/// \bug In the vector can be hole if a node is erased from the graph.

     };*/

   class SymListGraph : public ListGraph {

     typedef ListGraph Parent;

   public:

     typedef SymListGraph Graph;

     typedef ListGraph::Node Node;

     typedef ListGraph::NodeIt NodeIt;

     class SymEdge;

     class SymEdgeIt;

     class Edge;

     class EdgeIt;

     class OutEdgeIt;

     class InEdgeIt;

     template <typename Value>

     class NodeMap : public Parent::NodeMap<Value> {      

     public:

       NodeMap(const SymListGraph& g) 

 	: SymListGraph::Parent::NodeMap<Value>(g) {}

       NodeMap(const SymListGraph& g, Value v) 

 	: SymListGraph::Parent::NodeMap<Value>(g, v) {}

       template<typename TT> 

       NodeMap(const NodeMap<TT>& copy) 

 	: SymListGraph::Parent::NodeMap<Value>(copy) { }            

     };

     template <typename Value>

     class SymEdgeMap : public Parent::EdgeMap<Value> {

     public:

       typedef SymEdge KeyType;

       SymEdgeMap(const SymListGraph& g) 

 	: SymListGraph::Parent::EdgeMap<Value>(g) {}

       SymEdgeMap(const SymListGraph& g, Value v) 

 	: SymListGraph::Parent::EdgeMap<Value>(g, v) {}

       template<typename TT> 

       SymEdgeMap(const SymEdgeMap<TT>& copy) 

 	: SymListGraph::Parent::EdgeMap<Value>(copy) { }

     };

     // Create edge map registry.

     CREATE_EDGE_MAP_REGISTRY;

     // Create edge maps.

     CREATE_EDGE_MAP(ArrayMap);

     class Edge {

       friend class SymListGraph;

       friend class SymListGraph::EdgeIt;

       friend class SymListGraph::OutEdgeIt;

       friend class SymListGraph::InEdgeIt;

     protected:

       int id;

       Edge(int pid) { id = pid; }

     public:

       /// An Edge with id \c n.

       Edge() { }

       Edge (Invalid) { id = -1; }

       operator SymEdge(){ return SymEdge(id >> 1);}

       bool operator==(const Edge i) const {return id == i.id;}

       bool operator!=(const Edge i) const {return id != i.id;}

       bool operator<(const Edge i) const {return id < i.id;}

       //      ///Validity check

       //      operator bool() { return n!=-1; }

     };

     class SymEdge : public ListGraph::Edge {

       friend class SymListGraph;

       friend class SymListGraph::Edge;

       typedef ListGraph::Edge Parent;

     protected:      

       SymEdge(int pid) : Parent(pid) {}

     public:

       SymEdge() { }

       SymEdge(const ListGraph::Edge& i) : Parent(i) {} 

       SymEdge (Invalid) : Parent(INVALID) {}

     };

     class OutEdgeIt {

       Parent::OutEdgeIt out;

       Parent::InEdgeIt in;      

     public: 

       OutEdgeIt() {}

       OutEdgeIt(const SymListGraph& g, Edge e) { 

 	if ((e.id & 1) == 0) {	

 	  out = Parent::OutEdgeIt(g, SymEdge(e));

 	  in = Parent::InEdgeIt(g, g.tail(e));

 	} else {

 	  out = Parent::OutEdgeIt(INVALID);

 	  in = Parent::InEdgeIt(g, SymEdge(e));

 	}

       }

       OutEdgeIt (Invalid i) : out(INVALID), in(INVALID) { }

       OutEdgeIt(const SymListGraph& g, const Node v)

 	: out(g, v), in(g, v) {}

       OutEdgeIt &operator++() { 

 	if (out != INVALID) {

 	  ++out;

 	} else {

 	  ++in;

 	}

 	return *this; 

       }

       operator Edge() const {

 	if (out == INVALID && in == INVALID) return INVALID;

 	return out != INVALID ? forward(out) : backward(in);

       }

       bool operator==(const Edge i) const {return Edge(*this) == i;}

       bool operator!=(const Edge i) const {return Edge(*this) != i;}

       bool operator<(const Edge i) const {return Edge(*this) < i;}

     };

     class InEdgeIt {

       Parent::OutEdgeIt out;

       Parent::InEdgeIt in;      

     public: 

       InEdgeIt() {}

       InEdgeIt(const SymListGraph& g, Edge e) { 

 	if ((e.id & 1) == 0) {	

 	  out = Parent::OutEdgeIt(g, SymEdge(e));

 	  in = Parent::InEdgeIt(g, g.tail(e));

 	} else {

 	  out = Parent::OutEdgeIt(INVALID);

 	  in = Parent::InEdgeIt(g, SymEdge(e));

 	}

       }

       InEdgeIt (Invalid i) : out(INVALID), in(INVALID) { }

       InEdgeIt(const SymListGraph& g, const Node v)

 	: out(g, v), in(g, v) {}

       InEdgeIt &operator++() { 

 	if (out != INVALID) {

 	  ++out;

 	} else {

 	  ++in;

 	}

 	return *this; 

       }

       operator Edge() const {

 	if (out == INVALID && in == INVALID) return INVALID;

 	return out != INVALID ? backward(out) : forward(in);

       }

       bool operator==(const Edge i) const {return Edge(*this) == i;}

       bool operator!=(const Edge i) const {return Edge(*this) != i;}

       bool operator<(const Edge i) const {return Edge(*this) < i;}

     };

     class SymEdgeIt : public Parent::EdgeIt {

     public:

       SymEdgeIt() {}

       SymEdgeIt(const SymListGraph& g) 

 	: SymListGraph::Parent::EdgeIt(g) {}

       SymEdgeIt(const SymListGraph& g, SymEdge e) 

 	: SymListGraph::Parent::EdgeIt(g, e) {}

       SymEdgeIt(Invalid i) 

 	: SymListGraph::Parent::EdgeIt(INVALID) {}

       SymEdgeIt& operator++() {

 	SymListGraph::Parent::EdgeIt::operator++();

 	return *this;

       }

       operator SymEdge() const {

 	return SymEdge

 	  (static_cast<const SymListGraph::Parent::EdgeIt&>(*this));

       }

       bool operator==(const SymEdge i) const {return SymEdge(*this) == i;}

       bool operator!=(const SymEdge i) const {return SymEdge(*this) != i;}

       bool operator<(const SymEdge i) const {return SymEdge(*this) < i;}

     };

     class EdgeIt {

       SymEdgeIt it;

       bool fw;

     public:

       EdgeIt(const SymListGraph& g) : it(g), fw(true) {}

       EdgeIt (Invalid i) : it(i) { }

       EdgeIt(const SymListGraph& g, Edge e) 

 	: it(g, SymEdge(e)), fw(id(e) & 1 == 0) { }

       EdgeIt() { }

       EdgeIt& operator++() {

 	fw = !fw;

 	if (fw) ++it;

 	return *this;

       }

       operator Edge() const {

 	if (it == INVALID) return INVALID;

 	return fw ? forward(it) : backward(it);

       }

       bool operator==(const Edge i) const {return Edge(*this) == i;}

       bool operator!=(const Edge i) const {return Edge(*this) != i;}

       bool operator<(const Edge i) const {return Edge(*this) < i;}

     };

     ///Number of nodes.

     int nodeNum() const { return Parent::nodeNum(); }

     ///Number of edges.

     int edgeNum() const { return 2*Parent::edgeNum(); }

     ///Number of symmetric edges.

     int symEdgeNum() const { return Parent::edgeNum(); }

     ///Set the expected maximum number of edges.

     ///With this function, it is possible to set the expected number of edges.

     ///The use of this fasten the building of the graph and makes

     ///it possible to avoid the superfluous memory allocation.

     void reserveSymEdge(int n) { Parent::reserveEdge(n); };

     /// Maximum node ID.

     /// Maximum node ID.

     ///\sa id(Node)

     int maxNodeId() const { return Parent::maxNodeId(); } 

     /// Maximum edge ID.

     /// Maximum edge ID.

     ///\sa id(Edge)

     int maxEdgeId() const { return 2*Parent::maxEdgeId(); }

     /// Maximum symmetric edge ID.

     /// Maximum symmetric edge ID.

     ///\sa id(SymEdge)

     int maxSymEdgeId() const { return Parent::maxEdgeId(); }

     Node tail(Edge e) const { 

       return (e.id & 1) == 0 ? 

 	Parent::tail(SymEdge(e)) : Parent::head(SymEdge(e)); 

     }

     Node head(Edge e) const { 

       return (e.id & 1) == 0 ? 

 	Parent::head(SymEdge(e)) : Parent::tail(SymEdge(e)); 

     }

     Node tail(SymEdge e) const { 

       return Parent::tail(e); 

     }

     Node head(SymEdge e) const { 

       return Parent::head(e); 

     }

     NodeIt& first(NodeIt& v) const { 

       v=NodeIt(*this); return v; }

     EdgeIt& first(EdgeIt& e) const { 

       e=EdgeIt(*this); return e; }

     SymEdgeIt& first(SymEdgeIt& e) const {

       e=SymEdgeIt(*this); return e; }

     OutEdgeIt& first(OutEdgeIt& e, const Node v) const { 

       e=OutEdgeIt(*this,v); return e; }

     InEdgeIt& first(InEdgeIt& e, const Node v) const { 

       e=InEdgeIt(*this,v); return e; }

     /// Node ID.

     /// The ID of a valid Node is a nonnegative integer not greater than

     /// \ref maxNodeId(). The range of the ID's is not surely continuous

     /// and the greatest node ID can be actually less then \ref maxNodeId().

     ///

     /// The ID of the \ref INVALID node is -1.

     ///\return The ID of the node \c v. 

     static int id(Node v) { return Parent::id(v); }

     /// Edge ID.

     /// The ID of a valid Edge is a nonnegative integer not greater than

     /// \ref maxEdgeId(). The range of the ID's is not surely continuous

     /// and the greatest edge ID can be actually less then \ref maxEdgeId().

     ///

     /// The ID of the \ref INVALID edge is -1.

     ///\return The ID of the edge \c e. 

     static int id(Edge e) { return e.id; }

     /// The ID of a valid SymEdge is a nonnegative integer not greater than

     /// \ref maxSymEdgeId(). The range of the ID's is not surely continuous

     /// and the greatest edge ID can be actually less then \ref maxSymEdgeId().

     ///

     /// The ID of the \ref INVALID symmetric edge is -1.

     ///\return The ID of the edge \c e. 

     static int id(SymEdge e) { return Parent::id(e); }

     /// Adds a new node to the graph.

     /// \warning It adds the new node to the front of the list.

     /// (i.e. the lastly added node becomes the first.)

     Node addNode() {

       return Parent::addNode();

     }

     SymEdge addEdge(Node u, Node v) {

       SymEdge se = Parent::addEdge(u, v);

       edge_maps.add(forward(se));

       edge_maps.add(backward(se));

       return se;

     }

     /// Finds an edge between two nodes.

     /// Finds an edge from node \c u to node \c v.

     ///

     /// If \c prev is \ref INVALID (this is the default value), then

     /// It finds the first edge from \c u to \c v. Otherwise it looks for

     /// the next edge from \c u to \c v after \c prev.

     /// \return The found edge or INVALID if there is no such an edge.

     Edge findEdge(Node u, Node v, Edge prev = INVALID) 

     {     

       if (prev == INVALID || id(prev) & 1 == 0) {

 	SymEdge se = Parent::findEdge(u, v, SymEdge(prev));

 	if (se != INVALID) return forward(se);

       } else {

 	SymEdge se = Parent::findEdge(v, u, SymEdge(prev));

 	if (se != INVALID) return backward(se);	

       }

       return INVALID;

     }

 //     /// Finds an symmetric edge between two nodes.

 //     /// Finds an symmetric edge from node \c u to node \c v.

 //     ///

 //     /// If \c prev is \ref INVALID (this is the default value), then

 //     /// It finds the first edge from \c u to \c v. Otherwise it looks for

 //     /// the next edge from \c u to \c v after \c prev.

 //     /// \return The found edge or INVALID if there is no such an edge.

 //     SymEdge findEdge(Node u, Node v, SymEdge prev = INVALID) 

 //     {     

 //       if (prev == INVALID || id(prev) & 1 == 0) {

 // 	SymEdge se = Parent::findEdge(u, v, SymEdge(prev));

 // 	if (se != INVALID) return se;

 //       } else {

 // 	SymEdge se = Parent::findEdge(v, u, SymEdge(prev));

 // 	if (se != INVALID) return se;	

 //       }

 //       return INVALID;

 //     }

   public:

     void erase(Node n) {      

       for (OutEdgeIt it(*this, n); it != INVALID; ++it) {

 	edge_maps.erase(it);

 	edge_maps.erase(opposite(it));

       }

       Parent::erase(n);

     }

     void erase(SymEdge e) { 

       edge_maps.erase(forward(e));

       edge_maps.erase(backward(e));

       Parent::erase(e); 

     };

     void clear() {

       edge_maps.clear();

       Parent::clear();

     }

     static Edge opposite(Edge e) {

       return Edge(id(e) ^ 1);

     }

     static Edge forward(SymEdge e) {

       return Edge(id(e) << 1);

     }

     static Edge backward(SymEdge e) {

       return Edge((id(e) << 1) | 1);

     }