with \c 'a' and for \c Edge with \c 'e'.
 		#ifndef DOXYGEN
 		    template <char sel = '0'>
 		#endif
 		    class GraphItem {
 		    public:
 		      /// \brief Default constructor.
 		      ///
 		      /// Default constructor.
 		      /// \warning The default constructor is not required to set
 		      /// the item to some well-defined value. So you should consider it
 		      /// as uninitialized.
 		      GraphItem() {}
 		      /// \brief Copy constructor.
 		      ///
 		      /// Copy constructor.
 		      GraphItem(const GraphItem &) {}
 		      /// \brief Constructor for conversion from \c INVALID.
 		      ///
 		      GraphItem(const GraphItem &) {}
 		      /// \brief Invalid constructor \& conversion.
 		      ///
 		      /// This constructor initializes the item to be invalid.
 		      /// Constructor for conversion from \c INVALID.
 		      /// It initializes the item to be invalid.
 		      /// \sa Invalid for more details.
 		      GraphItem(Invalid) {}
-		      /// \brief Assign operator for nodes.
 		      /// \brief Assignment operator.
 		      ///
 		      /// The nodes are assignable.
 		      ///
-		      GraphItem& operator=(GraphItem const&) { return *this; }
+		      /// Assignment operator for the item.
 		      GraphItem& operator=(const GraphItem&) { return *this; }
 		      /// \brief Equality operator.
 		      ///
 		      /// Two iterators are equal if and only if they represents the
 		      /// same node in the graph or both are invalid.
-		      bool operator==(GraphItem) const { return false; }
+		      /// Equality operator.
 		      bool operator==(const GraphItem&) const { return false; }
 		      /// \brief Inequality operator.
 		      ///
-		      /// \sa operator==(const Node& n)
+		      /// Inequality operator.
 		      bool operator!=(const GraphItem&) const { return false; }
 		      /// \brief Ordering operator.
 		      ///
 		      bool operator!=(GraphItem) const { return false; }
 		      /// \brief Artificial ordering operator.
 		      ///
 		      /// To allow the use of graph descriptors as key type in std::map or
 		      /// similar associative container we require this.
 		      /// This operator defines an ordering of the items.
 		      /// It makes possible to use graph item types as key types in
 		      /// associative containers (e.g. \c std::map).
 		      ///
 		      /// \note This operator only have to define some strict ordering of
 		      /// the items; this order has nothing to do with the iteration
 		      /// ordering of the items.
 		      bool operator<(GraphItem) const { return false; }
+		      bool operator<(const GraphItem&) const { return false; }
 		      template<typename _GraphItem>
 		      struct Constraints {
 		        void constraints() {
 		          _GraphItem i1;
 		          _GraphItem i2 = i1;
 		          _GraphItem i3 = INVALID;
 		          i1 = i2 = i3;
 		          bool b;
 		          //          b = (ia == ib) && (ia != ib) && (ia < ib);
 		          b = (ia == ib) && (ia != ib);
 		          b = (ia == INVALID) && (ib != INVALID);
 		          b = (ia < ib);
+		        }
 		        const _GraphItem &ia;
 		        const _GraphItem &ib;
 		      };
 		    };
-		    /// \brief An empty base directed graph class.
+		    /// \brief Base skeleton class for directed graphs.
 		    ///
 		    /// This class provides the minimal set of features needed for a
 		    /// directed graph structure. All digraph concepts have to
 		    /// conform to this base directed graph. It just provides types
 		    /// for nodes and arcs and functions to get the source and the
-		    /// target of the arcs.
+		    /// This class describes the base interface of directed graph types.
 		    /// All digraph %concepts have to conform to this class.
 		    /// It just provides types for nodes and arcs and functions
 		    /// to get the source and the target nodes of arcs.
 		    class BaseDigraphComponent {
 		    public:
 		      typedef BaseDigraphComponent Digraph;
 		      /// \brief Node class of the digraph.
 		      ///
 		      /// This class represents the Nodes of the digraph.
 		      ///
 		      /// This class represents the nodes of the digraph.
 		      typedef GraphItem<'n'> Node;
 		      /// \brief Arc class of the digraph.
 		      ///
-		      /// This class represents the Arcs of the digraph.
+		      /// This class represents the arcs of the digraph.
 		      typedef GraphItem<'a'> Arc;
 		      /// \brief Return the source node of an arc.
 		      ///
-		      typedef GraphItem<'e'> Arc;
+		      /// This function returns the source node of an arc.
 		      Node source(const Arc&) const { return INVALID; }
-		      /// \brief Gives back the target node of an arc.
+		      /// \brief Return the target node of an arc.
 		      ///
-		      /// Gives back the target node of an arc.
+		      /// This function returns the target node of an arc.
 		      Node target(const Arc&) const { return INVALID; }
 		      /// \brief Return the opposite node on the given arc.
 		      ///
 		      Node target(const Arc&) const { return INVALID;}
 		      /// \brief Gives back the source node of an arc.
 		      ///
 		      /// Gives back the source node of an arc.
 		      ///
 		      Node source(const Arc&) const { return INVALID;}
 		      /// \brief Gives back the opposite node on the given arc.
 		      ///
-		      /// Gives back the opposite node on the given arc.
+		      /// This function returns the opposite node on the given arc.
 		      Node oppositeNode(const Node&, const Arc&) const {
 		        return INVALID;
+		      }
 		      template <typename _Digraph>
 		      struct Constraints {
 		        typedef typename _Digraph::Node Node;
 		        typedef typename _Digraph::Arc Arc;
 		        void constraints() {
 		          checkConcept<GraphItem<'n'>, Node>();
 		          checkConcept<GraphItem<'a'>, Arc>();
+		          {
 		            Node n;
 		            Arc e(INVALID);
 		            n = digraph.source(e);
 		            n = digraph.target(e);
 		            n = digraph.oppositeNode(n, e);
+		          }
+		        }
 		        const _Digraph& digraph;
 		      };
 		    };
-		    /// \brief An empty base undirected graph class.
+		    /// \brief Base skeleton class for undirected graphs.
 		    ///
 		    /// This class provides the minimal set of features needed for an
 		    /// undirected graph structure. All undirected graph concepts have
 		    /// to conform to this base graph. It just provides types for
 		    /// nodes, arcs and edges and functions to get the
 		    /// source and the target of the arcs and edges,
 		    /// conversion from arcs to edges and function to get
-		    /// both direction of the edges.
+		    /// This class describes the base interface of undirected graph types.
 		    /// All graph %concepts have to conform to this class.
 		    /// It extends the interface of \ref BaseDigraphComponent with an
 		    /// \c Edge type and functions to get the end nodes of edges,
 		    /// to convert from arcs to edges and to get both direction of edges.
 		    class BaseGraphComponent : public BaseDigraphComponent {
 		    public:
 		      typedef BaseDigraphComponent::Node Node;
 		      typedef BaseDigraphComponent::Arc Arc;
-		      /// \brief Undirected arc class of the graph.
 		      /// \brief Undirected edge class of the graph.
 		      ///
 		      /// This class represents the edges of the graph.
 		      /// The undirected graphs can be used as a directed graph which
 		      /// for each arc contains the opposite arc too so the graph is
 		      /// bidirected. The edge represents two opposite
 		      /// directed arcs.
 		      class Edge : public GraphItem<'u'> {
 		      /// This class represents the undirected edges of the graph.
 		      /// Undirected graphs can be used as directed graphs, each edge is
 		      /// represented by two opposite directed arcs.
 		      class Edge : public GraphItem<'e'> {
 		      public:
-		        typedef GraphItem<'u'> Parent;
+		        typedef GraphItem<'e'> Parent;
 		        /// \brief Default constructor.
 		        ///
 		        /// Default constructor.
 		        /// \warning The default constructor is not required to set
 		        /// the item to some well-defined value. So you should consider it
 		        /// as uninitialized.
 		        Edge() {}
 		        /// \brief Copy constructor.
 		        ///
 		        /// Copy constructor.
 		        Edge(const Edge &) : Parent() {}
 		        /// \brief Constructor for conversion from \c INVALID.
 		        ///
 		        Edge(const Edge &) : Parent() {}
 		        /// \brief Invalid constructor \& conversion.
 		        ///
 		        /// This constructor initializes the item to be invalid.
 		        /// Constructor for conversion from \c INVALID.
 		        /// It initializes the item to be invalid.
 		        /// \sa Invalid for more details.
 		        Edge(Invalid) {}
-		        /// \brief Converter from arc to edge.
 		        /// \brief Constructor for conversion from an arc.
 		        ///
 		        /// Constructor for conversion from an arc.
 		        /// Besides the core graph item functionality each arc should
 		        /// be convertible to the represented edge.
 		        Edge(const Arc&) {}
-		        /// \brief Assign arc to edge.
 		        /// \brief Assign an arc to an edge.
 		        ///
 		        /// This function assigns an arc to an edge.
 		        /// Besides the core graph item functionality each arc should
 		        /// be convertible to the represented edge.
 		        Edge& operator=(const Arc&) { return *this; }
 		      };
-		      /// \brief Returns the direction of the arc.
+		      /// \brief Return one end node of an edge.
 		      ///
 		      /// This function returns one end node of an edge.
 		      Node u(const Edge&) const { return INVALID; }
 		      /// \brief Return the other end node of an edge.
 		      ///
 		      /// This function returns the other end node of an edge.
 		      Node v(const Edge&) const { return INVALID; }
 		      /// \brief Return a directed arc related to an edge.
 		      ///
 		      /// This function returns a directed arc from its direction and the
 		      /// represented edge.
 		      Arc direct(const Edge&, bool) const { return INVALID; }
 		      /// \brief Return a directed arc related to an edge.
 		      ///
 		      /// This function returns a directed arc from its source node and the
 		      /// represented edge.
 		      Arc direct(const Edge&, const Node&) const { return INVALID; }
 		      /// \brief Return the direction of the arc.
 		      ///
 		      /// Returns the direction of the arc. Each arc represents an
 		      /// edge with a direction. It gives back the
 		      /// direction.
 		      bool direction(const Arc&) const { return true; }
-		      /// \brief Returns the directed arc.
+		      /// \brief Return the opposite arc.
 		      ///
 		      /// Returns the directed arc from its direction and the
 		      /// represented edge.
 		      Arc direct(const Edge&, bool) const { return INVALID;}
 		      /// \brief Returns the directed arc.
 		      ///
 		      /// Returns the directed arc from its source and the
 		      /// represented edge.
 		      Arc direct(const Edge&, const Node&) const { return INVALID;}
 		      /// \brief Returns the opposite arc.
 		      ///
 		      /// Returns the opposite arc. It is the arc representing the
 		      /// same edge and has opposite direction.
 		      Arc oppositeArc(const Arc&) const { return INVALID;}
 		      /// \brief Gives back one ending of an edge.
 		      ///
 		      /// Gives back one ending of an edge.
 		      Node u(const Edge&) const { return INVALID;}
 		      /// \brief Gives back the other ending of an edge.
 		      ///
 		      /// Gives back the other ending of an edge.
-		      Node v(const Edge&) const { return INVALID;}
+		      /// This function returns the opposite arc, i.e. the arc representing
 		      /// the same edge and has opposite direction.
 		      Arc oppositeArc(const Arc&) const { return INVALID; }
 		      template <typename _Graph>
 		      struct Constraints {
 		        typedef typename _Graph::Node Node;
 		        typedef typename _Graph::Arc Arc;
 		        typedef typename _Graph::Edge Edge;
 		        void constraints() {
 		          checkConcept<BaseDigraphComponent, _Graph>();
-		          checkConcept<GraphItem<'u'>, Edge>();
+		          checkConcept<GraphItem<'e'>, Edge>();
+		          {
 		            Node n;
 		            Edge ue(INVALID);
 		            Arc e;
 		            n = graph.u(ue);
 		            n = graph.v(ue);
 		            e = graph.direct(ue, true);
 		            e = graph.direct(ue, false);
 		            e = graph.direct(ue, n);
 		            e = graph.oppositeArc(e);
 		            ue = e;
 		            bool d = graph.direction(e);
 		            ignore_unused_variable_warning(d);
+		          }
+		        }
 		        const _Graph& graph;
 		      };
 		    };
-		    /// \brief An empty idable base digraph class.
+		    /// \brief Skeleton class for \e idable directed graphs.
 		    ///
 		    /// This class provides beside the core digraph features
 		    /// core id functions for the digraph structure.
 		    /// The most of the base digraphs should conform to this concept.
 		    /// The id's are unique and immutable.
 		    /// This class describes the interface of \e idable directed graphs.
 		    /// It extends \ref BaseDigraphComponent with the core ID functions.
 		    /// The ids of the items must be unique and immutable.
 		    /// This concept is part of the Digraph concept.
 		    template <typename BAS = BaseDigraphComponent>
 		    class IDableDigraphComponent : public BAS {
 		    public:
 		      typedef BAS Base;
 		      typedef typename Base::Node Node;
 		      typedef typename Base::Arc Arc;
-		      /// \brief Gives back an unique integer id for the Node.
+		      /// \brief Return a unique integer id for the given node.
 		      ///
-		      /// Gives back an unique integer id for the Node.
+		      /// This function returns a unique integer id for the given node.
 		      int id(const Node&) const { return -1; }
 		      /// \brief Return the node by its unique id.
 		      ///
-		      int id(const Node&) const { return -1;}
+		      /// This function returns the node by its unique id.
 		      /// If the digraph does not contain a node with the given id,
 		      /// then the result of the function is undefined.
 		      Node nodeFromId(int) const { return INVALID; }
-		      /// \brief Gives back the node by the unique id.
+		      /// \brief Return a unique integer id for the given arc.
 		      ///
 		      /// Gives back the node by the unique id.
 		      /// If the digraph does not contain node with the given id
 		      /// then the result of the function is undetermined.
 		      Node nodeFromId(int) const { return INVALID;}
 		      /// This function returns a unique integer id for the given arc.
 		      int id(const Arc&) const { return -1; }
-		      /// \brief Gives back an unique integer id for the Arc.
+		      /// \brief Return the arc by its unique id.
 		      ///
-		      /// Gives back an unique integer id for the Arc.
+		      /// This function returns the arc by its unique id.
 		      /// If the digraph does not contain an arc with the given id,
 		      /// then the result of the function is undefined.
 		      Arc arcFromId(int) const { return INVALID; }
 		      /// \brief Return an integer greater or equal to the maximum
 		      /// node id.
 		      ///
-		      int id(const Arc&) const { return -1;}
+		      /// This function returns an integer greater or equal to the
 		      /// maximum node id.
 		      int maxNodeId() const { return -1; }
-		      /// \brief Gives back the arc by the unique id.
+		      /// \brief Return an integer greater or equal to the maximum
 		      /// arc id.
 		      ///
 		      /// Gives back the arc by the unique id.
 		      /// If the digraph does not contain arc with the given id
 		      /// then the result of the function is undetermined.
 		      Arc arcFromId(int) const { return INVALID;}
 		      /// \brief Gives back an integer greater or equal to the maximum
 		      /// Node id.
 		      ///
 		      /// Gives back an integer greater or equal to the maximum Node
 		      /// id.
 		      int maxNodeId() const { return -1;}
 		      /// \brief Gives back an integer greater or equal to the maximum
 		      /// Arc id.
 		      ///
 		      /// Gives back an integer greater or equal to the maximum Arc
 		      /// id.
 		      int maxArcId() const { return -1;}
 		      /// This function returns an integer greater or equal to the
 		      /// maximum arc id.
 		      int maxArcId() const { return -1; }
 		      template <typename _Digraph>
 		      struct Constraints {
 		        void constraints() {
 		          checkConcept<Base, _Digraph >();
 		          typename _Digraph::Node node;
 		          int nid = digraph.id(node);
 		          nid = digraph.id(node);
 		          node = digraph.nodeFromId(nid);
 		          typename _Digraph::Arc arc;
 		          int eid = digraph.id(arc);
 		          eid = digraph.id(arc);
 		          arc = digraph.arcFromId(eid);
 		          nid = digraph.maxNodeId();
 		          ignore_unused_variable_warning(nid);
 		          eid = digraph.maxArcId();
 		          ignore_unused_variable_warning(eid);
+		        }
 		        const _Digraph& digraph;
 		      };
 		    };
-		    /// \brief An empty idable base undirected graph class.
+		    /// \brief Skeleton class for \e idable undirected graphs.
 		    ///
 		    /// This class provides beside the core undirected graph features
 		    /// core id functions for the undirected graph structure.  The
 		    /// most of the base undirected graphs should conform to this
 		    /// concept.  The id's are unique and immutable.
 		    /// This class describes the interface of \e idable undirected
 		    /// graphs. It extends \ref IDableDigraphComponent with the core ID
 		    /// functions of undirected graphs.
 		    /// The ids of the items must be unique and immutable.
 		    /// This concept is part of the Graph concept.
 		    template <typename BAS = BaseGraphComponent>
 		    class IDableGraphComponent : public IDableDigraphComponent<BAS> {
 		    public:
 		      typedef BAS Base;
 		      typedef typename Base::Edge Edge;
 		      using IDableDigraphComponent<Base>::id;
-		      /// \brief Gives back an unique integer id for the Edge.
+		      /// \brief Return a unique integer id for the given edge.
 		      ///
-		      /// Gives back an unique integer id for the Edge.
+		      /// This function returns a unique integer id for the given edge.
 		      int id(const Edge&) const { return -1; }
 		      /// \brief Return the edge by its unique id.
 		      ///
-		      int id(const Edge&) const { return -1;}
+		      /// This function returns the edge by its unique id.
 		      /// If the graph does not contain an edge with the given id,
 		      /// then the result of the function is undefined.
 		      Edge edgeFromId(int) const { return INVALID; }
-		      /// \brief Gives back the edge by the unique id.
+		      /// \brief Return an integer greater or equal to the maximum
 		      /// edge id.
 		      ///
 		      /// Gives back the edge by the unique id.  If the
 		      /// graph does not contain arc with the given id then the
 		      /// result of the function is undetermined.
 		      Edge edgeFromId(int) const { return INVALID;}
 		      /// \brief Gives back an integer greater or equal to the maximum
 		      /// Edge id.
 		      ///
 		      /// Gives back an integer greater or equal to the maximum Edge
 		      /// id.
-		      int maxEdgeId() const { return -1;}
+		      /// This function returns an integer greater or equal to the
 		      /// maximum edge id.
 		      int maxEdgeId() const { return -1; }
 		      template <typename _Graph>
 		      struct Constraints {
 		        void constraints() {
 		          checkConcept<Base, _Graph >();
 		          checkConcept<IDableDigraphComponent<Base>, _Graph >();
 		          typename _Graph::Edge edge;
 		          int ueid = graph.id(edge);
 		          ueid = graph.id(edge);
 		          edge = graph.edgeFromId(ueid);
 		          ueid = graph.maxEdgeId();
 		          ignore_unused_variable_warning(ueid);
+		        }
 		        const _Graph& graph;
 		      };
 		    };
-		    /// \brief Skeleton class for graph NodeIt and ArcIt
+		    /// \brief Concept class for \c NodeIt, \c ArcIt and \c EdgeIt types.
 		    ///
 		    /// Skeleton class for graph NodeIt and ArcIt.
 		    ///
 		    /// This class describes the concept of \c NodeIt, \c ArcIt and
 		    /// \c EdgeIt subtypes of digraph and graph types.
 		    template <typename GR, typename Item>
 		    class GraphItemIt : public Item {
 		    public:
 		      /// \brief Default constructor.
 		      ///
 		      /// @warning The default constructor sets the iterator
 		      /// to an undefined value.
 		      /// Default constructor.
 		      /// \warning The default constructor is not required to set
 		      /// the iterator to some well-defined value. So you should consider it
 		      /// as uninitialized.
 		      GraphItemIt() {}
 		      /// \brief Copy constructor.
 		      ///
 		      /// Copy constructor.
 		      GraphItemIt(const GraphItemIt& it) : Item(it) {}
 		      /// \brief Constructor that sets the iterator to the first item.
 		      ///
 		      GraphItemIt(const GraphItemIt& ) {}
 		      /// \brief Sets the iterator to the first item.
 		      /// Constructor that sets the iterator to the first item.
 		      explicit GraphItemIt(const GR&) {}
 		      /// \brief Constructor for conversion from \c INVALID.
 		      ///
 		      /// Sets the iterator to the first item of \c the graph.
 		      ///
 		      explicit GraphItemIt(const GR&) {}
 		      /// \brief Invalid constructor \& conversion.
 		      ///
 		      /// This constructor initializes the item to be invalid.
 		      /// Constructor for conversion from \c INVALID.
 		      /// It initializes the iterator to be invalid.
 		      /// \sa Invalid for more details.
 		      GraphItemIt(Invalid) {}
-		      /// \brief Assign operator for items.
 		      /// \brief Assignment operator.
 		      ///
-		      /// The items are assignable.
+		      /// Assignment operator for the iterator.
 		      GraphItemIt& operator=(const GraphItemIt&) { return *this; }
 		      /// \brief Increment the iterator.
 		      ///
 		      GraphItemIt& operator=(const GraphItemIt&) { return *this; }
 		      /// \brief Next item.
 		      ///
 		      /// Assign the iterator to the next item.
 		      ///
+		      /// This operator increments the iterator, i.e. assigns it to the
 		      /// next item.
 		      GraphItemIt& operator++() { return *this; }
 		      /// \brief Equality operator
 		      ///
 		      /// Equality operator.
 		      /// Two iterators are equal if and only if they point to the
 		      /// same object or both are invalid.
 		      bool operator==(const GraphItemIt&) const { return true;}
 		      /// \brief Inequality operator
 		      ///
 		      /// \sa operator==(Node n)
 		      ///
 		      /// Inequality operator.
 		      /// Two iterators are equal if and only if they point to the
 		      /// same object or both are invalid.
 		      bool operator!=(const GraphItemIt&) const { return true;}
 		      template<typename _GraphItemIt>
 		      struct Constraints {
 		        void constraints() {
 		          checkConcept<GraphItem<>, _GraphItemIt>();
 		          _GraphItemIt it1(g);
 		          _GraphItemIt it2;
 		          _GraphItemIt it3 = it1;
 		          _GraphItemIt it4 = INVALID;
 		          it2 = ++it1;
 		          ++it2 = it1;
 		          ++(++it1);
 		          Item bi = it1;
 		          bi = it2;
+		        }
 		        GR& g;
+		        const GR& g;
 		      };
 		    };
-		    /// \brief Skeleton class for graph InArcIt and OutArcIt
+		    /// \brief Concept class for \c InArcIt, \c OutArcIt and
 		    /// \c IncEdgeIt types.
 		    ///
 		    /// \note Because InArcIt and OutArcIt may not inherit from the same
 		    /// base class, the \c sel is a additional template parameter (selector).
 		    /// For InArcIt you should instantiate it with character 'i' and for
 		    /// OutArcIt with 'o'.
 		    /// This class describes the concept of \c InArcIt, \c OutArcIt
 		    /// and \c IncEdgeIt subtypes of digraph and graph types.
 		    ///
 		    /// \note Since these iterator classes do not inherit from the same
 		    /// base class, there is an additional template parameter (selector)
 		    /// \c sel. For \c InArcIt you should instantiate it with character
 		    /// \c 'i', for \c OutArcIt with \c 'o' and for \c IncEdgeIt with \c 'e'.
 		    template <typename GR,
 		              typename Item = typename GR::Arc,
 		              typename Base = typename GR::Node,
 		              char sel = '0'>
 		    class GraphIncIt : public Item {
 		    public:
 		      /// \brief Default constructor.
 		      ///
 		      /// @warning The default constructor sets the iterator
 		      /// to an undefined value.
 		      /// Default constructor.
 		      /// \warning The default constructor is not required to set
 		      /// the iterator to some well-defined value. So you should consider it
 		      /// as uninitialized.
 		      GraphIncIt() {}
 		      /// \brief Copy constructor.
 		      ///
 		      /// Copy constructor.
 		      GraphIncIt(const GraphIncIt& it) : Item(it) {}
 		      /// \brief Constructor that sets the iterator to the first
 		      /// incoming or outgoing arc.
 		      ///
 		      GraphIncIt(GraphIncIt const& gi) : Item(gi) {}
 		      /// \brief Sets the iterator to the first arc incoming into or outgoing
-		      /// from the node.
+		      /// Constructor that sets the iterator to the first arc
 		      /// incoming to or outgoing from the given node.
 		      explicit GraphIncIt(const GR&, const Base&) {}
 		      /// \brief Constructor for conversion from \c INVALID.
 		      ///
 		      /// Sets the iterator to the first arc incoming into or outgoing
 		      /// from the node.
 		      ///
 		      explicit GraphIncIt(const GR&, const Base&) {}
 		      /// \brief Invalid constructor \& conversion.
 		      ///
-		      /// This constructor initializes the item to be invalid.
+		      /// Constructor for conversion from \c INVALID.
 		      /// It initializes the iterator to be invalid.
 		      /// \sa Invalid for more details.
 		      GraphIncIt(Invalid) {}
-		      /// \brief Assign operator for iterators.
 		      /// \brief Assignment operator.
 		      ///
-		      /// The iterators are assignable.
+		      /// Assignment operator for the iterator.
 		      GraphIncIt& operator=(const GraphIncIt&) { return *this; }
 		      /// \brief Increment the iterator.
 		      ///
 		      GraphIncIt& operator=(GraphIncIt const&) { return *this; }
 		      /// \brief Next item.
 		      ///
 		      /// Assign the iterator to the next item.
 		      ///
+		      /// This operator increments the iterator, i.e. assigns it to the
 		      /// next arc incoming to or outgoing from the given node.
 		      GraphIncIt& operator++() { return *this; }
 		      /// \brief Equality operator
 		      ///
 		      /// Equality operator.
 		      /// Two iterators are equal if and only if they point to the
 		      /// same object or both are invalid.
 		      bool operator==(const GraphIncIt&) const { return true;}
 		      /// \brief Inequality operator
 		      ///
 		      /// \sa operator==(Node n)
 		      ///
 		      /// Inequality operator.
 		      /// Two iterators are equal if and only if they point to the
 		      /// same object or both are invalid.
 		      bool operator!=(const GraphIncIt&) const { return true;}
 		      template <typename _GraphIncIt>
 		      struct Constraints {
 		        void constraints() {
 		          checkConcept<GraphItem<sel>, _GraphIncIt>();
 		          _GraphIncIt it1(graph, node);
 		          _GraphIncIt it2;
 		          _GraphIncIt it3 = it1;
 		          _GraphIncIt it4 = INVALID;
 		          it2 = ++it1;
 		          ++it2 = it1;
 		          ++(++it1);
 		          Item e = it1;
 		          e = it2;
+		        }
 		        Item arc;
 		        Base node;
 		        GR graph;
-		        _GraphIncIt it;
+		        const Base& node;
 		        const GR& graph;
 		      };
 		    };
 		    /// \brief An empty iterable digraph class.
 		    /// \brief Skeleton class for iterable directed graphs.
 		    ///
 		    /// This class provides beside the core digraph features
 		    /// iterator based iterable interface for the digraph structure.
 		    /// This class describes the interface of iterable directed
 		    /// graphs. It extends \ref BaseDigraphComponent with the core
 		    /// iterable interface.
 		    /// This concept is part of the Digraph concept.
 		    template <typename BAS = BaseDigraphComponent>
 		    class IterableDigraphComponent : public BAS {
 		    public:
 		      typedef BAS Base;
 		      typedef typename Base::Node Node;
 		      typedef typename Base::Arc Arc;
 		      typedef IterableDigraphComponent Digraph;
 		      /// \name Base iteration
 		      ///
 		      /// This interface provides functions for iteration on digraph items
+		      /// This interface provides functions for iteration on digraph items.
 		      ///
 		      /// @{
-		      /// \brief Gives back the first node in the iterating order.
+		      /// \brief Return the first node.
 		      ///
 		      /// Gives back the first node in the iterating order.
 		      ///
 		      /// This function gives back the first node in the iteration order.
 		      void first(Node&) const {}
-		      /// \brief Gives back the next node in the iterating order.
+		      /// \brief Return the next node.
 		      ///
 		      /// Gives back the next node in the iterating order.
 		      ///
 		      /// This function gives back the next node in the iteration order.
 		      void next(Node&) const {}
-		      /// \brief Gives back the first arc in the iterating order.
+		      /// \brief Return the first arc.
 		      ///
 		      /// Gives back the first arc in the iterating order.
 		      ///
 		      /// This function gives back the first arc in the iteration order.
 		      void first(Arc&) const {}
-		      /// \brief Gives back the next arc in the iterating order.
+		      /// \brief Return the next arc.
 		      ///
 		      /// Gives back the next arc in the iterating order.
 		      ///
 		      /// This function gives back the next arc in the iteration order.
 		      void next(Arc&) const {}
 		      /// \brief Gives back the first of the arcs point to the given
 		      /// node.
+		      /// \brief Return the first arc incomming to the given node.
 		      ///
 		      /// Gives back the first of the arcs point to the given node.
 		      ///
 		      /// This function gives back the first arc incomming to the
 		      /// given node.
 		      void firstIn(Arc&, const Node&) const {}
 		      /// \brief Gives back the next of the arcs points to the given
 		      /// node.
 		      /// \brief Return the next arc incomming to the given node.
 		      ///
 		      /// Gives back the next of the arcs points to the given node.
 		      ///
 		      /// This function gives back the next arc incomming to the
 		      /// given node.
 		      void nextIn(Arc&) const {}
-		      /// \brief Gives back the first of the arcs start from the
+		      /// \brief Return the first arc outgoing form the given node.
 		      ///
 		      /// This function gives back the first arc outgoing form the
 		      /// given node.
 		      ///
 		      /// Gives back the first of the arcs start from the given node.
 		      ///
 		      void firstOut(Arc&, const Node&) const {}
 		      /// \brief Gives back the next of the arcs start from the given
 		      /// node.
 		      /// \brief Return the next arc outgoing form the given node.
 		      ///
 		      /// Gives back the next of the arcs start from the given node.
 		      ///
 		      /// This function gives back the next arc outgoing form the
 		      /// given node.
 		      void nextOut(Arc&) const {}
 		      /// @}
 		      /// \name Class based iteration
 		      ///
-		      /// This interface provides functions for iteration on digraph items
+		      /// This interface provides iterator classes for digraph items.
 		      ///
 		      /// @{
 		      /// \brief This iterator goes through each node.
 		      ///
 		      /// This iterator goes through each node.
 		      ///
 		      typedef GraphItemIt<Digraph, Node> NodeIt;
-		      /// \brief This iterator goes through each node.
+		      /// \brief This iterator goes through each arc.
 		      ///
-		      /// This iterator goes through each node.
+		      /// This iterator goes through each arc.
 		      ///
 		      typedef GraphItemIt<Digraph, Arc> ArcIt;
 		      /// \brief This iterator goes trough the incoming arcs of a node.
 		      ///
-		      /// This iterator goes trough the \e inccoming arcs of a certain node
+		      /// This iterator goes trough the \e incoming arcs of a certain node
 		      /// of a digraph.
 		      typedef GraphIncIt<Digraph, Arc, Node, 'i'> InArcIt;
 		      /// \brief This iterator goes trough the outgoing arcs of a node.
 		      ///
 		      /// This iterator goes trough the \e outgoing arcs of a certain node
 		      /// of a digraph.
 		      typedef GraphIncIt<Digraph, Arc, Node, 'o'> OutArcIt;
 		      /// \brief The base node of the iterator.
 		      ///
 		      /// Gives back the base node of the iterator.
 		      /// It is always the target of the pointed arc.
 		      /// This function gives back the base node of the iterator.
 		      /// It is always the target node of the pointed arc.
 		      Node baseNode(const InArcIt&) const { return INVALID; }
 		      /// \brief The running node of the iterator.
 		      ///
 		      /// Gives back the running node of the iterator.
 		      /// It is always the source of the pointed arc.
 		      /// This function gives back the running node of the iterator.
 		      /// It is always the source node of the pointed arc.
 		      Node runningNode(const InArcIt&) const { return INVALID; }
 		      /// \brief The base node of the iterator.
 		      ///
 		      /// Gives back the base node of the iterator.
 		      /// It is always the source of the pointed arc.
 		      /// This function gives back the base node of the iterator.
 		      /// It is always the source node of the pointed arc.
 		      Node baseNode(const OutArcIt&) const { return INVALID; }
 		      /// \brief The running node of the iterator.
 		      ///
 		      /// Gives back the running node of the iterator.
 		      /// It is always the target of the pointed arc.
 		      /// This function gives back the running node of the iterator.
 		      /// It is always the target node of the pointed arc.
 		      Node runningNode(const OutArcIt&) const { return INVALID; }
 		      /// @}
 		      template <typename _Digraph>
 		      struct Constraints {
 		        void constraints() {
 		          checkConcept<Base, _Digraph>();
+		          {
 		            typename _Digraph::Node node(INVALID);
 		            typename _Digraph::Arc arc(INVALID);
+		            {
 		              digraph.first(node);
 		              digraph.next(node);
+		            }
+		            {
 		              digraph.first(arc);
 		              digraph.next(arc);
+		            }
+		            {
 		              digraph.firstIn(arc, node);
 		              digraph.nextIn(arc);
+		            }
+		            {
 		              digraph.firstOut(arc, node);
 		              digraph.nextOut(arc);
+		            }
+		          }
+		          {
 		            checkConcept<GraphItemIt<_Digraph, typename _Digraph::Arc>,
 		              typename _Digraph::ArcIt >();
 		            checkConcept<GraphItemIt<_Digraph, typename _Digraph::Node>,
 		              typename _Digraph::NodeIt >();
 		            checkConcept<GraphIncIt<_Digraph, typename _Digraph::Arc,
 		              typename _Digraph::Node, 'i'>, typename _Digraph::InArcIt>();
 		            checkConcept<GraphIncIt<_Digraph, typename _Digraph::Arc,
 		              typename _Digraph::Node, 'o'>, typename _Digraph::OutArcIt>();
 		            typename _Digraph::Node n;
 		            typename _Digraph::InArcIt ieit(INVALID);
 		            typename _Digraph::OutArcIt oeit(INVALID);
 		            n = digraph.baseNode(ieit);
 		            n = digraph.runningNode(ieit);
 		            n = digraph.baseNode(oeit);
 		            n = digraph.runningNode(oeit);
 		            const typename _Digraph::InArcIt iait(INVALID);
 		            const typename _Digraph::OutArcIt oait(INVALID);
 		            n = digraph.baseNode(iait);
 		            n = digraph.runningNode(iait);
 		            n = digraph.baseNode(oait);
 		            n = digraph.runningNode(oait);
 		            ignore_unused_variable_warning(n);
+		          }
+		        }
 		        const _Digraph& digraph;
 		      };
 		    };
-		    /// \brief An empty iterable undirected graph class.
+		    /// \brief Skeleton class for iterable undirected graphs.
 		    ///
 		    /// This class provides beside the core graph features iterator
 		    /// based iterable interface for the undirected graph structure.
 		    /// This class describes the interface of iterable undirected
 		    /// graphs. It extends \ref IterableDigraphComponent with the core
 		    /// iterable interface of undirected graphs.
 		    /// This concept is part of the Graph concept.
 		    template <typename BAS = BaseGraphComponent>
 		    class IterableGraphComponent : public IterableDigraphComponent<BAS> {
 		    public:
 		      typedef BAS Base;
 		      typedef typename Base::Node Node;
 		      typedef typename Base::Arc Arc;
 		      typedef typename Base::Edge Edge;
 		      typedef IterableGraphComponent Graph;
 		      /// \name Base iteration
 		      ///
-		      /// This interface provides functions for iteration on graph items
+		      /// This interface provides functions for iteration on edges.
 		      ///
 		      /// @{
 		      using IterableDigraphComponent<Base>::first;
 		      using IterableDigraphComponent<Base>::next;
 		      /// \brief Gives back the first edge in the iterating
 		      /// order.
 		      /// \brief Return the first edge.
 		      ///
 		      /// Gives back the first edge in the iterating order.
 		      ///
 		      /// This function gives back the first edge in the iteration order.
 		      void first(Edge&) const {}
 		      /// \brief Gives back the next edge in the iterating
 		      /// order.
 		      /// \brief Return the next edge.
 		      ///
 		      /// Gives back the next edge in the iterating order.
 		      ///
 		      /// This function gives back the next edge in the iteration order.
 		      void next(Edge&) const {}
 		      /// \brief Gives back the first of the edges from the
 		      /// \brief Return the first edge incident to the given node.
 		      ///
 		      /// This function gives back the first edge incident to the given
 		      /// node. The bool parameter gives back the direction for which the
 		      /// source node of the directed arc representing the edge is the
 		      /// given node.
 		      ///
 		      /// Gives back the first of the edges from the given
 		      /// node. The bool parameter gives back that direction which
 		      /// gives a good direction of the edge so the source of the
 		      /// directed arc is the given node.
 		      void firstInc(Edge&, bool&, const Node&) const {}
 		      /// \brief Gives back the next of the edges from the
 		      /// given node.
 		      ///
 		      /// Gives back the next of the edges from the given
 		      /// node. The bool parameter should be used as the \c firstInc()
-		      /// use it.
+		      /// This function gives back the next edge incident to the given
 		      /// node. The bool parameter should be used as \c firstInc() use it.
 		      void nextInc(Edge&, bool&) const {}
 		      using IterableDigraphComponent<Base>::baseNode;
 		      using IterableDigraphComponent<Base>::runningNode;
 		      /// @}
 		      /// \name Class based iteration
 		      ///
-		      /// This interface provides functions for iteration on graph items
+		      /// This interface provides iterator classes for edges.
 		      ///
 		      /// @{
-		      /// \brief This iterator goes through each node.
+		      /// \brief This iterator goes through each edge.
 		      ///
-		      /// This iterator goes through each node.
+		      /// This iterator goes through each edge.
 		      typedef GraphItemIt<Graph, Edge> EdgeIt;
-		      /// \brief This iterator goes trough the incident arcs of a
 		      /// \brief This iterator goes trough the incident edges of a
 		      /// node.
 		      ///
-		      /// This iterator goes trough the incident arcs of a certain
+		      /// This iterator goes trough the incident edges of a certain
 		      /// node of a graph.
-		      typedef GraphIncIt<Graph, Edge, Node, 'u'> IncEdgeIt;
+		      typedef GraphIncIt<Graph, Edge, Node, 'e'> IncEdgeIt;
 		      /// \brief The base node of the iterator.
 		      ///
-		      /// Gives back the base node of the iterator.
+		      /// This function gives back the base node of the iterator.
 		      Node baseNode(const IncEdgeIt&) const { return INVALID; }
 		      /// \brief The running node of the iterator.
 		      ///
-		      /// Gives back the running node of the iterator.
+		      /// This function gives back the running node of the iterator.
 		      Node runningNode(const IncEdgeIt&) const { return INVALID; }
 		      /// @}
 		      template <typename _Graph>
 		      struct Constraints {
 		        void constraints() {
 		          checkConcept<IterableDigraphComponent<Base>, _Graph>();
+		          {
 		            typename _Graph::Node node(INVALID);
 		            typename _Graph::Edge edge(INVALID);
 		            bool dir;
+		            {
 		              graph.first(edge);
 		              graph.next(edge);
+		            }
+		            {
 		              graph.firstInc(edge, dir, node);
 		              graph.nextInc(edge, dir);
+		            }
+		          }
+		          {
 		            checkConcept<GraphItemIt<_Graph, typename _Graph::Edge>,
 		              typename _Graph::EdgeIt >();
 		            checkConcept<GraphIncIt<_Graph, typename _Graph::Edge,
-		              typename _Graph::Node, 'u'>, typename _Graph::IncEdgeIt>();
+		              typename _Graph::Node, 'e'>, typename _Graph::IncEdgeIt>();
 		            typename _Graph::Node n;
 		            typename _Graph::IncEdgeIt ueit(INVALID);
 		            n = graph.baseNode(ueit);
-		            n = graph.runningNode(ueit);
+		            const typename _Graph::IncEdgeIt ieit(INVALID);
 		            n = graph.baseNode(ieit);
 		            n = graph.runningNode(ieit);
+		          }
+		        }
 		        const _Graph& graph;
 		      };
 		    };
-		    /// \brief An empty alteration notifier digraph class.
+		    /// \brief Skeleton class for alterable directed graphs.
 		    ///
 		    /// This class provides beside the core digraph features alteration
 		    /// notifier interface for the digraph structure.  This implements
 		    /// This class describes the interface of alterable directed
 		    /// graphs. It extends \ref BaseDigraphComponent with the alteration
 		    /// notifier interface. It implements
 		    /// an observer-notifier pattern for each digraph item. More
 		    /// obsevers can be registered into the notifier and whenever an
 		    /// alteration occured in the digraph all the observers will
+		    /// alteration occured in the digraph all the observers will be
 		    /// notified about it.
 		    template <typename BAS = BaseDigraphComponent>
 		    class AlterableDigraphComponent : public BAS {
 		    public:
 		      typedef BAS Base;
 		      typedef typename Base::Node Node;
 		      typedef typename Base::Arc Arc;
-		      /// The node observer registry.
+		      /// Node alteration notifier class.
 		      typedef AlterationNotifier<AlterableDigraphComponent, Node>
 		      NodeNotifier;
-		      /// The arc observer registry.
+		      /// Arc alteration notifier class.
 		      typedef AlterationNotifier<AlterableDigraphComponent, Arc>
 		      ArcNotifier;
-		      /// \brief Gives back the node alteration notifier.
+		      /// \brief Return the node alteration notifier.
 		      ///
-		      /// Gives back the node alteration notifier.
+		      /// This function gives back the node alteration notifier.
 		      NodeNotifier& notifier(Node) const {
 		        return NodeNotifier();
+		         return NodeNotifier();
+		      }
-		      /// \brief Gives back the arc alteration notifier.
+		      /// \brief Return the arc alteration notifier.
 		      ///
-		      /// Gives back the arc alteration notifier.
+		      /// This function gives back the arc alteration notifier.
 		      ArcNotifier& notifier(Arc) const {
 		        return ArcNotifier();
+		      }
 		      template <typename _Digraph>
 		      struct Constraints {
 		        void constraints() {
 		          checkConcept<Base, _Digraph>();
 		          typename _Digraph::NodeNotifier& nn
 		            = digraph.notifier(typename _Digraph::Node());
 		          typename _Digraph::ArcNotifier& en
 		            = digraph.notifier(typename _Digraph::Arc());
 		          ignore_unused_variable_warning(nn);
 		          ignore_unused_variable_warning(en);
+		        }
 		        const _Digraph& digraph;
 		      };
 		    };
-		    /// \brief An empty alteration notifier undirected graph class.
+		    /// \brief Skeleton class for alterable undirected graphs.
 		    ///
 		    /// This class provides beside the core graph features alteration
 		    /// notifier interface for the graph structure.  This implements
-		    /// an observer-notifier pattern for each graph item. More
+		    /// This class describes the interface of alterable undirected
 		    /// graphs. It extends \ref AlterableDigraphComponent with the alteration
 		    /// notifier interface of undirected graphs. It implements
 		    /// an observer-notifier pattern for the edges. More
 		    /// obsevers can be registered into the notifier and whenever an
 		    /// alteration occured in the graph all the observers will
+		    /// alteration occured in the graph all the observers will be
 		    /// notified about it.
 		    template <typename BAS = BaseGraphComponent>
 		    class AlterableGraphComponent : public AlterableDigraphComponent<BAS> {
 		    public:
 		      typedef BAS Base;
 		      typedef typename Base::Edge Edge;
-		      /// The arc observer registry.
+		      /// Edge alteration notifier class.
 		      typedef AlterationNotifier<AlterableGraphComponent, Edge>
 		      EdgeNotifier;
-		      /// \brief Gives back the arc alteration notifier.
+		      /// \brief Return the edge alteration notifier.
 		      ///
-		      /// Gives back the arc alteration notifier.
+		      /// This function gives back the edge alteration notifier.
 		      EdgeNotifier& notifier(Edge) const {
 		        return EdgeNotifier();
+		      }
 		      template <typename _Graph>
 		      struct Constraints {
 		        void constraints() {
-		          checkConcept<AlterableGraphComponent<Base>, _Graph>();
+		          checkConcept<AlterableDigraphComponent<Base>, _Graph>();
 		          typename _Graph::EdgeNotifier& uen
 		            = graph.notifier(typename _Graph::Edge());
 		          ignore_unused_variable_warning(uen);
+		        }
 		        const _Graph& graph;
 		      };
 		    };
-		    /// \brief Class describing the concept of graph maps
+		    /// \brief Concept class for standard graph maps.
 		    ///
 		    /// This class describes the common interface of the graph maps
 		    /// (NodeMap, ArcMap), that is maps that can be used to
-		    /// associate data to graph descriptors (nodes or arcs).
+		    /// This class describes the concept of standard graph maps, i.e.
 		    /// the \c NodeMap, \c ArcMap and \c EdgeMap subtypes of digraph and
 		    /// graph types, which can be used for associating data to graph items.
 		    template <typename GR, typename K, typename V>
 		    class GraphMap : public ReadWriteMap<K, V> {
 		    public:
 		      typedef ReadWriteMap<K, V> Parent;
 		      /// The graph type of the map.
 		      typedef GR Graph;
 		      /// The key type of the map.
 		      typedef K Key;
 		      /// The value type of the map.
 		      typedef V Value;
 		      /// \brief Construct a new map.
 		      ///
 		      /// Construct a new map for the graph.
 		      explicit GraphMap(const Graph&) {}
 		      /// \brief Construct a new map with default value.
 		      ///
-		      /// Construct a new map for the graph and initalise the values.
+		      /// Construct a new map for the graph and initalize the values.
 		      GraphMap(const Graph&, const Value&) {}
 		    private:
 		      /// \brief Copy constructor.
 		      ///
 		      /// Copy Constructor.
 		      GraphMap(const GraphMap&) : Parent() {}
-		      /// \brief Assign operator.
+		      /// \brief Assignment operator.
 		      ///
-		      /// Assign operator. It does not mofify the underlying graph,
+		      /// Assignment operator. It does not mofify the underlying graph,
 		      /// it just iterates on the current item set and set the  map
 		      /// with the value returned by the assigned map.
 		      template <typename CMap>
 		      GraphMap& operator=(const CMap&) {
 		        checkConcept<ReadMap<Key, Value>, CMap>();
 		        return *this;
+		      }
 		    public:
 		      template<typename _Map>
 		      struct Constraints {
 		        void constraints() {
 		          checkConcept<ReadWriteMap<Key, Value>, _Map >();
 		          // Construction with a graph parameter
 		          _Map a(g);
 		          // Constructor with a graph and a default value parameter
 		          _Map a2(g,t);
 		          // Copy constructor.
 		          // _Map b(c);
 		          _Map m1(g);
 		          _Map m2(g,t);
 		          // Copy constructor
 		          // _Map m3(m);
 		          // Assignment operator
 		          // ReadMap<Key, Value> cmap;
-		          // b = cmap;
+		          // m3 = cmap;
 		          ignore_unused_variable_warning(a);
 		          ignore_unused_variable_warning(a2);
-		          // ignore_unused_variable_warning(b);
+		          ignore_unused_variable_warning(m1);
 		          ignore_unused_variable_warning(m2);
 		          // ignore_unused_variable_warning(m3);
+		        }
-		        const _Map &c;
+		        const _Map &m;
 		        const Graph &g;
 		        const typename GraphMap::Value &t;
 		      };
 		    };
-		    /// \brief An empty mappable digraph class.
+		    /// \brief Skeleton class for mappable directed graphs.
 		    ///
 		    /// This class provides beside the core digraph features
 		    /// map interface for the digraph structure.
 		    /// This class describes the interface of mappable directed graphs.
 		    /// It extends \ref BaseDigraphComponent with the standard digraph
 		    /// map classes, namely \c NodeMap and \c ArcMap.
 		    /// This concept is part of the Digraph concept.
 		    template <typename BAS = BaseDigraphComponent>
 		    class MappableDigraphComponent : public BAS  {
 		    public:
 		      typedef BAS Base;
 		      typedef typename Base::Node Node;
 		      typedef typename Base::Arc Arc;
 		      typedef MappableDigraphComponent Digraph;
-		      /// \brief ReadWrite map of the nodes.
+		      /// \brief Standard graph map for the nodes.
 		      ///
 		      /// ReadWrite map of the nodes.
 		      ///
 		      /// Standard graph map for the nodes.
 		      template <typename V>
-		      class NodeMap : public GraphMap<Digraph, Node, V> {
+		      class NodeMap : public GraphMap<MappableDigraphComponent, Node, V> {
 		      public:
 		        typedef GraphMap<MappableDigraphComponent, Node, V> Parent;
 		        /// \brief Construct a new map.
 		        ///
 		        /// Construct a new map for the digraph.
 		        explicit NodeMap(const MappableDigraphComponent& digraph)
 		          : Parent(digraph) {}
 		        /// \brief Construct a new map with default value.
 		        ///
-		        /// Construct a new map for the digraph and initalise the values.
+		        /// Construct a new map for the digraph and initalize the values.
 		        NodeMap(const MappableDigraphComponent& digraph, const V& value)
 		          : Parent(digraph, value) {}
 		      private:
 		        /// \brief Copy constructor.
 		        ///
 		        /// Copy Constructor.
 		        NodeMap(const NodeMap& nm) : Parent(nm) {}
-		        /// \brief Assign operator.
+		        /// \brief Assignment operator.
 		        ///
-		        /// Assign operator.
+		        /// Assignment operator.
 		        template <typename CMap>
 		        NodeMap& operator=(const CMap&) {
 		          checkConcept<ReadMap<Node, V>, CMap>();
 		          return *this;
+		        }
 		      };
-		      /// \brief ReadWrite map of the arcs.
+		      /// \brief Standard graph map for the arcs.
 		      ///
 		      /// ReadWrite map of the arcs.
 		      ///
 		      /// Standard graph map for the arcs.
 		      template <typename V>
-		      class ArcMap : public GraphMap<Digraph, Arc, V> {
+		      class ArcMap : public GraphMap<MappableDigraphComponent, Arc, V> {
 		      public:
 		        typedef GraphMap<MappableDigraphComponent, Arc, V> Parent;
 		        /// \brief Construct a new map.
 		        ///
 		        /// Construct a new map for the digraph.
 		        explicit ArcMap(const MappableDigraphComponent& digraph)
 		          : Parent(digraph) {}
 		        /// \brief Construct a new map with default value.
 		        ///
-		        /// Construct a new map for the digraph and initalise the values.
+		        /// Construct a new map for the digraph and initalize the values.
 		        ArcMap(const MappableDigraphComponent& digraph, const V& value)
 		          : Parent(digraph, value) {}
 		      private:
 		        /// \brief Copy constructor.
 		        ///
 		        /// Copy Constructor.
 		        ArcMap(const ArcMap& nm) : Parent(nm) {}
-		        /// \brief Assign operator.
+		        /// \brief Assignment operator.
 		        ///
-		        /// Assign operator.
+		        /// Assignment operator.
 		        template <typename CMap>
 		        ArcMap& operator=(const CMap&) {
 		          checkConcept<ReadMap<Arc, V>, CMap>();
 		          return *this;
+		        }
 		      };
 		      template <typename _Digraph>
 		      struct Constraints {
 		        struct Dummy {
 		          int value;
 		          Dummy() : value(0) {}
 		          Dummy(int _v) : value(_v) {}
 		        };
 		        void constraints() {
 		          checkConcept<Base, _Digraph>();
 		          { // int map test
 		            typedef typename _Digraph::template NodeMap<int> IntNodeMap;
 		            checkConcept<GraphMap<_Digraph, typename _Digraph::Node, int>,
 		              IntNodeMap >();
 		          } { // bool map test
 		            typedef typename _Digraph::template NodeMap<bool> BoolNodeMap;
 		            checkConcept<GraphMap<_Digraph, typename _Digraph::Node, bool>,
 		              BoolNodeMap >();
 		          } { // Dummy map test
 		            typedef typename _Digraph::template NodeMap<Dummy> DummyNodeMap;
 		            checkConcept<GraphMap<_Digraph, typename _Digraph::Node, Dummy>,
 		              DummyNodeMap >();
+		          }
 		          { // int map test
 		            typedef typename _Digraph::template ArcMap<int> IntArcMap;
 		            checkConcept<GraphMap<_Digraph, typename _Digraph::Arc, int>,
 		              IntArcMap >();
 		          } { // bool map test
 		            typedef typename _Digraph::template ArcMap<bool> BoolArcMap;
 		            checkConcept<GraphMap<_Digraph, typename _Digraph::Arc, bool>,
 		              BoolArcMap >();
 		          } { // Dummy map test
 		            typedef typename _Digraph::template ArcMap<Dummy> DummyArcMap;
 		            checkConcept<GraphMap<_Digraph, typename _Digraph::Arc, Dummy>,
 		              DummyArcMap >();
+		          }
+		        }
 		        _Digraph& digraph;
+		        const _Digraph& digraph;
 		      };
 		    };
-		    /// \brief An empty mappable base bipartite graph class.
+		    /// \brief Skeleton class for mappable undirected graphs.
 		    ///
 		    /// This class provides beside the core graph features
 		    /// map interface for the graph structure.
 		    /// This class describes the interface of mappable undirected graphs.
 		    /// It extends \ref MappableDigraphComponent with the standard graph
 		    /// map class for edges (\c EdgeMap).
 		    /// This concept is part of the Graph concept.
 		    template <typename BAS = BaseGraphComponent>
 		    class MappableGraphComponent : public MappableDigraphComponent<BAS>  {
 		    public:
 		      typedef BAS Base;
 		      typedef typename Base::Edge Edge;
 		      typedef MappableGraphComponent Graph;
-		      /// \brief ReadWrite map of the edges.
+		      /// \brief Standard graph map for the edges.
 		      ///
 		      /// ReadWrite map of the edges.
 		      ///
 		      /// Standard graph map for the edges.
 		      template <typename V>
-		      class EdgeMap : public GraphMap<Graph, Edge, V> {
+		      class EdgeMap : public GraphMap<MappableGraphComponent, Edge, V> {
 		      public:
 		        typedef GraphMap<MappableGraphComponent, Edge, V> Parent;
 		        /// \brief Construct a new map.
 		        ///
 		        /// Construct a new map for the graph.
 		        explicit EdgeMap(const MappableGraphComponent& graph)
 		          : Parent(graph) {}
 		        /// \brief Construct a new map with default value.
 		        ///
-		        /// Construct a new map for the graph and initalise the values.
+		        /// Construct a new map for the graph and initalize the values.
 		        EdgeMap(const MappableGraphComponent& graph, const V& value)
 		          : Parent(graph, value) {}
 		      private:
 		        /// \brief Copy constructor.
 		        ///
 		        /// Copy Constructor.
 		        EdgeMap(const EdgeMap& nm) : Parent(nm) {}
-		        /// \brief Assign operator.
+		        /// \brief Assignment operator.
 		        ///
-		        /// Assign operator.
+		        /// Assignment operator.
 		        template <typename CMap>
 		        EdgeMap& operator=(const CMap&) {
 		          checkConcept<ReadMap<Edge, V>, CMap>();
 		          return *this;
+		        }
 		      };
 		      template <typename _Graph>
 		      struct Constraints {
 		        struct Dummy {
 		          int value;
 		          Dummy() : value(0) {}
 		          Dummy(int _v) : value(_v) {}
 		        };
 		        void constraints() {
-		          checkConcept<MappableGraphComponent<Base>, _Graph>();
+		          checkConcept<MappableDigraphComponent<Base>, _Graph>();
 		          { // int map test
 		            typedef typename _Graph::template EdgeMap<int> IntEdgeMap;
 		            checkConcept<GraphMap<_Graph, typename _Graph::Edge, int>,
 		              IntEdgeMap >();
 		          } { // bool map test
 		            typedef typename _Graph::template EdgeMap<bool> BoolEdgeMap;
 		            checkConcept<GraphMap<_Graph, typename _Graph::Edge, bool>,
 		              BoolEdgeMap >();
 		          } { // Dummy map test
 		            typedef typename _Graph::template EdgeMap<Dummy> DummyEdgeMap;
 		            checkConcept<GraphMap<_Graph, typename _Graph::Edge, Dummy>,
 		              DummyEdgeMap >();
+		          }
+		        }
 		        _Graph& graph;
+		        const _Graph& graph;
 		      };
 		    };
-		    /// \brief An empty extendable digraph class.
+		    /// \brief Skeleton class for extendable directed graphs.
 		    ///
 		    /// This class provides beside the core digraph features digraph
 		    /// extendable interface for the digraph structure.  The main
 		    /// difference between the base and this interface is that the
 		    /// digraph alterations should handled already on this level.
 		    /// This class describes the interface of extendable directed graphs.
 		    /// It extends \ref BaseDigraphComponent with functions for adding
 		    /// nodes and arcs to the digraph.
 		    /// This concept requires \ref AlterableDigraphComponent.
 		    template <typename BAS = BaseDigraphComponent>
 		    class ExtendableDigraphComponent : public BAS {
 		    public:
 		      typedef BAS Base;
 		      typedef typename Base::Node Node;
 		      typedef typename Base::Arc Arc;
-		      /// \brief Adds a new node to the digraph.
+		      /// \brief Add a new node to the digraph.
 		      ///
 		      /// Adds a new node to the digraph.
 		      ///
 		      /// This function adds a new node to the digraph.
 		      Node addNode() {
 		        return INVALID;
+		      }
-		      /// \brief Adds a new arc connects the given two nodes.
+		      /// \brief Add a new arc connecting the given two nodes.
 		      ///
-		      /// Adds a new arc connects the the given two nodes.
+		      /// This function adds a new arc connecting the given two nodes
 		      /// of the digraph.
 		      Arc addArc(const Node&, const Node&) {
 		        return INVALID;
+		      }
 		      template <typename _Digraph>
 		      struct Constraints {
 		        void constraints() {
 		          checkConcept<Base, _Digraph>();
 		          typename _Digraph::Node node_a, node_b;
 		          node_a = digraph.addNode();
 		          node_b = digraph.addNode();
 		          typename _Digraph::Arc arc;
 		          arc = digraph.addArc(node_a, node_b);
+		        }
 		        _Digraph& digraph;
 		      };
 		    };
-		    /// \brief An empty extendable base undirected graph class.
+		    /// \brief Skeleton class for extendable undirected graphs.
 		    ///
 		    /// This class provides beside the core undirected graph features
 		    /// core undircted graph extend interface for the graph structure.
 		    /// The main difference between the base and this interface is
 		    /// that the graph alterations should handled already on this
-		    /// level.
+		    /// This class describes the interface of extendable undirected graphs.
 		    /// It extends \ref BaseGraphComponent with functions for adding
 		    /// nodes and edges to the graph.
 		    /// This concept requires \ref AlterableGraphComponent.
 		    template <typename BAS = BaseGraphComponent>
 		    class ExtendableGraphComponent : public BAS {
 		    public:
 		      typedef BAS Base;
 		      typedef typename Base::Node Node;
 		      typedef typename Base::Edge Edge;
-		      /// \brief Adds a new node to the graph.
+		      /// \brief Add a new node to the digraph.
 		      ///
 		      /// Adds a new node to the graph.
 		      ///
 		      /// This function adds a new node to the digraph.
 		      Node addNode() {
 		        return INVALID;
+		      }
-		      /// \brief Adds a new arc connects the given two nodes.
+		      /// \brief Add a new edge connecting the given two nodes.
 		      ///
 		      /// Adds a new arc connects the the given two nodes.
 		      Edge addArc(const Node&, const Node&) {
 		      /// This function adds a new edge connecting the given two nodes
 		      /// of the graph.
 		      Edge addEdge(const Node&, const Node&) {
 		        return INVALID;
+		      }
 		      template <typename _Graph>
 		      struct Constraints {
 		        void constraints() {
 		          checkConcept<Base, _Graph>();
 		          typename _Graph::Node node_a, node_b;
 		          node_a = graph.addNode();
 		          node_b = graph.addNode();
 		          typename _Graph::Edge edge;
 		          edge = graph.addEdge(node_a, node_b);
+		        }
 		        _Graph& graph;
 		      };
 		    };
-		    /// \brief An empty erasable digraph class.
+		    /// \brief Skeleton class for erasable directed graphs.
 		    ///
 		    /// This class provides beside the core digraph features core erase
 		    /// functions for the digraph structure. The main difference between
 		    /// the base and this interface is that the digraph alterations
 		    /// should handled already on this level.
 		    /// This class describes the interface of erasable directed graphs.
 		    /// It extends \ref BaseDigraphComponent with functions for removing
 		    /// nodes and arcs from the digraph.
 		    /// This concept requires \ref AlterableDigraphComponent.
 		    template <typename BAS = BaseDigraphComponent>
 		    class ErasableDigraphComponent : public BAS {
 		    public:
 		      typedef BAS Base;
 		      typedef typename Base::Node Node;
 		      typedef typename Base::Arc Arc;
 		      /// \brief Erase a node from the digraph.
 		      ///
 		      /// Erase a node from the digraph. This function should
 		      /// erase all arcs connecting to the node.
 		      /// This function erases the given node from the digraph and all arcs
 		      /// connected to the node.
 		      void erase(const Node&) {}
 		      /// \brief Erase an arc from the digraph.
 		      ///
 		      /// Erase an arc from the digraph.
 		      ///
 		      /// This function erases the given arc from the digraph.
 		      void erase(const Arc&) {}
 		      template <typename _Digraph>
 		      struct Constraints {
 		        void constraints() {
 		          checkConcept<Base, _Digraph>();
 		          typename _Digraph::Node node;
+		          const typename _Digraph::Node node(INVALID);
 		          digraph.erase(node);
 		          typename _Digraph::Arc arc;
+		          const typename _Digraph::Arc arc(INVALID);
 		          digraph.erase(arc);
+		        }
 		        _Digraph& digraph;
 		      };
 		    };
-		    /// \brief An empty erasable base undirected graph class.
+		    /// \brief Skeleton class for erasable undirected graphs.
 		    ///
 		    /// This class provides beside the core undirected graph features
 		    /// core erase functions for the undirceted graph structure. The
 		    /// main difference between the base and this interface is that
 		    /// the graph alterations should handled already on this level.
 		    /// This class describes the interface of erasable undirected graphs.
 		    /// It extends \ref BaseGraphComponent with functions for removing
 		    /// nodes and edges from the graph.
 		    /// This concept requires \ref AlterableGraphComponent.
 		    template <typename BAS = BaseGraphComponent>
 		    class ErasableGraphComponent : public BAS {
 		    public:
 		      typedef BAS Base;
 		      typedef typename Base::Node Node;
 		      typedef typename Base::Edge Edge;
 		      /// \brief Erase a node from the graph.
 		      ///
 		      /// Erase a node from the graph. This function should erase
 		      /// arcs connecting to the node.
 		      /// This function erases the given node from the graph and all edges
 		      /// connected to the node.
 		      void erase(const Node&) {}
-		      /// \brief Erase an arc from the graph.
+		      /// \brief Erase an edge from the digraph.
 		      ///
 		      /// Erase an arc from the graph.
 		      ///
 		      /// This function erases the given edge from the digraph.
 		      void erase(const Edge&) {}
 		      template <typename _Graph>
 		      struct Constraints {
 		        void constraints() {
 		          checkConcept<Base, _Graph>();
 		          typename _Graph::Node node;
+		          const typename _Graph::Node node(INVALID);
 		          graph.erase(node);
 		          typename _Graph::Edge edge;
+		          const typename _Graph::Edge edge(INVALID);
 		          graph.erase(edge);
+		        }
 		        _Graph& graph;
 		      };
 		    };
-		    /// \brief An empty clearable base digraph class.
+		    /// \brief Skeleton class for clearable directed graphs.
 		    ///
 		    /// This class provides beside the core digraph features core clear
 		    /// functions for the digraph structure. The main difference between
 		    /// the base and this interface is that the digraph alterations
 		    /// should handled already on this level.
 		    /// This class describes the interface of clearable directed graphs.
 		    /// It extends \ref BaseDigraphComponent with a function for clearing
 		    /// the digraph.
 		    /// This concept requires \ref AlterableDigraphComponent.
 		    template <typename BAS = BaseDigraphComponent>
 		    class ClearableDigraphComponent : public BAS {
 		    public:
 		      typedef BAS Base;
 		      /// \brief Erase all nodes and arcs from the digraph.
 		      ///
 		      /// Erase all nodes and arcs from the digraph.
 		      ///
 		      /// This function erases all nodes and arcs from the digraph.
 		      void clear() {}
 		      template <typename _Digraph>
 		      struct Constraints {
 		        void constraints() {
 		          checkConcept<Base, _Digraph>();
 		          digraph.clear();
+		        }
 		        _Digraph digraph;
+		        _Digraph& digraph;
 		      };
 		    };
-		    /// \brief An empty clearable base undirected graph class.
+		    /// \brief Skeleton class for clearable undirected graphs.
 		    ///
 		    /// This class provides beside the core undirected graph features
 		    /// core clear functions for the undirected graph structure. The
 		    /// main difference between the base and this interface is that
 		    /// the graph alterations should handled already on this level.
 		    /// This class describes the interface of clearable undirected graphs.
 		    /// It extends \ref BaseGraphComponent with a function for clearing
 		    /// the graph.
 		    /// This concept requires \ref AlterableGraphComponent.
 		    template <typename BAS = BaseGraphComponent>
 		    class ClearableGraphComponent : public ClearableDigraphComponent<BAS> {
 		    public:
 		      typedef BAS Base;
 		      /// \brief Erase all nodes and edges from the graph.
 		      ///
 		      /// This function erases all nodes and edges from the graph.
 		      void clear() {}
 		      template <typename _Graph>
 		      struct Constraints {
 		        void constraints() {
-		          checkConcept<ClearableGraphComponent<Base>, _Graph>();
 		          checkConcept<Base, _Graph>();
 		          graph.clear();
+		        }
 		        _Graph graph;
+		        _Graph& graph;
 		      };
 		    };
+		  }
+		}
 		#endif

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