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

@@ -1427,1536 +1427,1539 @@
 		  template<typename GR, typename NF, typename EF>
 		  SubGraph<const GR, const NF, EF>
 		  subGraph(const GR& graph, const NF& node_filter, EF& edge_filter) {
 		    return SubGraph<const GR, const NF, EF>
 		      (graph, node_filter, edge_filter);
+		  }
 		  template<typename GR, typename NF, typename EF>
 		  SubGraph<const GR, NF, const EF>
 		  subGraph(const GR& graph, NF& node_filter, const EF& edge_filter) {
 		    return SubGraph<const GR, NF, const EF>
 		      (graph, node_filter, edge_filter);
+		  }
 		  template<typename GR, typename NF, typename EF>
 		  SubGraph<const GR, const NF, const EF>
 		  subGraph(const GR& graph, const NF& node_filter, const EF& edge_filter) {
 		    return SubGraph<const GR, const NF, const EF>
 		      (graph, node_filter, edge_filter);
+		  }
 		  /// \ingroup graph_adaptors
 		  ///
 		  /// \brief Adaptor class for hiding nodes in a digraph or a graph.
 		  ///
 		  /// FilterNodes adaptor can be used for hiding nodes in a digraph or a
 		  /// graph. A \c bool node map must be specified, which defines the filter
 		  /// for the nodes. Only the nodes with \c true filter value and the
 		  /// arcs/edges incident to nodes both with \c true filter value are shown
 		  /// in the subgraph. This adaptor conforms to the \ref concepts::Digraph
 		  /// "Digraph" concept or the \ref concepts::Graph "Graph" concept
 		  /// depending on the \c GR template parameter.
 		  ///
 		  /// The adapted (di)graph can also be modified through this adaptor
 		  /// by adding or removing nodes or arcs/edges, unless the \c GR template
 		  /// parameter is set to be \c const.
 		  ///
 		  /// \tparam GR The type of the adapted digraph or graph.
 		  /// It must conform to the \ref concepts::Digraph "Digraph" concept
 		  /// or the \ref concepts::Graph "Graph" concept.
 		  /// It can also be specified to be \c const.
 		  /// \tparam NF The type of the node filter map.
 		  /// It must be a \c bool (or convertible) node map of the
 		  /// adapted (di)graph. The default type is
 		  /// \ref concepts::Graph::NodeMap "GR::NodeMap<bool>".
 		  ///
 		  /// \note The \c Node and <tt>Arc/Edge</tt> types of this adaptor and the
 		  /// adapted (di)graph are convertible to each other.
 		#ifdef DOXYGEN
 		  template<typename GR, typename NF>
 		  class FilterNodes {
 		#else
 		  template<typename GR,
 		           typename NF = typename GR::template NodeMap<bool>,
 		           typename Enable = void>
 		  class FilterNodes :
 		    public DigraphAdaptorExtender<
 		      SubDigraphBase<GR, NF, ConstMap<typename GR::Arc, Const<bool, true> >,
 		                     true> > {
 		#endif
 		  public:
 		    typedef GR Digraph;
 		    typedef NF NodeFilterMap;
 		    typedef DigraphAdaptorExtender<
 		      SubDigraphBase<GR, NF, ConstMap<typename GR::Arc, Const<bool, true> >,
 		                     true> > Parent;
 		    typedef typename Parent::Node Node;
 		  protected:
 		    ConstMap<typename Digraph::Arc, Const<bool, true> > const_true_map;
 		    FilterNodes() : const_true_map() {}
 		  public:
 		    /// \brief Constructor
 		    ///
 		    /// Creates a subgraph for the given digraph or graph with the
 		    /// given node filter map.
 		    FilterNodes(GR& graph, NF& node_filter)
 		      : Parent(), const_true_map()
+		    {
 		      Parent::initialize(graph, node_filter, const_true_map);
+		    }
 		    /// \brief Sets the status of the given node
 		    ///
 		    /// This function sets the status of the given node.
 		    /// It is done by simply setting the assigned value of \c n
 		    /// to \c v in the node filter map.
 		    void status(const Node& n, bool v) const { Parent::status(n, v); }
 		    /// \brief Returns the status of the given node
 		    ///
 		    /// This function returns the status of the given node.
 		    /// It is \c true if the given node is enabled (i.e. not hidden).
 		    bool status(const Node& n) const { return Parent::status(n); }
 		    /// \brief Disables the given node
 		    ///
 		    /// This function disables the given node, so the iteration
 		    /// jumps over it.
 		    /// It is the same as \ref status() "status(n, false)".
 		    void disable(const Node& n) const { Parent::status(n, false); }
 		    /// \brief Enables the given node
 		    ///
 		    /// This function enables the given node.
 		    /// It is the same as \ref status() "status(n, true)".
 		    void enable(const Node& n) const { Parent::status(n, true); }
 		  };
 		  template<typename GR, typename NF>
 		  class FilterNodes<GR, NF,
 		                    typename enable_if<UndirectedTagIndicator<GR> >::type> :
 		    public GraphAdaptorExtender<
 		      SubGraphBase<GR, NF, ConstMap<typename GR::Edge, Const<bool, true> >,
 		                   true> > {
 		  public:
 		    typedef GR Graph;
 		    typedef NF NodeFilterMap;
 		    typedef GraphAdaptorExtender<
 		      SubGraphBase<GR, NF, ConstMap<typename GR::Edge, Const<bool, true> >,
 		                   true> > Parent;
 		    typedef typename Parent::Node Node;
 		  protected:
 		    ConstMap<typename GR::Edge, Const<bool, true> > const_true_map;
 		    FilterNodes() : const_true_map() {}
 		  public:
 		    FilterNodes(GR& graph, NodeFilterMap& node_filter) :
 		      Parent(), const_true_map() {
 		      Parent::initialize(graph, node_filter, const_true_map);
+		    }
 		    void status(const Node& n, bool v) const { Parent::status(n, v); }
 		    bool status(const Node& n) const { return Parent::status(n); }
 		    void disable(const Node& n) const { Parent::status(n, false); }
 		    void enable(const Node& n) const { Parent::status(n, true); }
 		  };
 		  /// \brief Returns a read-only FilterNodes adaptor
 		  ///
 		  /// This function just returns a read-only \ref FilterNodes adaptor.
 		  /// \ingroup graph_adaptors
 		  /// \relates FilterNodes
 		  template<typename GR, typename NF>
 		  FilterNodes<const GR, NF>
 		  filterNodes(const GR& graph, NF& node_filter) {
 		    return FilterNodes<const GR, NF>(graph, node_filter);
+		  }
 		  template<typename GR, typename NF>
 		  FilterNodes<const GR, const NF>
 		  filterNodes(const GR& graph, const NF& node_filter) {
 		    return FilterNodes<const GR, const NF>(graph, node_filter);
+		  }
 		  /// \ingroup graph_adaptors
 		  ///
 		  /// \brief Adaptor class for hiding arcs in a digraph.
 		  ///
 		  /// FilterArcs adaptor can be used for hiding arcs in a digraph.
 		  /// A \c bool arc map must be specified, which defines the filter for
 		  /// the arcs. Only the arcs with \c true filter value are shown in the
 		  /// subdigraph. This adaptor conforms to the \ref concepts::Digraph
 		  /// "Digraph" concept.
 		  ///
 		  /// The adapted digraph can also be modified through this adaptor
 		  /// by adding or removing nodes or arcs, 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.
 		  /// \tparam AF The type of the arc filter map.
 		  /// It must be a \c bool (or convertible) arc map of the
 		  /// adapted digraph. The default type is
 		  /// \ref concepts::Digraph::ArcMap "DGR::ArcMap<bool>".
 		  ///
 		  /// \note The \c Node and \c Arc types of this adaptor and the adapted
 		  /// digraph are convertible to each other.
 		#ifdef DOXYGEN
 		  template<typename DGR,
 		           typename AF>
 		  class FilterArcs {
 		#else
 		  template<typename DGR,
 		           typename AF = typename DGR::template ArcMap<bool> >
 		  class FilterArcs :
 		    public DigraphAdaptorExtender<
 		      SubDigraphBase<DGR, ConstMap<typename DGR::Node, Const<bool, true> >,
 		                     AF, false> > {
 		#endif
 		  public:
 		    /// The type of the adapted digraph.
 		    typedef DGR Digraph;
 		    /// The type of the arc filter map.
 		    typedef AF ArcFilterMap;
 		    typedef DigraphAdaptorExtender<
 		      SubDigraphBase<DGR, ConstMap<typename DGR::Node, Const<bool, true> >,
 		                     AF, false> > Parent;
 		    typedef typename Parent::Arc Arc;
 		  protected:
 		    ConstMap<typename DGR::Node, Const<bool, true> > const_true_map;
 		    FilterArcs() : const_true_map() {}
 		  public:
 		    /// \brief Constructor
 		    ///
 		    /// Creates a subdigraph for the given digraph with the given arc
 		    /// filter map.
 		    FilterArcs(DGR& digraph, ArcFilterMap& arc_filter)
 		      : Parent(), const_true_map() {
 		      Parent::initialize(digraph, const_true_map, arc_filter);
+		    }
 		    /// \brief Sets the status of the given arc
 		    ///
 		    /// This function sets the status of the given arc.
 		    /// It is done by simply setting the assigned value of \c a
 		    /// to \c v in the arc filter map.
 		    void status(const Arc& a, bool v) const { Parent::status(a, v); }
 		    /// \brief Returns the status of the given arc
 		    ///
 		    /// This function returns the status of the given arc.
 		    /// It is \c true if the given arc is enabled (i.e. not hidden).
 		    bool status(const Arc& a) const { return Parent::status(a); }
 		    /// \brief Disables the given arc
 		    ///
 		    /// This function disables the given arc in the subdigraph,
 		    /// so the iteration jumps over it.
 		    /// It is the same as \ref status() "status(a, false)".
 		    void disable(const Arc& a) const { Parent::status(a, false); }
 		    /// \brief Enables the given arc
 		    ///
 		    /// This function enables the given arc in the subdigraph.
 		    /// It is the same as \ref status() "status(a, true)".
 		    void enable(const Arc& a) const { Parent::status(a, true); }
 		  };
 		  /// \brief Returns a read-only FilterArcs adaptor
 		  ///
 		  /// This function just returns a read-only \ref FilterArcs adaptor.
 		  /// \ingroup graph_adaptors
 		  /// \relates FilterArcs
 		  template<typename DGR, typename AF>
 		  FilterArcs<const DGR, AF>
 		  filterArcs(const DGR& digraph, AF& arc_filter) {
 		    return FilterArcs<const DGR, AF>(digraph, arc_filter);
+		  }
 		  template<typename DGR, typename AF>
 		  FilterArcs<const DGR, const AF>
 		  filterArcs(const DGR& digraph, const AF& arc_filter) {
 		    return FilterArcs<const DGR, const AF>(digraph, arc_filter);
+		  }
 		  /// \ingroup graph_adaptors
 		  ///
 		  /// \brief Adaptor class for hiding edges in a graph.
 		  ///
 		  /// FilterEdges adaptor can be used for hiding edges in a graph.
 		  /// A \c bool edge map must be specified, which defines the filter for
 		  /// the edges. Only the edges with \c true filter value are shown in the
 		  /// subgraph. This adaptor conforms to the \ref concepts::Graph
 		  /// "Graph" concept.
 		  ///
 		  /// The adapted graph 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 GR The type of the adapted graph.
 		  /// It must conform to the \ref concepts::Graph "Graph" concept.
 		  /// It can also be specified to be \c const.
 		  /// \tparam EF The type of the edge filter map.
 		  /// It must be a \c bool (or convertible) edge map of the
 		  /// adapted graph. The default type is
 		  /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<bool>".
 		  ///
 		  /// \note The \c Node, \c Edge and \c Arc types of this adaptor and the
 		  /// adapted graph are convertible to each other.
 		#ifdef DOXYGEN
 		  template<typename GR,
 		           typename EF>
 		  class FilterEdges {
 		#else
 		  template<typename GR,
 		           typename EF = typename GR::template EdgeMap<bool> >
 		  class FilterEdges :
 		    public GraphAdaptorExtender<
 		      SubGraphBase<GR, ConstMap<typename GR::Node, Const<bool, true> >,
 		                   EF, false> > {
 		#endif
 		  public:
 		    /// The type of the adapted graph.
 		    typedef GR Graph;
 		    /// The type of the edge filter map.
 		    typedef EF EdgeFilterMap;
 		    typedef GraphAdaptorExtender<
 		      SubGraphBase<GR, ConstMap<typename GR::Node, Const<bool, true > >,
 		                   EF, false> > Parent;
 		    typedef typename Parent::Edge Edge;
 		  protected:
 		    ConstMap<typename GR::Node, Const<bool, true> > const_true_map;
 		    FilterEdges() : const_true_map(true) {
 		      Parent::setNodeFilterMap(const_true_map);
+		    }
 		  public:
 		    /// \brief Constructor
 		    ///
 		    /// Creates a subgraph for the given graph with the given edge
 		    /// filter map.
 		    FilterEdges(GR& graph, EF& edge_filter)
 		      : Parent(), const_true_map() {
 		      Parent::initialize(graph, const_true_map, edge_filter);
+		    }
 		    /// \brief Sets the status of the given edge
 		    ///
 		    /// This function sets the status of the given edge.
 		    /// It is done by simply setting the assigned value of \c e
 		    /// to \c v in the edge filter map.
 		    void status(const Edge& e, bool v) const { Parent::status(e, v); }
 		    /// \brief Returns the status of the given edge
 		    ///
 		    /// This function returns the status of the given edge.
 		    /// It is \c true if the given edge is enabled (i.e. not hidden).
 		    bool status(const Edge& e) const { return Parent::status(e); }
 		    /// \brief Disables the given edge
 		    ///
 		    /// This function disables the given edge in the subgraph,
 		    /// so the iteration jumps over it.
 		    /// It is the same as \ref status() "status(e, false)".
 		    void disable(const Edge& e) const { Parent::status(e, false); }
 		    /// \brief Enables the given edge
 		    ///
 		    /// This function enables the given edge in the subgraph.
 		    /// It is the same as \ref status() "status(e, true)".
 		    void enable(const Edge& e) const { Parent::status(e, true); }
 		  };
 		  /// \brief Returns a read-only FilterEdges adaptor
 		  ///
 		  /// This function just returns a read-only \ref FilterEdges adaptor.
 		  /// \ingroup graph_adaptors
 		  /// \relates FilterEdges
 		  template<typename GR, typename EF>
 		  FilterEdges<const GR, EF>
 		  filterEdges(const GR& graph, EF& edge_filter) {
 		    return FilterEdges<const GR, EF>(graph, edge_filter);
+		  }
 		  template<typename GR, typename EF>
 		  FilterEdges<const GR, const EF>
 		  filterEdges(const GR& graph, const EF& edge_filter) {
 		    return FilterEdges<const GR, const EF>(graph, edge_filter);
+		  }
 		  template <typename DGR>
 		  class UndirectorBase {
 		  public:
 		    typedef DGR Digraph;
 		    typedef UndirectorBase Adaptor;
 		    typedef True UndirectedTag;
 		    typedef typename Digraph::Arc Edge;
 		    typedef typename Digraph::Node Node;
 		    class Arc : public Edge {
 		      friend class UndirectorBase;
 		    protected:
 		      bool _forward;
 		      Arc(const Edge& edge, bool forward) :
 		        Edge(edge), _forward(forward) {}
 		    public:
 		      Arc() {}
 		      Arc(Invalid) : Edge(INVALID), _forward(true) {}
 		      bool operator==(const Arc &other) const {
 		        return _forward == other._forward &&
 		          static_cast<const Edge&>(*this) == static_cast<const Edge&>(other);
+		      }
 		      bool operator!=(const Arc &other) const {
 		        return _forward != other._forward ||
 		          static_cast<const Edge&>(*this) != static_cast<const Edge&>(other);
+		      }
 		      bool operator<(const Arc &other) const {
 		        return _forward < other._forward ||
 		          (_forward == other._forward &&
 		           static_cast<const Edge&>(*this) < static_cast<const Edge&>(other));
+		      }
 		    };
 		    void first(Node& n) const {
 		      _digraph->first(n);
+		    }
 		    void next(Node& n) const {
 		      _digraph->next(n);
+		    }
 		    void first(Arc& a) const {
 		      _digraph->first(a);
 		      a._forward = true;
+		    }
 		    void next(Arc& a) const {
 		      if (a._forward) {
 		        a._forward = false;
 		      } else {
 		        _digraph->next(a);
 		        a._forward = true;
+		      }
+		    }
 		    void first(Edge& e) const {
 		      _digraph->first(e);
+		    }
 		    void next(Edge& e) const {
 		      _digraph->next(e);
+		    }
 		    void firstOut(Arc& a, const Node& n) const {
 		      _digraph->firstIn(a, n);
 		      if( static_cast<const Edge&>(a) != INVALID ) {
 		        a._forward = false;
 		      } else {
 		        _digraph->firstOut(a, n);
 		        a._forward = true;
+		      }
+		    }
 		    void nextOut(Arc &a) const {
 		      if (!a._forward) {
 		        Node n = _digraph->target(a);
 		        _digraph->nextIn(a);
 		        if (static_cast<const Edge&>(a) == INVALID ) {
 		          _digraph->firstOut(a, n);
 		          a._forward = true;
+		        }
+		      }
 		      else {
 		        _digraph->nextOut(a);
+		      }
+		    }
 		    void firstIn(Arc &a, const Node &n) const {
 		      _digraph->firstOut(a, n);
 		      if (static_cast<const Edge&>(a) != INVALID ) {
 		        a._forward = false;
 		      } else {
 		        _digraph->firstIn(a, n);
 		        a._forward = true;
+		      }
+		    }
 		    void nextIn(Arc &a) const {
 		      if (!a._forward) {
 		        Node n = _digraph->source(a);
 		        _digraph->nextOut(a);
 		        if( static_cast<const Edge&>(a) == INVALID ) {
 		          _digraph->firstIn(a, n);
 		          a._forward = true;
+		        }
+		      }
 		      else {
 		        _digraph->nextIn(a);
+		      }
+		    }
 		    void firstInc(Edge &e, bool &d, const Node &n) const {
 		      d = true;
 		      _digraph->firstOut(e, n);
 		      if (e != INVALID) return;
 		      d = false;
 		      _digraph->firstIn(e, n);
+		    }
 		    void nextInc(Edge &e, bool &d) const {
 		      if (d) {
 		        Node s = _digraph->source(e);
 		        _digraph->nextOut(e);
 		        if (e != INVALID) return;
 		        d = false;
 		        _digraph->firstIn(e, s);
 		      } else {
 		        _digraph->nextIn(e);
+		      }
+		    }
 		    Node u(const Edge& e) const {
 		      return _digraph->source(e);
+		    }
 		    Node v(const Edge& e) const {
 		      return _digraph->target(e);
+		    }
 		    Node source(const Arc &a) const {
 		      return a._forward ? _digraph->source(a) : _digraph->target(a);
+		    }
 		    Node target(const Arc &a) const {
 		      return a._forward ? _digraph->target(a) : _digraph->source(a);
+		    }
 		    static Arc direct(const Edge &e, bool d) {
 		      return Arc(e, d);
+		    }
 		    Arc direct(const Edge &e, const Node& n) const {
 		      return Arc(e, _digraph->source(e) == n);
+		    }
 		    static bool direction(const Arc &a) { return a._forward; }
 		    Node nodeFromId(int ix) const { return _digraph->nodeFromId(ix); }
 		    Arc arcFromId(int ix) const {
 		      return direct(_digraph->arcFromId(ix >> 1), bool(ix & 1));
+		    }
 		    Edge edgeFromId(int ix) const { return _digraph->arcFromId(ix); }
 		    int id(const Node &n) const { return _digraph->id(n); }
 		    int id(const Arc &a) const {
 		      return  (_digraph->id(a) << 1) | (a._forward ? 1 : 0);
+		    }
 		    int id(const Edge &e) const { return _digraph->id(e); }
 		    int maxNodeId() const { return _digraph->maxNodeId(); }
 		    int maxArcId() const { return (_digraph->maxArcId() << 1) | 1; }
 		    int maxEdgeId() const { return _digraph->maxArcId(); }
 		    Node addNode() { return _digraph->addNode(); }
 		    Edge addEdge(const Node& u, const Node& v) {
 		      return _digraph->addArc(u, v);
+		    }
 		    void erase(const Node& i) { _digraph->erase(i); }
 		    void erase(const Edge& i) { _digraph->erase(i); }
 		    void clear() { _digraph->clear(); }
 		    typedef NodeNumTagIndicator<Digraph> NodeNumTag;
 		    int nodeNum() const { return _digraph->nodeNum(); }
 		    typedef ArcNumTagIndicator<Digraph> ArcNumTag;
 		    int arcNum() const { return 2 * _digraph->arcNum(); }
 		    typedef ArcNumTag EdgeNumTag;
 		    int edgeNum() const { return _digraph->arcNum(); }
 		    typedef FindArcTagIndicator<Digraph> FindArcTag;
 		    Arc findArc(Node s, Node t, Arc p = INVALID) const {
 		      if (p == INVALID) {
 		        Edge arc = _digraph->findArc(s, t);
 		        if (arc != INVALID) return direct(arc, true);
 		        arc = _digraph->findArc(t, s);
 		        if (arc != INVALID) return direct(arc, false);
 		      } else if (direction(p)) {
 		        Edge arc = _digraph->findArc(s, t, p);
 		        if (arc != INVALID) return direct(arc, true);
 		        arc = _digraph->findArc(t, s);
 		        if (arc != INVALID) return direct(arc, false);
 		      } else {
 		        Edge arc = _digraph->findArc(t, s, p);
 		        if (arc != INVALID) return direct(arc, false);
+		      }
 		      return INVALID;
+		    }
 		    typedef FindArcTag FindEdgeTag;
 		    Edge findEdge(Node s, Node t, Edge p = INVALID) const {
 		      if (s != t) {
 		        if (p == INVALID) {
 		          Edge arc = _digraph->findArc(s, t);
 		          if (arc != INVALID) return arc;
 		          arc = _digraph->findArc(t, s);
 		          if (arc != INVALID) return arc;
 		        } else if (_digraph->source(p) == s) {
 		          Edge arc = _digraph->findArc(s, t, p);
 		          if (arc != INVALID) return arc;
 		          arc = _digraph->findArc(t, s);
 		          if (arc != INVALID) return arc;
 		        } else {
 		          Edge arc = _digraph->findArc(t, s, p);
 		          if (arc != INVALID) return arc;
+		        }
 		      } else {
 		        return _digraph->findArc(s, t, p);
+		      }
 		      return INVALID;
+		    }
 		  private:
 		    template <typename V>
 		    class ArcMapBase {
 		    private:
 		      typedef typename DGR::template ArcMap<V> MapImpl;
 		    public:
 		      typedef typename MapTraits<MapImpl>::ReferenceMapTag ReferenceMapTag;
 		      typedef V Value;
 		      typedef Arc Key;
 		      typedef typename MapTraits<MapImpl>::ConstReturnValue ConstReturnValue;
 		      typedef typename MapTraits<MapImpl>::ReturnValue ReturnValue;
 		      typedef typename MapTraits<MapImpl>::ConstReturnValue ConstReference;
 		      typedef typename MapTraits<MapImpl>::ReturnValue Reference;
 		      ArcMapBase(const UndirectorBase<DGR>& adaptor) :
 		        _forward(*adaptor._digraph), _backward(*adaptor._digraph) {}
 		      ArcMapBase(const UndirectorBase<DGR>& adaptor, const V& value)
 		        : _forward(*adaptor._digraph, value),
 		          _backward(*adaptor._digraph, value) {}
 		      void set(const Arc& a, const V& value) {
 		        if (direction(a)) {
 		          _forward.set(a, value);
 		        } else {
 		          _backward.set(a, value);
+		        }
+		      }
 		      ConstReturnValue operator[](const Arc& a) const {
 		        if (direction(a)) {
 		          return _forward[a];
 		        } else {
 		          return _backward[a];
+		        }
+		      }
 		      ReturnValue operator[](const Arc& a) {
 		        if (direction(a)) {
 		          return _forward[a];
 		        } 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 {
 		        if (Parent::direction(e)) {
 		          return (*_forward)[e];
 		        } else {
 		          return (*_backward)[e];
+		        }
+		      }
 		      /// Returns a reference to the value associated with the given key.
 		      ReturnValue operator[](const Key& e) {
 		        if (Parent::direction(e)) {
 		          return (*_forward)[e];
 		        } else {
 		          return (*_backward)[e];
+		        }
+		      }
 		    protected:
 		      FW* _forward;
 		      BK* _backward;
 		    };
 		    /// \brief Returns a combined arc map
 		    ///
 		    /// This function just returns a combined arc map.
 		    template <typename FW, typename BK>
 		    static CombinedArcMap<FW, BK>
 		    combinedArcMap(FW& forward, BK& backward) {
 		      return CombinedArcMap<FW, BK>(forward, backward);
+		    }
 		    template <typename FW, typename BK>
 		    static CombinedArcMap<const FW, BK>
 		    combinedArcMap(const FW& forward, BK& backward) {
 		      return CombinedArcMap<const FW, BK>(forward, backward);
+		    }
 		    template <typename FW, typename BK>
 		    static CombinedArcMap<FW, const BK>
 		    combinedArcMap(FW& forward, const BK& backward) {
 		      return CombinedArcMap<FW, const BK>(forward, backward);
+		    }
 		    template <typename FW, typename BK>
 		    static CombinedArcMap<const FW, const BK>
 		    combinedArcMap(const FW& forward, const BK& backward) {
 		      return CombinedArcMap<const FW, const BK>(forward, backward);
+		    }
 		  };
 		  /// \brief Returns a read-only Undirector adaptor
 		  ///
 		  /// This function just returns a read-only \ref Undirector adaptor.
 		  /// \ingroup graph_adaptors
 		  /// \relates Undirector
 		  template<typename DGR>
 		  Undirector<const DGR> undirector(const DGR& digraph) {
 		    return Undirector<const DGR>(digraph);
+		  }
 		  template <typename GR, typename DM>
 		  class OrienterBase {
 		  public:
 		    typedef GR Graph;
 		    typedef DM DirectionMap;
 		    typedef typename GR::Node Node;
 		    typedef typename GR::Edge Arc;
 		    void reverseArc(const Arc& arc) {
 		      _direction->set(arc, !(*_direction)[arc]);
+		    }
 		    void first(Node& i) const { _graph->first(i); }
 		    void first(Arc& i) const { _graph->first(i); }
 		    void firstIn(Arc& i, const Node& n) const {
 		      bool d = true;
 		      _graph->firstInc(i, d, n);
 		      while (i != INVALID && d == (*_direction)[i]) _graph->nextInc(i, d);
+		    }
 		    void firstOut(Arc& i, const Node& n ) const {
 		      bool d = true;
 		      _graph->firstInc(i, d, n);
 		      while (i != INVALID && d != (*_direction)[i]) _graph->nextInc(i, d);
+		    }
 		    void next(Node& i) const { _graph->next(i); }
 		    void next(Arc& i) const { _graph->next(i); }
 		    void nextIn(Arc& i) const {
 		      bool d = !(*_direction)[i];
 		      _graph->nextInc(i, d);
 		      while (i != INVALID && d == (*_direction)[i]) _graph->nextInc(i, d);
+		    }
 		    void nextOut(Arc& i) const {
 		      bool d = (*_direction)[i];
 		      _graph->nextInc(i, d);
 		      while (i != INVALID && d != (*_direction)[i]) _graph->nextInc(i, d);
+		    }
 		    Node source(const Arc& e) const {
 		      return (*_direction)[e] ? _graph->u(e) : _graph->v(e);
+		    }
 		    Node target(const Arc& e) const {
 		      return (*_direction)[e] ? _graph->v(e) : _graph->u(e);
+		    }
 		    typedef NodeNumTagIndicator<Graph> NodeNumTag;
 		    int nodeNum() const { return _graph->nodeNum(); }
 		    typedef EdgeNumTagIndicator<Graph> ArcNumTag;
 		    int arcNum() const { return _graph->edgeNum(); }
 		    typedef FindEdgeTagIndicator<Graph> FindArcTag;
 		    Arc findArc(const Node& u, const Node& v,
 		                const Arc& prev = INVALID) const {
 		      Arc arc = _graph->findEdge(u, v, prev);
 		      while (arc != INVALID && source(arc) != u) {
 		        arc = _graph->findEdge(u, v, arc);
+		      }
 		      return arc;
+		    }
 		    Node addNode() {
 		      return Node(_graph->addNode());
+		    }
 		    Arc addArc(const Node& u, const Node& v) {
 		      Arc arc = _graph->addEdge(u, v);
 		      _direction->set(arc, _graph->u(arc) == u);
 		      return arc;
+		    }
 		    void erase(const Node& i) { _graph->erase(i); }
 		    void erase(const Arc& i) { _graph->erase(i); }
 		    void clear() { _graph->clear(); }
 		    int id(const Node& v) const { return _graph->id(v); }
 		    int id(const Arc& e) const { return _graph->id(e); }
 		    Node nodeFromId(int idx) const { return _graph->nodeFromId(idx); }
 		    Arc arcFromId(int idx) const { return _graph->edgeFromId(idx); }
 		    int maxNodeId() const { return _graph->maxNodeId(); }
 		    int maxArcId() const { return _graph->maxEdgeId(); }
 		    typedef typename ItemSetTraits<GR, Node>::ItemNotifier NodeNotifier;
 		    NodeNotifier& notifier(Node) const { return _graph->notifier(Node()); }
 		    typedef typename ItemSetTraits<GR, Arc>::ItemNotifier ArcNotifier;
 		    ArcNotifier& notifier(Arc) const { return _graph->notifier(Arc()); }
 		    template <typename V>
 		    class NodeMap : public GR::template NodeMap<V> {
 		    public:
 		      typedef typename GR::template NodeMap<V> Parent;
 		      explicit NodeMap(const OrienterBase<GR, DM>& adapter)
 		        : Parent(*adapter._graph) {}
 		      NodeMap(const OrienterBase<GR, DM>& adapter, const V& value)
 		        : Parent(*adapter._graph, 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 GR::template EdgeMap<V> {
 		    public:
 		      typedef typename Graph::template EdgeMap<V> Parent;
 		      explicit ArcMap(const OrienterBase<GR, DM>& adapter)
 		        : Parent(*adapter._graph) { }
 		      ArcMap(const OrienterBase<GR, DM>& adapter, const V& value)
 		        : Parent(*adapter._graph, value) { }
 		    private:
 		      ArcMap& operator=(const ArcMap& cmap) {
 		        return operator=<ArcMap>(cmap);
+		      }
 		      template <typename CMap>
 		      ArcMap& operator=(const CMap& cmap) {
 		        Parent::operator=(cmap);
 		        return *this;
+		      }
 		    };
 		  protected:
 		    Graph* _graph;
 		    DM* _direction;
 		    void initialize(GR& graph, DM& direction) {
 		      _graph = &graph;
 		      _direction = &direction;
+		    }
 		  };
 		  /// \ingroup graph_adaptors
 		  ///
 		  /// \brief Adaptor class for orienting the edges of a graph to get a digraph
 		  ///
 		  /// Orienter adaptor can be used for orienting the edges of a graph to
 		  /// get a digraph. A \c bool edge map of the underlying graph must be
 		  /// specified, which define the direction of the arcs in the adaptor.
 		  /// The arcs can be easily reversed by the \c reverseArc() member function
 		  /// of the adaptor.
 		  /// This class conforms to the \ref concepts::Digraph "Digraph" concept.
 		  ///
 		  /// The adapted graph can also be modified through this adaptor
 		  /// by adding or removing nodes or arcs, unless the \c GR template
 		  /// parameter is set to be \c const.
 		  ///
 		  /// \tparam GR The type of the adapted graph.
 		  /// It must conform to the \ref concepts::Graph "Graph" concept.
 		  /// It can also be specified to be \c const.
 		  /// \tparam DM The type of the direction map.
 		  /// It must be a \c bool (or convertible) edge map of the
 		  /// adapted graph. The default type is
 		  /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<bool>".
 		  ///
 		  /// \note The \c Node type of this adaptor and the adapted graph are
 		  /// convertible to each other, moreover the \c Arc type of the adaptor
 		  /// and the \c Edge type of the adapted graph are also convertible to
 		  /// each other.
 		#ifdef DOXYGEN
 		  template<typename GR,
 		           typename DM>
 		  class Orienter {
 		#else
 		  template<typename GR,
 		           typename DM = typename GR::template EdgeMap<bool> >
 		  class Orienter :
 		    public DigraphAdaptorExtender<OrienterBase<GR, DM> > {
 		#endif
 		  public:
 		    /// The type of the adapted graph.
 		    typedef GR Graph;
 		    /// The type of the direction edge map.
 		    typedef DM DirectionMap;
 		    typedef DigraphAdaptorExtender<OrienterBase<GR, DM> > Parent;
 		    typedef typename Parent::Arc Arc;
 		  protected:
 		    Orienter() { }
 		  public:
 		    /// \brief Constructor
 		    ///
 		    /// Constructor of the adaptor.
 		    Orienter(GR& graph, DM& direction) {
 		      Parent::initialize(graph, direction);
+		    }
 		    /// \brief Reverses the given arc
 		    ///
 		    /// This function reverses the given arc.
 		    /// It is done by simply negate the assigned value of \c a
 		    /// in the direction map.
 		    void reverseArc(const Arc& a) {
 		      Parent::reverseArc(a);
+		    }
 		  };
 		  /// \brief Returns a read-only Orienter adaptor
 		  ///
 		  /// This function just returns a read-only \ref Orienter adaptor.
 		  /// \ingroup graph_adaptors
 		  /// \relates Orienter
 		  template<typename GR, typename DM>
 		  Orienter<const GR, DM>
 		  orienter(const GR& graph, DM& direction) {
 		    return Orienter<const GR, DM>(graph, direction);
+		  }
 		  template<typename GR, typename DM>
 		  Orienter<const GR, const DM>
 		  orienter(const GR& graph, const DM& direction) {
 		    return Orienter<const GR, const DM>(graph, direction);
+		  }
 		  namespace _adaptor_bits {
 		    template <typename DGR, typename CM, typename FM, typename TL>
 		    class ResForwardFilter {
 		    public:
 		      typedef typename DGR::Arc Key;
 		      typedef bool Value;
 		    private:
 		      const CM* _capacity;
 		      const FM* _flow;
 		      TL _tolerance;
 		    public:
 		      ResForwardFilter(const CM& capacity, const FM& flow,
 		                       const TL& tolerance = TL())
 		        : _capacity(&capacity), _flow(&flow), _tolerance(tolerance) { }
 		      bool operator[](const typename DGR::Arc& a) const {
 		        return _tolerance.positive((*_capacity)[a] - (*_flow)[a]);
+		      }
 		    };
 		    template<typename DGR,typename CM, typename FM, typename TL>
 		    class ResBackwardFilter {
 		    public:
 		      typedef typename DGR::Arc Key;
 		      typedef bool Value;
 		    private:
 		      const CM* _capacity;
 		      const FM* _flow;
 		      TL _tolerance;
 		    public:
 		      ResBackwardFilter(const CM& capacity, const FM& flow,
 		                        const TL& tolerance = TL())
 		        : _capacity(&capacity), _flow(&flow), _tolerance(tolerance) { }
 		      bool operator[](const typename DGR::Arc& a) const {
 		        return _tolerance.positive((*_flow)[a]);
+		      }
 		    };
+		  }
 		  /// \ingroup graph_adaptors
 		  ///
 		  /// \brief Adaptor class for composing the residual digraph for directed
 		  /// flow and circulation problems.
 		  ///
 		  /// ResidualDigraph can be used for composing the \e residual digraph
 		  /// for directed flow and circulation problems. Let \f$ G=(V, A) \f$
 		  /// be a directed graph and let \f$ F \f$ be a number type.
 		  /// Let \f$ flow, cap: A\to F \f$ be functions on the arcs.
 		  /// This adaptor implements a digraph structure with node set \f$ V \f$
 		  /// and arc set \f$ A_{forward}\cup A_{backward} \f$,
 		  /// where \f$ A_{forward}=\{uv : uv\in A, flow(uv)<cap(uv)\} \f$ and
 		  /// \f$ A_{backward}=\{vu : uv\in A, flow(uv)>0\} \f$, i.e. the so
 		  /// called residual digraph.
 		  /// When the union \f$ A_{forward}\cup A_{backward} \f$ is taken,
 		  /// multiplicities are counted, i.e. the adaptor has exactly
 		  /// \f$ |A_{forward}| + |A_{backward}|\f$ arcs (it may have parallel
 		  /// arcs).
 		  /// This class conforms to the \ref concepts::Digraph "Digraph" concept.
 		  ///
 		  /// \tparam DGR The type of the adapted digraph.
 		  /// It must conform to the \ref concepts::Digraph "Digraph" concept.
 		  /// It is implicitly \c const.
 		  /// \tparam CM The type of the capacity map.
 		  /// It must be an arc map of some numerical type, which defines
 		  /// the capacities in the flow problem. It is implicitly \c const.
 		  /// The default type is
 		  /// \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
 		  /// \tparam FM The type of the flow map.
 		  /// It must be an arc map of some numerical type, which defines
 		  /// the flow values in the flow problem. The default type is \c CM.
 		  /// \tparam TL The tolerance type for handling inexact computation.
 		  /// The default tolerance type depends on the value type of the
 		  /// capacity map.
 		  ///
 		  /// \note This adaptor is implemented using Undirector and FilterArcs
 		  /// adaptors.
 		  ///
 		  /// \note The \c Node type of this adaptor and the adapted digraph are
 		  /// convertible to each other, moreover the \c Arc type of the adaptor
 		  /// is convertible to the \c Arc type of the adapted digraph.
 		#ifdef DOXYGEN
 		  template<typename DGR, typename CM, typename FM, typename TL>
 		  class ResidualDigraph
 		#else
 		  template<typename DGR,
 		           typename CM = typename DGR::template ArcMap<int>,
 		           typename FM = CM,
 		           typename TL = Tolerance<typename CM::Value> >
 		  class ResidualDigraph
 		    : public SubDigraph<
 		        Undirector<const DGR>,
 		        ConstMap<typename DGR::Node, Const<bool, true> >,
 		        typename Undirector<const DGR>::template CombinedArcMap<
 		          _adaptor_bits::ResForwardFilter<const DGR, CM, FM, TL>,
 		          _adaptor_bits::ResBackwardFilter<const DGR, CM, FM, TL> > >
 		#endif
+		  {
 		  public:
 		    /// The type of the underlying digraph.
 		    typedef DGR Digraph;
 		    /// The type of the capacity map.
 		    typedef CM CapacityMap;
 		    /// The type of the flow map.
 		    typedef FM FlowMap;
 		    /// The tolerance type.
 		    typedef TL Tolerance;
 		    typedef typename CapacityMap::Value Value;
 		    typedef ResidualDigraph Adaptor;
 		  protected:
 		    typedef Undirector<const Digraph> Undirected;
 		    typedef ConstMap<typename DGR::Node, Const<bool, true> > NodeFilter;
 		    typedef _adaptor_bits::ResForwardFilter<const DGR, CM,
 		                                            FM, TL> ForwardFilter;
 		    typedef _adaptor_bits::ResBackwardFilter<const DGR, CM,
 		                                             FM, TL> BackwardFilter;
 		    typedef typename Undirected::
 		      template CombinedArcMap<ForwardFilter, BackwardFilter> ArcFilter;
 		    typedef SubDigraph<Undirected, NodeFilter, ArcFilter> Parent;
 		    const CapacityMap* _capacity;
 		    FlowMap* _flow;
 		    Undirected _graph;
 		    NodeFilter _node_filter;
 		    ForwardFilter _forward_filter;
 		    BackwardFilter _backward_filter;
 		    ArcFilter _arc_filter;
 		  public:
 		    /// \brief Constructor
 		    ///
 		    /// Constructor of the residual digraph adaptor. The parameters are the
 		    /// digraph, the capacity map, the flow map, and a tolerance object.
 		    ResidualDigraph(const DGR& digraph, const CM& capacity,
 		                    FM& flow, const TL& tolerance = Tolerance())
 		      : Parent(), _capacity(&capacity), _flow(&flow),
 		        _graph(digraph), _node_filter(),
 		        _forward_filter(capacity, flow, tolerance),
 		        _backward_filter(capacity, flow, tolerance),
 		        _arc_filter(_forward_filter, _backward_filter)
+		    {
 		      Parent::initialize(_graph, _node_filter, _arc_filter);
+		    }
 		    typedef typename Parent::Arc Arc;
 		    /// \brief Returns the residual capacity of the given arc.
 		    ///
 		    /// Returns the residual capacity of the given arc.
 		    Value residualCapacity(const Arc& a) const {
 		      if (Undirected::direction(a)) {
 		        return (*_capacity)[a] - (*_flow)[a];
 		      } else {
 		        return (*_flow)[a];
+		      }
+		    }
 		    /// \brief Augments on the given arc in the residual digraph.
 		    ///
 		    /// Augments on the given arc in the residual digraph. It increases
 		    /// or decreases the flow value on the original arc according to the
 		    /// direction of the residual arc.
 		    void augment(const Arc& a, const Value& v) const {
 		      if (Undirected::direction(a)) {
 		        _flow->set(a, (*_flow)[a] + v);
 		      } else {
 		        _flow->set(a, (*_flow)[a] - v);
+		      }
+		    }
 		    /// \brief Returns \c true if the given residual arc is a forward arc.
 		    ///
 		    /// Returns \c true if the given residual arc has the same orientation
 		    /// as the original arc, i.e. it is a so called forward arc.
 		    static bool forward(const Arc& a) {
 		      return Undirected::direction(a);
+		    }
 		    /// \brief Returns \c true if the given residual arc is a backward arc.
 		    ///
 		    /// Returns \c true if the given residual arc has the opposite orientation
 		    /// than the original arc, i.e. it is a so called backward arc.
 		    static bool backward(const Arc& a) {
 		      return !Undirected::direction(a);
+		    }
 		    /// \brief Returns the forward oriented residual arc.
 		    ///
 		    /// Returns the forward oriented residual arc related to the given
 		    /// arc of the underlying digraph.
 		    static Arc forward(const typename Digraph::Arc& a) {
 		      return Undirected::direct(a, true);
+		    }
 		    /// \brief Returns the backward oriented residual arc.
 		    ///
 		    /// Returns the backward oriented residual arc related to the given
 		    /// arc of the underlying digraph.
 		    static Arc backward(const typename Digraph::Arc& a) {
 		      return Undirected::direct(a, false);
+		    }
 		    /// \brief Residual capacity map.
 		    ///
 		    /// This map adaptor class can be used for obtaining the residual
 		    /// capacities as an arc map of the residual digraph.
 		    /// Its value type is inherited from the capacity map.
 		    class ResidualCapacity {
 		    protected:
 		      const Adaptor* _adaptor;
 		    public:
 		      /// The key type of the map
 		      typedef Arc Key;
 		      /// The value type of the map
 		      typedef typename CapacityMap::Value Value;
 		      /// Constructor
 		      ResidualCapacity(const ResidualDigraph<DGR, CM, FM, TL>& adaptor)
 		        : _adaptor(&adaptor) {}
 		      /// Returns the value associated with the given residual arc
 		      Value operator[](const Arc& a) const {
 		        return _adaptor->residualCapacity(a);
+		      }
 		    };
 		    /// \brief Returns a residual capacity map
 		    ///
 		    /// This function just returns a residual capacity map.
 		    ResidualCapacity residualCapacity() const {
 		      return ResidualCapacity(*this);
+		    }
 		  };
 		  /// \brief Returns a (read-only) Residual adaptor
 		  ///
 		  /// This function just returns a (read-only) \ref ResidualDigraph adaptor.
 		  /// \ingroup graph_adaptors
 		  /// \relates ResidualDigraph
 		    template<typename DGR, typename CM, typename FM>
 		  ResidualDigraph<DGR, CM, FM>
 		  residualDigraph(const DGR& digraph, const CM& capacity_map, FM& flow_map) {
 		    return ResidualDigraph<DGR, CM, FM> (digraph, capacity_map, flow_map);
+		  }
 		  template <typename DGR>
 		  class SplitNodesBase {
 		  public:
 		    typedef DGR Digraph;
 		    typedef DigraphAdaptorBase<const DGR> Parent;
 		    typedef SplitNodesBase Adaptor;
 		    typedef typename DGR::Node DigraphNode;
 		    typedef typename DGR::Arc DigraphArc;
 		    class Node;
 		    class Arc;
 		  private:
 		    template <typename T> class NodeMapBase;
 		    template <typename T> class ArcMapBase;
 		  public:
 		    class Node : public DigraphNode {
 		      friend class SplitNodesBase;
 		      template <typename T> friend class NodeMapBase;
 		    private:
 		      bool _in;
 		      Node(DigraphNode node, bool in)
 		        : DigraphNode(node), _in(in) {}
 		    public:
 		      Node() {}
 		      Node(Invalid) : DigraphNode(INVALID), _in(true) {}
 		      bool operator==(const Node& node) const {
 		        return DigraphNode::operator==(node) && _in == node._in;
+		      }
 		      bool operator!=(const Node& node) const {
 		        return !(*this == node);
+		      }
 		      bool operator<(const Node& node) const {
 		        return DigraphNode::operator<(node) ||
 		          (DigraphNode::operator==(node) && _in < node._in);
+		      }
 		    };
 		    class Arc {
 		      friend class SplitNodesBase;
 		      template <typename T> friend class ArcMapBase;
 		    private:
 		      typedef BiVariant<DigraphArc, DigraphNode> ArcImpl;
 		      explicit Arc(const DigraphArc& arc) : _item(arc) {}
 		      explicit Arc(const DigraphNode& node) : _item(node) {}
 		      ArcImpl _item;
 		    public:
 		      Arc() {}
 		      Arc(Invalid) : _item(DigraphArc(INVALID)) {}
 		      bool operator==(const Arc& arc) const {
 		        if (_item.firstState()) {
 		          if (arc._item.firstState()) {
 		            return _item.first() == arc._item.first();
+		          }
 		        } else {
 		          if (arc._item.secondState()) {
 		            return _item.second() == arc._item.second();
+		          }
+		        }
 		        return false;
+		      }
 		      bool operator!=(const Arc& arc) const {
 		        return !(*this == arc);
+		      }
 		      bool operator<(const Arc& arc) const {
 		        if (_item.firstState()) {
 		          if (arc._item.firstState()) {
 		            return _item.first() < arc._item.first();
+		          }
 		          return false;
 		        } else {
 		          if (arc._item.secondState()) {
 		            return _item.second() < arc._item.second();
+		          }
 		          return true;
+		        }
+		      }
 		      operator DigraphArc() const { return _item.first(); }
 		      operator DigraphNode() const { return _item.second(); }
 		    };

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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