diff --git a/lemon/Makefile.am b/lemon/Makefile.am
--- a/lemon/Makefile.am
+++ b/lemon/Makefile.am
@@ -30,6 +30,7 @@
         lemon/dijkstra.h \
         lemon/dim2.h \
         lemon/dimacs.h \
+	lemon/edge_set.h \
 	lemon/elevator.h \
 	lemon/error.h \
 	lemon/full_graph.h \
@@ -60,6 +61,7 @@
 	lemon/bits/base_extender.h \
         lemon/bits/bezier.h \
 	lemon/bits/default_map.h \
+	lemon/bits/edge_set_extender.h \
         lemon/bits/enable_if.h \
 	lemon/bits/graph_adaptor_extender.h \
 	lemon/bits/graph_extender.h \
diff --git a/lemon/bits/edge_set_extender.h b/lemon/bits/edge_set_extender.h
new file mode 100644
--- /dev/null
+++ b/lemon/bits/edge_set_extender.h
@@ -0,0 +1,628 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2008
+ * 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.
+ *
+ */
+
+#ifndef LEMON_BITS_EDGE_SET_EXTENDER_H
+#define LEMON_BITS_EDGE_SET_EXTENDER_H
+
+#include <lemon/error.h>
+#include <lemon/bits/default_map.h>
+
+///\ingroup digraphbits
+///\file
+///\brief Extenders for the arc set types
+namespace lemon {
+
+  /// \ingroup digraphbits
+  ///
+  /// \brief Extender for the ArcSets
+  template <typename Base>
+  class ArcSetExtender : public Base {
+  public:
+
+    typedef Base Parent;
+    typedef ArcSetExtender Digraph;
+
+    // Base extensions
+
+    typedef typename Parent::Node Node;
+    typedef typename Parent::Arc Arc;
+
+    int maxId(Node) const {
+      return Parent::maxNodeId();
+    }
+
+    int maxId(Arc) const {
+      return Parent::maxArcId();
+    }
+
+    Node fromId(int id, Node) const {
+      return Parent::nodeFromId(id);
+    }
+
+    Arc fromId(int id, Arc) const {
+      return Parent::arcFromId(id);
+    }
+
+    Node oppositeNode(const Node &n, const Arc &e) const {
+      if (n == Parent::source(e))
+	return Parent::target(e);
+      else if(n==Parent::target(e))
+	return Parent::source(e);
+      else
+	return INVALID;
+    }
+
+
+    // Alteration notifier extensions
+
+    /// The arc observer registry.
+    typedef AlterationNotifier<ArcSetExtender, Arc> ArcNotifier;
+
+  protected:
+
+    mutable ArcNotifier arc_notifier;
+
+  public:
+
+    using Parent::notifier;
+
+    /// \brief Gives back the arc alteration notifier.
+    ///
+    /// Gives back the arc alteration notifier.
+    ArcNotifier& notifier(Arc) const {
+      return arc_notifier;
+    }
+
+    // Iterable extensions
+
+    class NodeIt : public Node { 
+      const Digraph* digraph;
+    public:
+
+      NodeIt() {}
+
+      NodeIt(Invalid i) : Node(i) { }
+
+      explicit NodeIt(const Digraph& _graph) : digraph(&_graph) {
+	_graph.first(static_cast<Node&>(*this));
+      }
+
+      NodeIt(const Digraph& _graph, const Node& node) 
+	: Node(node), digraph(&_graph) {}
+
+      NodeIt& operator++() { 
+	digraph->next(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class ArcIt : public Arc { 
+      const Digraph* digraph;
+    public:
+
+      ArcIt() { }
+
+      ArcIt(Invalid i) : Arc(i) { }
+
+      explicit ArcIt(const Digraph& _graph) : digraph(&_graph) {
+	_graph.first(static_cast<Arc&>(*this));
+      }
+
+      ArcIt(const Digraph& _graph, const Arc& e) : 
+	Arc(e), digraph(&_graph) { }
+
+      ArcIt& operator++() { 
+	digraph->next(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class OutArcIt : public Arc { 
+      const Digraph* digraph;
+    public:
+
+      OutArcIt() { }
+
+      OutArcIt(Invalid i) : Arc(i) { }
+
+      OutArcIt(const Digraph& _graph, const Node& node) 
+	: digraph(&_graph) {
+	_graph.firstOut(*this, node);
+      }
+
+      OutArcIt(const Digraph& _graph, const Arc& arc) 
+	: Arc(arc), digraph(&_graph) {}
+
+      OutArcIt& operator++() { 
+	digraph->nextOut(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class InArcIt : public Arc { 
+      const Digraph* digraph;
+    public:
+
+      InArcIt() { }
+
+      InArcIt(Invalid i) : Arc(i) { }
+
+      InArcIt(const Digraph& _graph, const Node& node) 
+	: digraph(&_graph) {
+	_graph.firstIn(*this, node);
+      }
+
+      InArcIt(const Digraph& _graph, const Arc& arc) : 
+	Arc(arc), digraph(&_graph) {}
+
+      InArcIt& operator++() { 
+	digraph->nextIn(*this);
+	return *this; 
+      }
+
+    };
+
+    /// \brief Base node of the iterator
+    ///
+    /// Returns the base node (ie. the source in this case) of the iterator
+    Node baseNode(const OutArcIt &e) const {
+      return Parent::source(static_cast<const Arc&>(e));
+    }
+    /// \brief Running node of the iterator
+    ///
+    /// Returns the running node (ie. the target in this case) of the
+    /// iterator
+    Node runningNode(const OutArcIt &e) const {
+      return Parent::target(static_cast<const Arc&>(e));
+    }
+
+    /// \brief Base node of the iterator
+    ///
+    /// Returns the base node (ie. the target in this case) of the iterator
+    Node baseNode(const InArcIt &e) const {
+      return Parent::target(static_cast<const Arc&>(e));
+    }
+    /// \brief Running node of the iterator
+    ///
+    /// Returns the running node (ie. the source in this case) of the
+    /// iterator
+    Node runningNode(const InArcIt &e) const {
+      return Parent::source(static_cast<const Arc&>(e));
+    }
+
+    using Parent::first;
+
+    // Mappable extension
+    
+    template <typename _Value>
+    class ArcMap 
+      : public MapExtender<DefaultMap<Digraph, Arc, _Value> > {
+    public:
+      typedef ArcSetExtender Digraph;
+      typedef MapExtender<DefaultMap<Digraph, Arc, _Value> > Parent;
+
+      explicit ArcMap(const Digraph& _g) 
+	: Parent(_g) {}
+      ArcMap(const Digraph& _g, const _Value& _v) 
+	: Parent(_g, _v) {}
+
+      ArcMap& operator=(const ArcMap& cmap) {
+	return operator=<ArcMap>(cmap);
+      }
+
+      template <typename CMap>
+      ArcMap& operator=(const CMap& cmap) {
+        Parent::operator=(cmap);
+	return *this;
+      }
+
+    };
+
+
+    // Alteration extension
+
+    Arc addArc(const Node& from, const Node& to) {
+      Arc arc = Parent::addArc(from, to);
+      notifier(Arc()).add(arc);
+      return arc;
+    }
+    
+    void clear() {
+      notifier(Arc()).clear();
+      Parent::clear();
+    }
+
+    void erase(const Arc& arc) {
+      notifier(Arc()).erase(arc);
+      Parent::erase(arc);
+    }
+
+    ArcSetExtender() {
+      arc_notifier.setContainer(*this);
+    }
+
+    ~ArcSetExtender() {
+      arc_notifier.clear();
+    }
+
+  };
+
+
+  /// \ingroup digraphbits
+  ///
+  /// \brief Extender for the EdgeSets
+  template <typename Base>
+  class EdgeSetExtender : public Base {
+
+  public:
+
+    typedef Base Parent;
+    typedef EdgeSetExtender Digraph;
+
+    typedef typename Parent::Node Node;
+    typedef typename Parent::Arc Arc;
+    typedef typename Parent::Edge Edge;
+
+
+    int maxId(Node) const {
+      return Parent::maxNodeId();
+    }
+
+    int maxId(Arc) const {
+      return Parent::maxArcId();
+    }
+
+    int maxId(Edge) const {
+      return Parent::maxEdgeId();
+    }
+
+    Node fromId(int id, Node) const {
+      return Parent::nodeFromId(id);
+    }
+
+    Arc fromId(int id, Arc) const {
+      return Parent::arcFromId(id);
+    }
+
+    Edge fromId(int id, Edge) const {
+      return Parent::edgeFromId(id);
+    }
+
+    Node oppositeNode(const Node &n, const Edge &e) const {
+      if( n == Parent::u(e))
+	return Parent::v(e);
+      else if( n == Parent::v(e))
+	return Parent::u(e);
+      else
+	return INVALID;
+    }
+
+    Arc oppositeArc(const Arc &e) const {
+      return Parent::direct(e, !Parent::direction(e));
+    }
+
+    using Parent::direct;
+    Arc direct(const Edge &e, const Node &s) const {
+      return Parent::direct(e, Parent::u(e) == s);
+    }
+
+    typedef AlterationNotifier<EdgeSetExtender, Arc> ArcNotifier;
+    typedef AlterationNotifier<EdgeSetExtender, Edge> EdgeNotifier;
+
+
+  protected:
+
+    mutable ArcNotifier arc_notifier;
+    mutable EdgeNotifier edge_notifier;
+
+  public:
+
+    using Parent::notifier;
+    
+    ArcNotifier& notifier(Arc) const {
+      return arc_notifier;
+    }
+
+    EdgeNotifier& notifier(Edge) const {
+      return edge_notifier;
+    }
+
+
+    class NodeIt : public Node { 
+      const Digraph* digraph;
+    public:
+
+      NodeIt() {}
+
+      NodeIt(Invalid i) : Node(i) { }
+
+      explicit NodeIt(const Digraph& _graph) : digraph(&_graph) {
+	_graph.first(static_cast<Node&>(*this));
+      }
+
+      NodeIt(const Digraph& _graph, const Node& node) 
+	: Node(node), digraph(&_graph) {}
+
+      NodeIt& operator++() { 
+	digraph->next(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class ArcIt : public Arc { 
+      const Digraph* digraph;
+    public:
+
+      ArcIt() { }
+
+      ArcIt(Invalid i) : Arc(i) { }
+
+      explicit ArcIt(const Digraph& _graph) : digraph(&_graph) {
+	_graph.first(static_cast<Arc&>(*this));
+      }
+
+      ArcIt(const Digraph& _graph, const Arc& e) : 
+	Arc(e), digraph(&_graph) { }
+
+      ArcIt& operator++() { 
+	digraph->next(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class OutArcIt : public Arc { 
+      const Digraph* digraph;
+    public:
+
+      OutArcIt() { }
+
+      OutArcIt(Invalid i) : Arc(i) { }
+
+      OutArcIt(const Digraph& _graph, const Node& node) 
+	: digraph(&_graph) {
+	_graph.firstOut(*this, node);
+      }
+
+      OutArcIt(const Digraph& _graph, const Arc& arc) 
+	: Arc(arc), digraph(&_graph) {}
+
+      OutArcIt& operator++() { 
+	digraph->nextOut(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class InArcIt : public Arc { 
+      const Digraph* digraph;
+    public:
+
+      InArcIt() { }
+
+      InArcIt(Invalid i) : Arc(i) { }
+
+      InArcIt(const Digraph& _graph, const Node& node) 
+	: digraph(&_graph) {
+	_graph.firstIn(*this, node);
+      }
+
+      InArcIt(const Digraph& _graph, const Arc& arc) : 
+	Arc(arc), digraph(&_graph) {}
+
+      InArcIt& operator++() { 
+	digraph->nextIn(*this);
+	return *this; 
+      }
+
+    };
+
+
+    class EdgeIt : public Parent::Edge { 
+      const Digraph* digraph;
+    public:
+
+      EdgeIt() { }
+
+      EdgeIt(Invalid i) : Edge(i) { }
+
+      explicit EdgeIt(const Digraph& _graph) : digraph(&_graph) {
+	_graph.first(static_cast<Edge&>(*this));
+      }
+
+      EdgeIt(const Digraph& _graph, const Edge& e) : 
+	Edge(e), digraph(&_graph) { }
+
+      EdgeIt& operator++() { 
+	digraph->next(*this);
+	return *this; 
+      }
+
+    };
+
+    class IncEdgeIt : public Parent::Edge {
+      friend class EdgeSetExtender;
+      const Digraph* digraph;
+      bool direction;
+    public:
+
+      IncEdgeIt() { }
+
+      IncEdgeIt(Invalid i) : Edge(i), direction(false) { }
+
+      IncEdgeIt(const Digraph& _graph, const Node &n) : digraph(&_graph) {
+	_graph.firstInc(*this, direction, n);
+      }
+
+      IncEdgeIt(const Digraph& _graph, const Edge &ue, const Node &n)
+	: digraph(&_graph), Edge(ue) {
+	direction = (_graph.source(ue) == n);
+      }
+
+      IncEdgeIt& operator++() {
+	digraph->nextInc(*this, direction);
+	return *this; 
+      }
+    };
+
+    /// \brief Base node of the iterator
+    ///
+    /// Returns the base node (ie. the source in this case) of the iterator
+    Node baseNode(const OutArcIt &e) const {
+      return Parent::source(static_cast<const Arc&>(e));
+    }
+    /// \brief Running node of the iterator
+    ///
+    /// Returns the running node (ie. the target in this case) of the
+    /// iterator
+    Node runningNode(const OutArcIt &e) const {
+      return Parent::target(static_cast<const Arc&>(e));
+    }
+
+    /// \brief Base node of the iterator
+    ///
+    /// Returns the base node (ie. the target in this case) of the iterator
+    Node baseNode(const InArcIt &e) const {
+      return Parent::target(static_cast<const Arc&>(e));
+    }
+    /// \brief Running node of the iterator
+    ///
+    /// Returns the running node (ie. the source in this case) of the
+    /// iterator
+    Node runningNode(const InArcIt &e) const {
+      return Parent::source(static_cast<const Arc&>(e));
+    }
+
+    /// Base node of the iterator
+    ///
+    /// Returns the base node of the iterator
+    Node baseNode(const IncEdgeIt &e) const {
+      return e.direction ? u(e) : v(e);
+    }
+    /// Running node of the iterator
+    ///
+    /// Returns the running node of the iterator
+    Node runningNode(const IncEdgeIt &e) const {
+      return e.direction ? v(e) : u(e);
+    }
+
+
+    template <typename _Value>
+    class ArcMap 
+      : public MapExtender<DefaultMap<Digraph, Arc, _Value> > {
+    public:
+      typedef EdgeSetExtender Digraph;
+      typedef MapExtender<DefaultMap<Digraph, Arc, _Value> > Parent;
+
+      ArcMap(const Digraph& _g) 
+	: Parent(_g) {}
+      ArcMap(const Digraph& _g, const _Value& _v) 
+	: Parent(_g, _v) {}
+
+      ArcMap& operator=(const ArcMap& cmap) {
+	return operator=<ArcMap>(cmap);
+      }
+
+      template <typename CMap>
+      ArcMap& operator=(const CMap& cmap) {
+        Parent::operator=(cmap);
+	return *this;
+      }
+
+    };
+
+
+    template <typename _Value>
+    class EdgeMap 
+      : public MapExtender<DefaultMap<Digraph, Edge, _Value> > {
+    public:
+      typedef EdgeSetExtender Digraph;
+      typedef MapExtender<DefaultMap<Digraph, Edge, _Value> > Parent;
+
+      EdgeMap(const Digraph& _g) 
+	: Parent(_g) {}
+
+      EdgeMap(const Digraph& _g, const _Value& _v) 
+	: Parent(_g, _v) {}
+
+      EdgeMap& operator=(const EdgeMap& cmap) {
+	return operator=<EdgeMap>(cmap);
+      }
+
+      template <typename CMap>
+      EdgeMap& operator=(const CMap& cmap) {
+        Parent::operator=(cmap);
+	return *this;
+      }
+
+    };
+
+
+    // Alteration extension
+
+    Edge addEdge(const Node& from, const Node& to) {
+      Edge edge = Parent::addEdge(from, to);
+      notifier(Edge()).add(edge);
+      std::vector<Arc> arcs;
+      arcs.push_back(Parent::direct(edge, true));
+      arcs.push_back(Parent::direct(edge, false));
+      notifier(Arc()).add(arcs);
+      return edge;
+    }
+    
+    void clear() {
+      notifier(Arc()).clear();
+      notifier(Edge()).clear();
+      Parent::clear();
+    }
+
+    void erase(const Edge& edge) {
+      std::vector<Arc> arcs;
+      arcs.push_back(Parent::direct(edge, true));
+      arcs.push_back(Parent::direct(edge, false));
+      notifier(Arc()).erase(arcs);
+      notifier(Edge()).erase(edge);
+      Parent::erase(edge);
+    }
+
+
+    EdgeSetExtender() {
+      arc_notifier.setContainer(*this);
+      edge_notifier.setContainer(*this);
+    }
+
+    ~EdgeSetExtender() {
+      edge_notifier.clear();
+      arc_notifier.clear();
+    }
+    
+  };
+
+}
+
+#endif
diff --git a/lemon/edge_set.h b/lemon/edge_set.h
new file mode 100644
--- /dev/null
+++ b/lemon/edge_set.h
@@ -0,0 +1,1410 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2008
+ * 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.
+ *
+ */
+
+#ifndef LEMON_EDGE_SET_H
+#define LEMON_EDGE_SET_H
+
+#include <lemon/core.h>
+#include <lemon/bits/edge_set_extender.h>
+
+/// \ingroup semi_adaptors
+/// \file
+/// \brief ArcSet and EdgeSet classes.
+///
+/// Graphs which use another graph's node-set as own.
+namespace lemon {
+
+  template <typename _Graph>
+  class ListArcSetBase {
+  public:
+
+    typedef _Graph Graph;
+    typedef typename Graph::Node Node;
+    typedef typename Graph::NodeIt NodeIt;
+
+  protected:
+
+    struct NodeT {
+      int first_out, first_in;
+      NodeT() : first_out(-1), first_in(-1) {}
+    };
+
+    typedef typename ItemSetTraits<Graph, Node>::
+    template Map<NodeT>::Type NodesImplBase;
+
+    NodesImplBase* nodes;
+
+    struct ArcT {
+      Node source, target;
+      int next_out, next_in;
+      int prev_out, prev_in;
+      ArcT() : prev_out(-1), prev_in(-1) {}
+    };
+
+    std::vector<ArcT> arcs;
+
+    int first_arc;
+    int first_free_arc;
+
+    const Graph* graph;
+
+    void initalize(const Graph& _graph, NodesImplBase& _nodes) {
+      graph = &_graph;
+      nodes = &_nodes;
+    }
+
+  public:
+
+    class Arc {
+      friend class ListArcSetBase<Graph>;
+    protected:
+      Arc(int _id) : id(_id) {}
+      int id;
+    public:
+      Arc() {}
+      Arc(Invalid) : id(-1) {}
+      bool operator==(const Arc& arc) const { return id == arc.id; }
+      bool operator!=(const Arc& arc) const { return id != arc.id; }
+      bool operator<(const Arc& arc) const { return id < arc.id; }
+    };
+
+    ListArcSetBase() : first_arc(-1), first_free_arc(-1) {}
+
+    Arc addArc(const Node& u, const Node& v) {
+      int n;
+      if (first_free_arc == -1) {
+        n = arcs.size();
+        arcs.push_back(ArcT());
+      } else {
+        n = first_free_arc;
+        first_free_arc = arcs[first_free_arc].next_in;
+      }
+      arcs[n].next_in = (*nodes)[v].first_in;
+      if ((*nodes)[v].first_in != -1) {
+        arcs[(*nodes)[v].first_in].prev_in = n;
+      }
+      (*nodes)[v].first_in = n;
+      arcs[n].next_out = (*nodes)[u].first_out;
+      if ((*nodes)[u].first_out != -1) {
+        arcs[(*nodes)[u].first_out].prev_out = n;
+      }
+      (*nodes)[u].first_out = n;
+      arcs[n].source = u;
+      arcs[n].target = v;
+      return Arc(n);
+    }
+
+    void erase(const Arc& arc) {
+      int n = arc.id;
+      if (arcs[n].prev_in != -1) {
+        arcs[arcs[n].prev_in].next_in = arcs[n].next_in;
+      } else {
+        (*nodes)[arcs[n].target].first_in = arcs[n].next_in;
+      }
+      if (arcs[n].next_in != -1) {
+        arcs[arcs[n].next_in].prev_in = arcs[n].prev_in;
+      }
+
+      if (arcs[n].prev_out != -1) {
+        arcs[arcs[n].prev_out].next_out = arcs[n].next_out;
+      } else {
+        (*nodes)[arcs[n].source].first_out = arcs[n].next_out;
+      }
+      if (arcs[n].next_out != -1) {
+        arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;
+      }
+
+    }
+
+    void clear() {
+      Node node;
+      for (first(node); node != INVALID; next(node)) {
+        (*nodes)[node].first_in = -1;
+        (*nodes)[node].first_out = -1;
+      }
+      arcs.clear();
+      first_arc = -1;
+      first_free_arc = -1;
+    }
+
+    void first(Node& node) const {
+      graph->first(node);
+    }
+
+    void next(Node& node) const {
+      graph->next(node);
+    }
+
+    void first(Arc& arc) const {
+      Node node;
+      first(node);
+      while (node != INVALID && (*nodes)[node].first_in == -1) {
+        next(node);
+      }
+      arc.id = (node == INVALID) ? -1 : (*nodes)[node].first_in;
+    }
+
+    void next(Arc& arc) const {
+      if (arcs[arc.id].next_in != -1) {
+        arc.id = arcs[arc.id].next_in;
+      } else {
+        Node node = arcs[arc.id].target;
+        next(node);
+        while (node != INVALID && (*nodes)[node].first_in == -1) {
+          next(node);
+        }
+        arc.id = (node == INVALID) ? -1 : (*nodes)[node].first_in;
+      }
+    }
+
+    void firstOut(Arc& arc, const Node& node) const {
+      arc.id = (*nodes)[node].first_out;
+    }
+
+    void nextOut(Arc& arc) const {
+      arc.id = arcs[arc.id].next_out;
+    }
+
+    void firstIn(Arc& arc, const Node& node) const {
+      arc.id = (*nodes)[node].first_in;
+    }
+
+    void nextIn(Arc& arc) const {
+      arc.id = arcs[arc.id].next_in;
+    }
+
+    int id(const Node& node) const { return graph->id(node); }
+    int id(const Arc& arc) const { return arc.id; }
+
+    Node nodeFromId(int ix) const { return graph->nodeFromId(ix); }
+    Arc arcFromId(int ix) const { return Arc(ix); }
+
+    int maxNodeId() const { return graph->maxNodeId(); };
+    int maxArcId() const { return arcs.size() - 1; }
+
+    Node source(const Arc& arc) const { return arcs[arc.id].source;}
+    Node target(const Arc& arc) const { return arcs[arc.id].target;}
+
+    typedef typename ItemSetTraits<Graph, Node>::ItemNotifier NodeNotifier;
+
+    NodeNotifier& notifier(Node) const {
+      return graph->notifier(Node());
+    }
+
+    template <typename _Value>
+    class NodeMap : public Graph::template NodeMap<_Value> {
+    public:
+
+      typedef typename _Graph::template NodeMap<_Value> Parent;
+
+      explicit NodeMap(const ListArcSetBase<Graph>& arcset)
+        : Parent(*arcset.graph) {}
+
+      NodeMap(const ListArcSetBase<Graph>& arcset, const _Value& value)
+        : Parent(*arcset.graph, value) {}
+
+      NodeMap& operator=(const NodeMap& cmap) {
+        return operator=<NodeMap>(cmap);
+      }
+
+      template <typename CMap>
+      NodeMap& operator=(const CMap& cmap) {
+        Parent::operator=(cmap);
+        return *this;
+      }
+    };
+
+  };
+
+  /// \ingroup semi_adaptors
+  ///
+  /// \brief Digraph using a node set of another digraph or graph and
+  /// an own arc set.
+  ///
+  /// This structure can be used to establish another directed graph
+  /// over a node set of an existing one. This class uses the same
+  /// Node type as the underlying graph, and each valid node of the
+  /// original graph is valid in this arc set, therefore the node
+  /// objects of the original graph can be used directly with this
+  /// class. The node handling functions (id handling, observing, and
+  /// iterators) works equivalently as in the original graph.
+  ///
+  /// This implementation is based on doubly-linked lists, from each
+  /// node the outgoing and the incoming arcs make up lists, therefore
+  /// one arc can be erased in constant time. It also makes possible,
+  /// that node can be removed from the underlying graph, in this case
+  /// all arcs incident to the given node is erased from the arc set.
+  ///
+  /// \param _Graph The type of the graph which shares its node set with
+  /// this class. Its interface must conform to the
+  /// \ref concepts::Digraph "Digraph" or \ref concepts::Graph "Graph"
+  /// concept.
+  ///
+  /// This class is fully conform to the \ref concepts::Digraph
+  /// "Digraph" concept.
+  template <typename _Graph>
+  class ListArcSet : public ArcSetExtender<ListArcSetBase<_Graph> > {
+
+  public:
+
+    typedef ArcSetExtender<ListArcSetBase<_Graph> > Parent;
+
+    typedef typename Parent::Node Node;
+    typedef typename Parent::Arc Arc;
+
+    typedef _Graph Graph;
+
+
+    typedef typename Parent::NodesImplBase NodesImplBase;
+
+    void eraseNode(const Node& node) {
+      Arc arc;
+      Parent::firstOut(arc, node);
+      while (arc != INVALID ) {
+        erase(arc);
+        Parent::firstOut(arc, node);
+      }
+
+      Parent::firstIn(arc, node);
+      while (arc != INVALID ) {
+        erase(arc);
+        Parent::firstIn(arc, node);
+      }
+    }
+
+    void clearNodes() {
+      Parent::clear();
+    }
+
+    class NodesImpl : public NodesImplBase {
+    public:
+      typedef NodesImplBase Parent;
+
+      NodesImpl(const Graph& graph, ListArcSet& arcset)
+        : Parent(graph), _arcset(arcset) {}
+
+      virtual ~NodesImpl() {}
+
+    protected:
+
+      virtual void erase(const Node& node) {
+        _arcset.eraseNode(node);
+        Parent::erase(node);
+      }
+      virtual void erase(const std::vector<Node>& nodes) {
+        for (int i = 0; i < int(nodes.size()); ++i) {
+          _arcset.eraseNode(nodes[i]);
+        }
+        Parent::erase(nodes);
+      }
+      virtual void clear() {
+        _arcset.clearNodes();
+        Parent::clear();
+      }
+
+    private:
+      ListArcSet& _arcset;
+    };
+
+    NodesImpl nodes;
+
+  public:
+
+    /// \brief Constructor of the ArcSet.
+    ///
+    /// Constructor of the ArcSet.
+    ListArcSet(const Graph& graph) : nodes(graph, *this) {
+      Parent::initalize(graph, nodes);
+    }
+
+    /// \brief Add a new arc to the digraph.
+    ///
+    /// Add a new arc to the digraph with source node \c s
+    /// and target node \c t.
+    /// \return the new arc.
+    Arc addArc(const Node& s, const Node& t) {
+      return Parent::addArc(s, t);
+    }
+
+    /// \brief Erase an arc from the digraph.
+    ///
+    /// Erase an arc \c a from the digraph.
+    void erase(const Arc& a) {
+      return Parent::erase(a);
+    }
+
+  };
+
+  template <typename _Graph>
+  class ListEdgeSetBase {
+  public:
+
+    typedef _Graph Graph;
+    typedef typename Graph::Node Node;
+    typedef typename Graph::NodeIt NodeIt;
+
+  protected:
+
+    struct NodeT {
+      int first_out;
+      NodeT() : first_out(-1) {}
+    };
+
+    typedef typename ItemSetTraits<Graph, Node>::
+    template Map<NodeT>::Type NodesImplBase;
+
+    NodesImplBase* nodes;
+
+    struct ArcT {
+      Node target;
+      int prev_out, next_out;
+      ArcT() : prev_out(-1), next_out(-1) {}
+    };
+
+    std::vector<ArcT> arcs;
+
+    int first_arc;
+    int first_free_arc;
+
+    const Graph* graph;
+
+    void initalize(const Graph& _graph, NodesImplBase& _nodes) {
+      graph = &_graph;
+      nodes = &_nodes;
+    }
+
+  public:
+
+    class Edge {
+      friend class ListEdgeSetBase;
+    protected:
+
+      int id;
+      explicit Edge(int _id) { id = _id;}
+
+    public:
+      Edge() {}
+      Edge (Invalid) { id = -1; }
+      bool operator==(const Edge& arc) const {return id == arc.id;}
+      bool operator!=(const Edge& arc) const {return id != arc.id;}
+      bool operator<(const Edge& arc) const {return id < arc.id;}
+    };
+
+    class Arc {
+      friend class ListEdgeSetBase;
+    protected:
+      Arc(int _id) : id(_id) {}
+      int id;
+    public:
+      operator Edge() const { return edgeFromId(id / 2); }
+
+      Arc() {}
+      Arc(Invalid) : id(-1) {}
+      bool operator==(const Arc& arc) const { return id == arc.id; }
+      bool operator!=(const Arc& arc) const { return id != arc.id; }
+      bool operator<(const Arc& arc) const { return id < arc.id; }
+    };
+
+    ListEdgeSetBase() : first_arc(-1), first_free_arc(-1) {}
+
+    Edge addEdge(const Node& u, const Node& v) {
+      int n;
+
+      if (first_free_arc == -1) {
+        n = arcs.size();
+        arcs.push_back(ArcT());
+        arcs.push_back(ArcT());
+      } else {
+        n = first_free_arc;
+        first_free_arc = arcs[n].next_out;
+      }
+
+      arcs[n].target = u;
+      arcs[n | 1].target = v;
+
+      arcs[n].next_out = (*nodes)[v].first_out;
+      if ((*nodes)[v].first_out != -1) {
+        arcs[(*nodes)[v].first_out].prev_out = n;
+      }
+      (*nodes)[v].first_out = n;
+      arcs[n].prev_out = -1;
+
+      if ((*nodes)[u].first_out != -1) {
+        arcs[(*nodes)[u].first_out].prev_out = (n | 1);
+      }
+      arcs[n | 1].next_out = (*nodes)[u].first_out;
+      (*nodes)[u].first_out = (n | 1);
+      arcs[n | 1].prev_out = -1;
+
+      return Edge(n / 2);
+    }
+
+    void erase(const Edge& arc) {
+      int n = arc.id * 2;
+
+      if (arcs[n].next_out != -1) {
+        arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;
+      }
+
+      if (arcs[n].prev_out != -1) {
+        arcs[arcs[n].prev_out].next_out = arcs[n].next_out;
+      } else {
+        (*nodes)[arcs[n | 1].target].first_out = arcs[n].next_out;
+      }
+
+      if (arcs[n | 1].next_out != -1) {
+        arcs[arcs[n | 1].next_out].prev_out = arcs[n | 1].prev_out;
+      }
+
+      if (arcs[n | 1].prev_out != -1) {
+        arcs[arcs[n | 1].prev_out].next_out = arcs[n | 1].next_out;
+      } else {
+        (*nodes)[arcs[n].target].first_out = arcs[n | 1].next_out;
+      }
+
+      arcs[n].next_out = first_free_arc;
+      first_free_arc = n;
+
+    }
+
+    void clear() {
+      Node node;
+      for (first(node); node != INVALID; next(node)) {
+        (*nodes)[node].first_out = -1;
+      }
+      arcs.clear();
+      first_arc = -1;
+      first_free_arc = -1;
+    }
+
+    void first(Node& node) const {
+      graph->first(node);
+    }
+
+    void next(Node& node) const {
+      graph->next(node);
+    }
+
+    void first(Arc& arc) const {
+      Node node;
+      first(node);
+      while (node != INVALID && (*nodes)[node].first_out == -1) {
+        next(node);
+      }
+      arc.id = (node == INVALID) ? -1 : (*nodes)[node].first_out;
+    }
+
+    void next(Arc& arc) const {
+      if (arcs[arc.id].next_out != -1) {
+        arc.id = arcs[arc.id].next_out;
+      } else {
+        Node node = arcs[arc.id ^ 1].target;
+        next(node);
+        while(node != INVALID && (*nodes)[node].first_out == -1) {
+          next(node);
+        }
+        arc.id = (node == INVALID) ? -1 : (*nodes)[node].first_out;
+      }
+    }
+
+    void first(Edge& edge) const {
+      Node node;
+      first(node);
+      while (node != INVALID) {
+        edge.id = (*nodes)[node].first_out;
+        while ((edge.id & 1) != 1) {
+          edge.id = arcs[edge.id].next_out;
+        }
+        if (edge.id != -1) {
+          edge.id /= 2;
+          return;
+        }
+        next(node);
+      }
+      edge.id = -1;
+    }
+
+    void next(Edge& edge) const {
+      Node node = arcs[edge.id * 2].target;
+      edge.id = arcs[(edge.id * 2) | 1].next_out;
+      while ((edge.id & 1) != 1) {
+        edge.id = arcs[edge.id].next_out;
+      }
+      if (edge.id != -1) {
+        edge.id /= 2;
+        return;
+      }
+      next(node);
+      while (node != INVALID) {
+        edge.id = (*nodes)[node].first_out;
+        while ((edge.id & 1) != 1) {
+          edge.id = arcs[edge.id].next_out;
+        }
+        if (edge.id != -1) {
+          edge.id /= 2;
+          return;
+        }
+        next(node);
+      }
+      edge.id = -1;
+    }
+
+    void firstOut(Arc& arc, const Node& node) const {
+      arc.id = (*nodes)[node].first_out;
+    }
+
+    void nextOut(Arc& arc) const {
+      arc.id = arcs[arc.id].next_out;
+    }
+
+    void firstIn(Arc& arc, const Node& node) const {
+      arc.id = (((*nodes)[node].first_out) ^ 1);
+      if (arc.id == -2) arc.id = -1;
+    }
+
+    void nextIn(Arc& arc) const {
+      arc.id = ((arcs[arc.id ^ 1].next_out) ^ 1);
+      if (arc.id == -2) arc.id = -1;
+    }
+
+    void firstInc(Edge &arc, bool& dir, const Node& node) const {
+      int de = (*nodes)[node].first_out;
+      if (de != -1 ) {
+        arc.id = de / 2;
+        dir = ((de & 1) == 1);
+      } else {
+        arc.id = -1;
+        dir = true;
+      }
+    }
+    void nextInc(Edge &arc, bool& dir) const {
+      int de = (arcs[(arc.id * 2) | (dir ? 1 : 0)].next_out);
+      if (de != -1 ) {
+        arc.id = de / 2;
+        dir = ((de & 1) == 1);
+      } else {
+        arc.id = -1;
+        dir = true;
+      }
+    }
+
+    static bool direction(Arc arc) {
+      return (arc.id & 1) == 1;
+    }
+
+    static Arc direct(Edge edge, bool dir) {
+      return Arc(edge.id * 2 + (dir ? 1 : 0));
+    }
+
+    int id(const Node& node) const { return graph->id(node); }
+    static int id(Arc e) { return e.id; }
+    static int id(Edge e) { return e.id; }
+
+    Node nodeFromId(int id) const { return graph->nodeFromId(id); }
+    static Arc arcFromId(int id) { return Arc(id);}
+    static Edge edgeFromId(int id) { return Edge(id);}
+
+    int maxNodeId() const { return graph->maxNodeId(); };
+    int maxEdgeId() const { return arcs.size() / 2 - 1; }
+    int maxArcId() const { return arcs.size()-1; }
+
+    Node source(Arc e) const { return arcs[e.id ^ 1].target; }
+    Node target(Arc e) const { return arcs[e.id].target; }
+
+    Node u(Edge e) const { return arcs[2 * e.id].target; }
+    Node v(Edge e) const { return arcs[2 * e.id + 1].target; }
+
+    typedef typename ItemSetTraits<Graph, Node>::ItemNotifier NodeNotifier;
+
+    NodeNotifier& notifier(Node) const {
+      return graph->notifier(Node());
+    }
+
+    template <typename _Value>
+    class NodeMap : public Graph::template NodeMap<_Value> {
+    public:
+
+      typedef typename _Graph::template NodeMap<_Value> Parent;
+
+      explicit NodeMap(const ListEdgeSetBase<Graph>& arcset)
+        : Parent(*arcset.graph) {}
+
+      NodeMap(const ListEdgeSetBase<Graph>& arcset, const _Value& value)
+        : Parent(*arcset.graph, value) {}
+
+      NodeMap& operator=(const NodeMap& cmap) {
+        return operator=<NodeMap>(cmap);
+      }
+
+      template <typename CMap>
+      NodeMap& operator=(const CMap& cmap) {
+        Parent::operator=(cmap);
+        return *this;
+      }
+    };
+
+  };
+
+  /// \ingroup semi_adaptors
+  ///
+  /// \brief Graph using a node set of another digraph or graph and an
+  /// own edge set.
+  ///
+  /// This structure can be used to establish another graph over a
+  /// node set of an existing one. This class uses the same Node type
+  /// as the underlying graph, and each valid node of the original
+  /// graph is valid in this arc set, therefore the node objects of
+  /// the original graph can be used directly with this class. The
+  /// node handling functions (id handling, observing, and iterators)
+  /// works equivalently as in the original graph.
+  ///
+  /// This implementation is based on doubly-linked lists, from each
+  /// node the incident edges make up lists, therefore one edge can be
+  /// erased in constant time. It also makes possible, that node can
+  /// be removed from the underlying graph, in this case all edges
+  /// incident to the given node is erased from the arc set.
+  ///
+  /// \param _Graph The type of the graph which shares its node set
+  /// with this class. Its interface must conform to the
+  /// \ref concepts::Digraph "Digraph" or \ref concepts::Graph "Graph"
+  /// concept.
+  ///
+  /// This class is fully conform to the \ref concepts::Graph "Graph"
+  /// concept.
+  template <typename _Graph>
+  class ListEdgeSet : public EdgeSetExtender<ListEdgeSetBase<_Graph> > {
+
+  public:
+
+    typedef EdgeSetExtender<ListEdgeSetBase<_Graph> > Parent;
+
+    typedef typename Parent::Node Node;
+    typedef typename Parent::Arc Arc;
+    typedef typename Parent::Edge Edge;
+
+    typedef _Graph Graph;
+
+
+    typedef typename Parent::NodesImplBase NodesImplBase;
+
+    void eraseNode(const Node& node) {
+      Arc arc;
+      Parent::firstOut(arc, node);
+      while (arc != INVALID ) {
+        erase(arc);
+        Parent::firstOut(arc, node);
+      }
+
+    }
+
+    void clearNodes() {
+      Parent::clear();
+    }
+
+    class NodesImpl : public NodesImplBase {
+    public:
+      typedef NodesImplBase Parent;
+
+      NodesImpl(const Graph& graph, ListEdgeSet& arcset)
+        : Parent(graph), _arcset(arcset) {}
+
+      virtual ~NodesImpl() {}
+
+    protected:
+
+      virtual void erase(const Node& node) {
+        _arcset.eraseNode(node);
+        Parent::erase(node);
+      }
+      virtual void erase(const std::vector<Node>& nodes) {
+        for (int i = 0; i < int(nodes.size()); ++i) {
+          _arcset.eraseNode(nodes[i]);
+        }
+        Parent::erase(nodes);
+      }
+      virtual void clear() {
+        _arcset.clearNodes();
+        Parent::clear();
+      }
+
+    private:
+      ListEdgeSet& _arcset;
+    };
+
+    NodesImpl nodes;
+
+  public:
+
+    /// \brief Constructor of the EdgeSet.
+    ///
+    /// Constructor of the EdgeSet.
+    ListEdgeSet(const Graph& graph) : nodes(graph, *this) {
+      Parent::initalize(graph, nodes);
+    }
+
+    /// \brief Add a new edge to the graph.
+    ///
+    /// Add a new edge to the graph with node \c u
+    /// and node \c v endpoints.
+    /// \return the new edge.
+    Edge addEdge(const Node& u, const Node& v) {
+      return Parent::addEdge(u, v);
+    }
+
+    /// \brief Erase an edge from the graph.
+    ///
+    /// Erase the edge \c e from the graph.
+    void erase(const Edge& e) {
+      return Parent::erase(e);
+    }
+
+  };
+
+  template <typename _Graph>
+  class SmartArcSetBase {
+  public:
+
+    typedef _Graph Graph;
+    typedef typename Graph::Node Node;
+    typedef typename Graph::NodeIt NodeIt;
+
+  protected:
+
+    struct NodeT {
+      int first_out, first_in;
+      NodeT() : first_out(-1), first_in(-1) {}
+    };
+
+    typedef typename ItemSetTraits<Graph, Node>::
+    template Map<NodeT>::Type NodesImplBase;
+
+    NodesImplBase* nodes;
+
+    struct ArcT {
+      Node source, target;
+      int next_out, next_in;
+      ArcT() {}
+    };
+
+    std::vector<ArcT> arcs;
+
+    const Graph* graph;
+
+    void initalize(const Graph& _graph, NodesImplBase& _nodes) {
+      graph = &_graph;
+      nodes = &_nodes;
+    }
+
+  public:
+
+    class Arc {
+      friend class SmartArcSetBase<Graph>;
+    protected:
+      Arc(int _id) : id(_id) {}
+      int id;
+    public:
+      Arc() {}
+      Arc(Invalid) : id(-1) {}
+      bool operator==(const Arc& arc) const { return id == arc.id; }
+      bool operator!=(const Arc& arc) const { return id != arc.id; }
+      bool operator<(const Arc& arc) const { return id < arc.id; }
+    };
+
+    SmartArcSetBase() {}
+
+    Arc addArc(const Node& u, const Node& v) {
+      int n = arcs.size();
+      arcs.push_back(ArcT());
+      arcs[n].next_in = (*nodes)[v].first_in;
+      (*nodes)[v].first_in = n;
+      arcs[n].next_out = (*nodes)[u].first_out;
+      (*nodes)[u].first_out = n;
+      arcs[n].source = u;
+      arcs[n].target = v;
+      return Arc(n);
+    }
+
+    void clear() {
+      Node node;
+      for (first(node); node != INVALID; next(node)) {
+        (*nodes)[node].first_in = -1;
+        (*nodes)[node].first_out = -1;
+      }
+      arcs.clear();
+    }
+
+    void first(Node& node) const {
+      graph->first(node);
+    }
+
+    void next(Node& node) const {
+      graph->next(node);
+    }
+
+    void first(Arc& arc) const {
+      arc.id = arcs.size() - 1;
+    }
+
+    void next(Arc& arc) const {
+      --arc.id;
+    }
+
+    void firstOut(Arc& arc, const Node& node) const {
+      arc.id = (*nodes)[node].first_out;
+    }
+
+    void nextOut(Arc& arc) const {
+      arc.id = arcs[arc.id].next_out;
+    }
+
+    void firstIn(Arc& arc, const Node& node) const {
+      arc.id = (*nodes)[node].first_in;
+    }
+
+    void nextIn(Arc& arc) const {
+      arc.id = arcs[arc.id].next_in;
+    }
+
+    int id(const Node& node) const { return graph->id(node); }
+    int id(const Arc& arc) const { return arc.id; }
+
+    Node nodeFromId(int ix) const { return graph->nodeFromId(ix); }
+    Arc arcFromId(int ix) const { return Arc(ix); }
+
+    int maxNodeId() const { return graph->maxNodeId(); };
+    int maxArcId() const { return arcs.size() - 1; }
+
+    Node source(const Arc& arc) const { return arcs[arc.id].source;}
+    Node target(const Arc& arc) const { return arcs[arc.id].target;}
+
+    typedef typename ItemSetTraits<Graph, Node>::ItemNotifier NodeNotifier;
+
+    NodeNotifier& notifier(Node) const {
+      return graph->notifier(Node());
+    }
+
+    template <typename _Value>
+    class NodeMap : public Graph::template NodeMap<_Value> {
+    public:
+
+      typedef typename _Graph::template NodeMap<_Value> Parent;
+
+      explicit NodeMap(const SmartArcSetBase<Graph>& arcset)
+        : Parent(*arcset.graph) { }
+
+      NodeMap(const SmartArcSetBase<Graph>& arcset, const _Value& value)
+        : Parent(*arcset.graph, value) { }
+
+      NodeMap& operator=(const NodeMap& cmap) {
+        return operator=<NodeMap>(cmap);
+      }
+
+      template <typename CMap>
+      NodeMap& operator=(const CMap& cmap) {
+        Parent::operator=(cmap);
+        return *this;
+      }
+    };
+
+  };
+
+
+  /// \ingroup semi_adaptors
+  ///
+  /// \brief Digraph using a node set of another digraph or graph and
+  /// an own arc set.
+  ///
+  /// This structure can be used to establish another directed graph
+  /// over a node set of an existing one. This class uses the same
+  /// Node type as the underlying graph, and each valid node of the
+  /// original graph is valid in this arc set, therefore the node
+  /// objects of the original graph can be used directly with this
+  /// class. The node handling functions (id handling, observing, and
+  /// iterators) works equivalently as in the original graph.
+  ///
+  /// \param _Graph The type of the graph which shares its node set with
+  /// this class. Its interface must conform to the
+  /// \ref concepts::Digraph "Digraph" or \ref concepts::Graph "Graph"
+  /// concept.
+  ///
+  /// This implementation is slightly faster than the \c ListArcSet,
+  /// because it uses continuous storage for arcs and it uses just
+  /// single-linked lists for enumerate outgoing and incoming
+  /// arcs. Therefore the arcs cannot be erased from the arc sets.
+  ///
+  /// \warning If a node is erased from the underlying graph and this
+  /// node is the source or target of one arc in the arc set, then
+  /// the arc set is invalidated, and it cannot be used anymore. The
+  /// validity can be checked with the \c valid() member function.
+  ///
+  /// This class is fully conform to the \ref concepts::Digraph
+  /// "Digraph" concept.
+  template <typename _Graph>
+  class SmartArcSet : public ArcSetExtender<SmartArcSetBase<_Graph> > {
+
+  public:
+
+    typedef ArcSetExtender<SmartArcSetBase<_Graph> > Parent;
+
+    typedef typename Parent::Node Node;
+    typedef typename Parent::Arc Arc;
+
+    typedef _Graph Graph;
+
+  protected:
+
+    typedef typename Parent::NodesImplBase NodesImplBase;
+
+    void eraseNode(const Node& node) {
+      if (typename Parent::InArcIt(*this, node) == INVALID &&
+          typename Parent::OutArcIt(*this, node) == INVALID) {
+        return;
+      }
+      throw typename NodesImplBase::Notifier::ImmediateDetach();
+    }
+
+    void clearNodes() {
+      Parent::clear();
+    }
+
+    class NodesImpl : public NodesImplBase {
+    public:
+      typedef NodesImplBase Parent;
+
+      NodesImpl(const Graph& graph, SmartArcSet& arcset)
+        : Parent(graph), _arcset(arcset) {}
+
+      virtual ~NodesImpl() {}
+
+      bool attached() const {
+        return Parent::attached();
+      }
+
+    protected:
+
+      virtual void erase(const Node& node) {
+        try {
+          _arcset.eraseNode(node);
+          Parent::erase(node);
+        } catch (const typename NodesImplBase::Notifier::ImmediateDetach&) {
+          Parent::clear();
+          throw;
+        }
+      }
+      virtual void erase(const std::vector<Node>& nodes) {
+        try {
+          for (int i = 0; i < int(nodes.size()); ++i) {
+            _arcset.eraseNode(nodes[i]);
+          }
+          Parent::erase(nodes);
+        } catch (const typename NodesImplBase::Notifier::ImmediateDetach&) {
+          Parent::clear();
+          throw;
+        }
+      }
+      virtual void clear() {
+        _arcset.clearNodes();
+        Parent::clear();
+      }
+
+    private:
+      SmartArcSet& _arcset;
+    };
+
+    NodesImpl nodes;
+
+  public:
+
+    /// \brief Constructor of the ArcSet.
+    ///
+    /// Constructor of the ArcSet.
+    SmartArcSet(const Graph& graph) : nodes(graph, *this) {
+      Parent::initalize(graph, nodes);
+    }
+
+    /// \brief Add a new arc to the digraph.
+    ///
+    /// Add a new arc to the digraph with source node \c s
+    /// and target node \c t.
+    /// \return the new arc.
+    Arc addArc(const Node& s, const Node& t) {
+      return Parent::addArc(s, t);
+    }
+
+    /// \brief Validity check
+    ///
+    /// This functions gives back false if the ArcSet is
+    /// invalidated. It occurs when a node in the underlying graph is
+    /// erased and it is not isolated in the ArcSet.
+    bool valid() const {
+      return nodes.attached();
+    }
+
+  };
+
+
+  template <typename _Graph>
+  class SmartEdgeSetBase {
+  public:
+
+    typedef _Graph Graph;
+    typedef typename Graph::Node Node;
+    typedef typename Graph::NodeIt NodeIt;
+
+  protected:
+
+    struct NodeT {
+      int first_out;
+      NodeT() : first_out(-1) {}
+    };
+
+    typedef typename ItemSetTraits<Graph, Node>::
+    template Map<NodeT>::Type NodesImplBase;
+
+    NodesImplBase* nodes;
+
+    struct ArcT {
+      Node target;
+      int next_out;
+      ArcT() {}
+    };
+
+    std::vector<ArcT> arcs;
+
+    const Graph* graph;
+
+    void initalize(const Graph& _graph, NodesImplBase& _nodes) {
+      graph = &_graph;
+      nodes = &_nodes;
+    }
+
+  public:
+
+    class Edge {
+      friend class SmartEdgeSetBase;
+    protected:
+
+      int id;
+      explicit Edge(int _id) { id = _id;}
+
+    public:
+      Edge() {}
+      Edge (Invalid) { id = -1; }
+      bool operator==(const Edge& arc) const {return id == arc.id;}
+      bool operator!=(const Edge& arc) const {return id != arc.id;}
+      bool operator<(const Edge& arc) const {return id < arc.id;}
+    };
+
+    class Arc {
+      friend class SmartEdgeSetBase;
+    protected:
+      Arc(int _id) : id(_id) {}
+      int id;
+    public:
+      operator Edge() const { return edgeFromId(id / 2); }
+
+      Arc() {}
+      Arc(Invalid) : id(-1) {}
+      bool operator==(const Arc& arc) const { return id == arc.id; }
+      bool operator!=(const Arc& arc) const { return id != arc.id; }
+      bool operator<(const Arc& arc) const { return id < arc.id; }
+    };
+
+    SmartEdgeSetBase() {}
+
+    Edge addEdge(const Node& u, const Node& v) {
+      int n = arcs.size();
+      arcs.push_back(ArcT());
+      arcs.push_back(ArcT());
+
+      arcs[n].target = u;
+      arcs[n | 1].target = v;
+
+      arcs[n].next_out = (*nodes)[v].first_out;
+      (*nodes)[v].first_out = n;
+
+      arcs[n | 1].next_out = (*nodes)[u].first_out;
+      (*nodes)[u].first_out = (n | 1);
+
+      return Edge(n / 2);
+    }
+
+    void clear() {
+      Node node;
+      for (first(node); node != INVALID; next(node)) {
+        (*nodes)[node].first_out = -1;
+      }
+      arcs.clear();
+    }
+
+    void first(Node& node) const {
+      graph->first(node);
+    }
+
+    void next(Node& node) const {
+      graph->next(node);
+    }
+
+    void first(Arc& arc) const {
+      arc.id = arcs.size() - 1;
+    }
+
+    void next(Arc& arc) const {
+      --arc.id;
+    }
+
+    void first(Edge& arc) const {
+      arc.id = arcs.size() / 2 - 1;
+    }
+
+    void next(Edge& arc) const {
+      --arc.id;
+    }
+
+    void firstOut(Arc& arc, const Node& node) const {
+      arc.id = (*nodes)[node].first_out;
+    }
+
+    void nextOut(Arc& arc) const {
+      arc.id = arcs[arc.id].next_out;
+    }
+
+    void firstIn(Arc& arc, const Node& node) const {
+      arc.id = (((*nodes)[node].first_out) ^ 1);
+      if (arc.id == -2) arc.id = -1;
+    }
+
+    void nextIn(Arc& arc) const {
+      arc.id = ((arcs[arc.id ^ 1].next_out) ^ 1);
+      if (arc.id == -2) arc.id = -1;
+    }
+
+    void firstInc(Edge &arc, bool& dir, const Node& node) const {
+      int de = (*nodes)[node].first_out;
+      if (de != -1 ) {
+        arc.id = de / 2;
+        dir = ((de & 1) == 1);
+      } else {
+        arc.id = -1;
+        dir = true;
+      }
+    }
+    void nextInc(Edge &arc, bool& dir) const {
+      int de = (arcs[(arc.id * 2) | (dir ? 1 : 0)].next_out);
+      if (de != -1 ) {
+        arc.id = de / 2;
+        dir = ((de & 1) == 1);
+      } else {
+        arc.id = -1;
+        dir = true;
+      }
+    }
+
+    static bool direction(Arc arc) {
+      return (arc.id & 1) == 1;
+    }
+
+    static Arc direct(Edge edge, bool dir) {
+      return Arc(edge.id * 2 + (dir ? 1 : 0));
+    }
+
+    int id(Node node) const { return graph->id(node); }
+    static int id(Arc arc) { return arc.id; }
+    static int id(Edge arc) { return arc.id; }
+
+    Node nodeFromId(int id) const { return graph->nodeFromId(id); }
+    static Arc arcFromId(int id) { return Arc(id); }
+    static Edge edgeFromId(int id) { return Edge(id);}
+
+    int maxNodeId() const { return graph->maxNodeId(); };
+    int maxArcId() const { return arcs.size() - 1; }
+    int maxEdgeId() const { return arcs.size() / 2 - 1; }
+
+    Node source(Arc e) const { return arcs[e.id ^ 1].target; }
+    Node target(Arc e) const { return arcs[e.id].target; }
+
+    Node u(Edge e) const { return arcs[2 * e.id].target; }
+    Node v(Edge e) const { return arcs[2 * e.id + 1].target; }
+
+    typedef typename ItemSetTraits<Graph, Node>::ItemNotifier NodeNotifier;
+
+    NodeNotifier& notifier(Node) const {
+      return graph->notifier(Node());
+    }
+
+    template <typename _Value>
+    class NodeMap : public Graph::template NodeMap<_Value> {
+    public:
+
+      typedef typename _Graph::template NodeMap<_Value> Parent;
+
+      explicit NodeMap(const SmartEdgeSetBase<Graph>& arcset)
+        : Parent(*arcset.graph) { }
+
+      NodeMap(const SmartEdgeSetBase<Graph>& arcset, const _Value& value)
+        : Parent(*arcset.graph, value) { }
+
+      NodeMap& operator=(const NodeMap& cmap) {
+        return operator=<NodeMap>(cmap);
+      }
+
+      template <typename CMap>
+      NodeMap& operator=(const CMap& cmap) {
+        Parent::operator=(cmap);
+        return *this;
+      }
+    };
+
+  };
+
+  /// \ingroup semi_adaptors
+  ///
+  /// \brief Graph using a node set of another digraph or graph and an
+  /// own edge set.
+  ///
+  /// This structure can be used to establish another graph over a
+  /// node set of an existing one. This class uses the same Node type
+  /// as the underlying graph, and each valid node of the original
+  /// graph is valid in this arc set, therefore the node objects of
+  /// the original graph can be used directly with this class. The
+  /// node handling functions (id handling, observing, and iterators)
+  /// works equivalently as in the original graph.
+  ///
+  /// \param _Graph The type of the graph which shares its node set
+  /// with this class. Its interface must conform to the
+  /// \ref concepts::Digraph "Digraph" or \ref concepts::Graph "Graph"
+  ///  concept.
+  ///
+  /// This implementation is slightly faster than the \c ListEdgeSet,
+  /// because it uses continuous storage for edges and it uses just
+  /// single-linked lists for enumerate incident edges. Therefore the
+  /// edges cannot be erased from the edge sets.
+  ///
+  /// \warning If a node is erased from the underlying graph and this
+  /// node is incident to one edge in the edge set, then the edge set
+  /// is invalidated, and it cannot be used anymore. The validity can
+  /// be checked with the \c valid() member function.
+  ///
+  /// This class is fully conform to the \ref concepts::Graph
+  /// "Graph" concept.
+  template <typename _Graph>
+  class SmartEdgeSet : public EdgeSetExtender<SmartEdgeSetBase<_Graph> > {
+
+  public:
+
+    typedef EdgeSetExtender<SmartEdgeSetBase<_Graph> > Parent;
+
+    typedef typename Parent::Node Node;
+    typedef typename Parent::Arc Arc;
+    typedef typename Parent::Edge Edge;
+
+    typedef _Graph Graph;
+
+  protected:
+
+    typedef typename Parent::NodesImplBase NodesImplBase;
+
+    void eraseNode(const Node& node) {
+      if (typename Parent::IncEdgeIt(*this, node) == INVALID) {
+        return;
+      }
+      throw typename NodesImplBase::Notifier::ImmediateDetach();
+    }
+
+    void clearNodes() {
+      Parent::clear();
+    }
+
+    class NodesImpl : public NodesImplBase {
+    public:
+      typedef NodesImplBase Parent;
+
+      NodesImpl(const Graph& graph, SmartEdgeSet& arcset)
+        : Parent(graph), _arcset(arcset) {}
+
+      virtual ~NodesImpl() {}
+
+      bool attached() const {
+        return Parent::attached();
+      }
+
+    protected:
+
+      virtual void erase(const Node& node) {
+        try {
+          _arcset.eraseNode(node);
+          Parent::erase(node);
+        } catch (const typename NodesImplBase::Notifier::ImmediateDetach&) {
+          Parent::clear();
+          throw;
+        }
+      }
+      virtual void erase(const std::vector<Node>& nodes) {
+        try {
+          for (int i = 0; i < int(nodes.size()); ++i) {
+            _arcset.eraseNode(nodes[i]);
+          }
+          Parent::erase(nodes);
+        } catch (const typename NodesImplBase::Notifier::ImmediateDetach&) {
+          Parent::clear();
+          throw;
+        }
+      }
+      virtual void clear() {
+        _arcset.clearNodes();
+        Parent::clear();
+      }
+
+    private:
+      SmartEdgeSet& _arcset;
+    };
+
+    NodesImpl nodes;
+
+  public:
+
+    /// \brief Constructor of the EdgeSet.
+    ///
+    /// Constructor of the EdgeSet.
+    SmartEdgeSet(const Graph& graph) : nodes(graph, *this) {
+      Parent::initalize(graph, nodes);
+    }
+
+    /// \brief Add a new edge to the graph.
+    ///
+    /// Add a new edge to the graph with node \c u
+    /// and node \c v endpoints.
+    /// \return the new edge.
+    Edge addEdge(const Node& u, const Node& v) {
+      return Parent::addEdge(u, v);
+    }
+
+    /// \brief Validity check
+    ///
+    /// This functions gives back false if the EdgeSet is
+    /// invalidated. It occurs when a node in the underlying graph is
+    /// erased and it is not isolated in the EdgeSet.
+    bool valid() const {
+      return nodes.attached();
+    }
+
+  };
+
+}
+
+#endif
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -10,6 +10,7 @@
   dijkstra_test
   dim_test
   error_test
+  edge_set_test
   graph_copy_test
   graph_test
   graph_utils_test
diff --git a/test/Makefile.am b/test/Makefile.am
--- a/test/Makefile.am
+++ b/test/Makefile.am
@@ -15,6 +15,7 @@
 	test/digraph_test \
 	test/dijkstra_test \
         test/dim_test \
+	test/edge_set_test \
 	test/error_test \
 	test/graph_adaptor_test \
 	test/graph_copy_test \
@@ -44,6 +45,7 @@
 test_digraph_test_SOURCES = test/digraph_test.cc
 test_dijkstra_test_SOURCES = test/dijkstra_test.cc
 test_dim_test_SOURCES = test/dim_test.cc
+test_edge_set_test_SOURCES = test/edge_set_test.cc
 test_error_test_SOURCES = test/error_test.cc
 test_graph_adaptor_test_SOURCES = test/graph_adaptor_test.cc
 test_graph_copy_test_SOURCES = test/graph_copy_test.cc
diff --git a/test/edge_set_test.cc b/test/edge_set_test.cc
new file mode 100644
--- /dev/null
+++ b/test/edge_set_test.cc
@@ -0,0 +1,380 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2008
+ * 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.
+ *
+ */
+
+#include <iostream>
+#include <vector>
+
+#include <lemon/concepts/digraph.h>
+#include <lemon/concepts/graph.h>
+#include <lemon/concept_check.h>
+
+#include <lemon/list_graph.h>
+
+#include <lemon/edge_set.h>
+
+#include "graph_test.h"
+#include "test_tools.h"
+
+using namespace lemon;
+
+void checkSmartArcSet() {
+  checkConcept<concepts::Digraph, SmartArcSet<concepts::Digraph> >();
+
+  typedef ListDigraph Digraph;
+  typedef SmartArcSet<Digraph> ArcSet;
+
+  Digraph digraph;
+  Digraph::Node
+    n1 = digraph.addNode(),
+    n2 = digraph.addNode();
+
+  Digraph::Arc ga1 = digraph.addArc(n1, n2);
+
+  ArcSet arc_set(digraph);
+
+  Digraph::Arc ga2 = digraph.addArc(n2, n1);
+
+  checkGraphNodeList(arc_set, 2);
+  checkGraphArcList(arc_set, 0);
+
+  Digraph::Node
+    n3 = digraph.addNode();
+  checkGraphNodeList(arc_set, 3);
+  checkGraphArcList(arc_set, 0);
+
+  ArcSet::Arc a1 = arc_set.addArc(n1, n2);
+  check(arc_set.source(a1) == n1 && arc_set.target(a1) == n2, "Wrong arc");
+  checkGraphNodeList(arc_set, 3);
+  checkGraphArcList(arc_set, 1);
+
+  checkGraphOutArcList(arc_set, n1, 1);
+  checkGraphOutArcList(arc_set, n2, 0);
+  checkGraphOutArcList(arc_set, n3, 0);
+
+  checkGraphInArcList(arc_set, n1, 0);
+  checkGraphInArcList(arc_set, n2, 1);
+  checkGraphInArcList(arc_set, n3, 0);
+
+  checkGraphConArcList(arc_set, 1);
+
+  ArcSet::Arc a2 = arc_set.addArc(n2, n1),
+    a3 = arc_set.addArc(n2, n3),
+    a4 = arc_set.addArc(n2, n3);
+  checkGraphNodeList(arc_set, 3);
+  checkGraphArcList(arc_set, 4);
+
+  checkGraphOutArcList(arc_set, n1, 1);
+  checkGraphOutArcList(arc_set, n2, 3);
+  checkGraphOutArcList(arc_set, n3, 0);
+
+  checkGraphInArcList(arc_set, n1, 1);
+  checkGraphInArcList(arc_set, n2, 1);
+  checkGraphInArcList(arc_set, n3, 2);
+
+  checkGraphConArcList(arc_set, 4);
+
+  checkNodeIds(arc_set);
+  checkArcIds(arc_set);
+  checkGraphNodeMap(arc_set);
+  checkGraphArcMap(arc_set);
+
+  check(arc_set.valid(), "Wrong validity");
+  digraph.erase(n1);
+  check(!arc_set.valid(), "Wrong validity");
+}
+
+void checkListArcSet() {
+  checkConcept<concepts::Digraph, SmartArcSet<concepts::Digraph> >();
+
+  typedef ListDigraph Digraph;
+  typedef ListArcSet<Digraph> ArcSet;
+
+  Digraph digraph;
+  Digraph::Node
+    n1 = digraph.addNode(),
+    n2 = digraph.addNode();
+
+  Digraph::Arc ga1 = digraph.addArc(n1, n2);
+
+  ArcSet arc_set(digraph);
+
+  Digraph::Arc ga2 = digraph.addArc(n2, n1);
+
+  checkGraphNodeList(arc_set, 2);
+  checkGraphArcList(arc_set, 0);
+
+  Digraph::Node
+    n3 = digraph.addNode();
+  checkGraphNodeList(arc_set, 3);
+  checkGraphArcList(arc_set, 0);
+
+  ArcSet::Arc a1 = arc_set.addArc(n1, n2);
+  check(arc_set.source(a1) == n1 && arc_set.target(a1) == n2, "Wrong arc");
+  checkGraphNodeList(arc_set, 3);
+  checkGraphArcList(arc_set, 1);
+
+  checkGraphOutArcList(arc_set, n1, 1);
+  checkGraphOutArcList(arc_set, n2, 0);
+  checkGraphOutArcList(arc_set, n3, 0);
+
+  checkGraphInArcList(arc_set, n1, 0);
+  checkGraphInArcList(arc_set, n2, 1);
+  checkGraphInArcList(arc_set, n3, 0);
+
+  checkGraphConArcList(arc_set, 1);
+
+  ArcSet::Arc a2 = arc_set.addArc(n2, n1),
+    a3 = arc_set.addArc(n2, n3),
+    a4 = arc_set.addArc(n2, n3);
+  checkGraphNodeList(arc_set, 3);
+  checkGraphArcList(arc_set, 4);
+
+  checkGraphOutArcList(arc_set, n1, 1);
+  checkGraphOutArcList(arc_set, n2, 3);
+  checkGraphOutArcList(arc_set, n3, 0);
+
+  checkGraphInArcList(arc_set, n1, 1);
+  checkGraphInArcList(arc_set, n2, 1);
+  checkGraphInArcList(arc_set, n3, 2);
+
+  checkGraphConArcList(arc_set, 4);
+
+  checkNodeIds(arc_set);
+  checkArcIds(arc_set);
+  checkGraphNodeMap(arc_set);
+  checkGraphArcMap(arc_set);
+
+  digraph.erase(n1);
+
+  checkGraphNodeList(arc_set, 2);
+  checkGraphArcList(arc_set, 2);
+
+  checkGraphOutArcList(arc_set, n2, 2);
+  checkGraphOutArcList(arc_set, n3, 0);
+
+  checkGraphInArcList(arc_set, n2, 0);
+  checkGraphInArcList(arc_set, n3, 2);
+
+  checkNodeIds(arc_set);
+  checkArcIds(arc_set);
+  checkGraphNodeMap(arc_set);
+  checkGraphArcMap(arc_set);
+
+  checkGraphConArcList(arc_set, 2);
+}
+
+void checkSmartEdgeSet() {
+  checkConcept<concepts::Digraph, SmartEdgeSet<concepts::Digraph> >();
+
+  typedef ListDigraph Digraph;
+  typedef SmartEdgeSet<Digraph> EdgeSet;
+
+  Digraph digraph;
+  Digraph::Node
+    n1 = digraph.addNode(),
+    n2 = digraph.addNode();
+
+  Digraph::Arc ga1 = digraph.addArc(n1, n2);
+
+  EdgeSet edge_set(digraph);
+
+  Digraph::Arc ga2 = digraph.addArc(n2, n1);
+
+  checkGraphNodeList(edge_set, 2);
+  checkGraphArcList(edge_set, 0);
+  checkGraphEdgeList(edge_set, 0);
+
+  Digraph::Node
+    n3 = digraph.addNode();
+  checkGraphNodeList(edge_set, 3);
+  checkGraphArcList(edge_set, 0);
+  checkGraphEdgeList(edge_set, 0);
+
+  EdgeSet::Edge e1 = edge_set.addEdge(n1, n2);
+  check((edge_set.u(e1) == n1 && edge_set.v(e1) == n2) ||
+        (edge_set.v(e1) == n1 && edge_set.u(e1) == n2), "Wrong edge");
+  checkGraphNodeList(edge_set, 3);
+  checkGraphArcList(edge_set, 2);
+  checkGraphEdgeList(edge_set, 1);
+
+  checkGraphOutArcList(edge_set, n1, 1);
+  checkGraphOutArcList(edge_set, n2, 1);
+  checkGraphOutArcList(edge_set, n3, 0);
+
+  checkGraphInArcList(edge_set, n1, 1);
+  checkGraphInArcList(edge_set, n2, 1);
+  checkGraphInArcList(edge_set, n3, 0);
+
+  checkGraphIncEdgeList(edge_set, n1, 1);
+  checkGraphIncEdgeList(edge_set, n2, 1);
+  checkGraphIncEdgeList(edge_set, n3, 0);
+
+  checkGraphConEdgeList(edge_set, 1);
+  checkGraphConArcList(edge_set, 2);
+
+  EdgeSet::Edge e2 = edge_set.addEdge(n2, n1),
+    e3 = edge_set.addEdge(n2, n3),
+    e4 = edge_set.addEdge(n2, n3);
+  checkGraphNodeList(edge_set, 3);
+  checkGraphEdgeList(edge_set, 4);
+
+  checkGraphOutArcList(edge_set, n1, 2);
+  checkGraphOutArcList(edge_set, n2, 4);
+  checkGraphOutArcList(edge_set, n3, 2);
+
+  checkGraphInArcList(edge_set, n1, 2);
+  checkGraphInArcList(edge_set, n2, 4);
+  checkGraphInArcList(edge_set, n3, 2);
+
+  checkGraphIncEdgeList(edge_set, n1, 2);
+  checkGraphIncEdgeList(edge_set, n2, 4);
+  checkGraphIncEdgeList(edge_set, n3, 2);
+
+  checkGraphConEdgeList(edge_set, 4);
+  checkGraphConArcList(edge_set, 8);
+
+  checkArcDirections(edge_set);
+
+  checkNodeIds(edge_set);
+  checkArcIds(edge_set);
+  checkEdgeIds(edge_set);
+  checkGraphNodeMap(edge_set);
+  checkGraphArcMap(edge_set);
+  checkGraphEdgeMap(edge_set);
+
+  check(edge_set.valid(), "Wrong validity");
+  digraph.erase(n1);
+  check(!edge_set.valid(), "Wrong validity");
+}
+
+void checkListEdgeSet() {
+  checkConcept<concepts::Digraph, ListEdgeSet<concepts::Digraph> >();
+
+  typedef ListDigraph Digraph;
+  typedef ListEdgeSet<Digraph> EdgeSet;
+
+  Digraph digraph;
+  Digraph::Node
+    n1 = digraph.addNode(),
+    n2 = digraph.addNode();
+
+  Digraph::Arc ga1 = digraph.addArc(n1, n2);
+
+  EdgeSet edge_set(digraph);
+
+  Digraph::Arc ga2 = digraph.addArc(n2, n1);
+
+  checkGraphNodeList(edge_set, 2);
+  checkGraphArcList(edge_set, 0);
+  checkGraphEdgeList(edge_set, 0);
+
+  Digraph::Node
+    n3 = digraph.addNode();
+  checkGraphNodeList(edge_set, 3);
+  checkGraphArcList(edge_set, 0);
+  checkGraphEdgeList(edge_set, 0);
+
+  EdgeSet::Edge e1 = edge_set.addEdge(n1, n2);
+  check((edge_set.u(e1) == n1 && edge_set.v(e1) == n2) ||
+        (edge_set.v(e1) == n1 && edge_set.u(e1) == n2), "Wrong edge");
+  checkGraphNodeList(edge_set, 3);
+  checkGraphArcList(edge_set, 2);
+  checkGraphEdgeList(edge_set, 1);
+
+  checkGraphOutArcList(edge_set, n1, 1);
+  checkGraphOutArcList(edge_set, n2, 1);
+  checkGraphOutArcList(edge_set, n3, 0);
+
+  checkGraphInArcList(edge_set, n1, 1);
+  checkGraphInArcList(edge_set, n2, 1);
+  checkGraphInArcList(edge_set, n3, 0);
+
+  checkGraphIncEdgeList(edge_set, n1, 1);
+  checkGraphIncEdgeList(edge_set, n2, 1);
+  checkGraphIncEdgeList(edge_set, n3, 0);
+
+  checkGraphConEdgeList(edge_set, 1);
+  checkGraphConArcList(edge_set, 2);
+
+  EdgeSet::Edge e2 = edge_set.addEdge(n2, n1),
+    e3 = edge_set.addEdge(n2, n3),
+    e4 = edge_set.addEdge(n2, n3);
+  checkGraphNodeList(edge_set, 3);
+  checkGraphEdgeList(edge_set, 4);
+
+  checkGraphOutArcList(edge_set, n1, 2);
+  checkGraphOutArcList(edge_set, n2, 4);
+  checkGraphOutArcList(edge_set, n3, 2);
+
+  checkGraphInArcList(edge_set, n1, 2);
+  checkGraphInArcList(edge_set, n2, 4);
+  checkGraphInArcList(edge_set, n3, 2);
+
+  checkGraphIncEdgeList(edge_set, n1, 2);
+  checkGraphIncEdgeList(edge_set, n2, 4);
+  checkGraphIncEdgeList(edge_set, n3, 2);
+
+  checkGraphConEdgeList(edge_set, 4);
+  checkGraphConArcList(edge_set, 8);
+
+  checkArcDirections(edge_set);
+
+  checkNodeIds(edge_set);
+  checkArcIds(edge_set);
+  checkEdgeIds(edge_set);
+  checkGraphNodeMap(edge_set);
+  checkGraphArcMap(edge_set);
+  checkGraphEdgeMap(edge_set);
+
+  digraph.erase(n1);
+
+  checkGraphNodeList(edge_set, 2);
+  checkGraphArcList(edge_set, 4);
+  checkGraphEdgeList(edge_set, 2);
+
+  checkGraphOutArcList(edge_set, n2, 2);
+  checkGraphOutArcList(edge_set, n3, 2);
+
+  checkGraphInArcList(edge_set, n2, 2);
+  checkGraphInArcList(edge_set, n3, 2);
+
+  checkGraphIncEdgeList(edge_set, n2, 2);
+  checkGraphIncEdgeList(edge_set, n3, 2);
+
+  checkNodeIds(edge_set);
+  checkArcIds(edge_set);
+  checkEdgeIds(edge_set);
+  checkGraphNodeMap(edge_set);
+  checkGraphArcMap(edge_set);
+  checkGraphEdgeMap(edge_set);
+
+  checkGraphConEdgeList(edge_set, 2);
+  checkGraphConArcList(edge_set, 4);
+
+}
+
+
+int main() {
+
+  checkSmartArcSet();
+  checkListArcSet();
+  checkSmartEdgeSet();
+  checkListEdgeSet();
+
+  return 0;
+}