/// \ingroup graph_adaptors

 ///\ingroup graph_adaptors

 /// \file

 ///\file

 /// \brief Several graph adaptors.

 ///\brief Several graph adaptors.

 /// This file contains several useful graph adaptor functions.

 ///This file contains several useful graph adaptor functions.

 /// \author Marton Makai and Balazs Dezso

 ///\author Marton Makai and Balazs Dezso

   ///Let \f$ G=(V, A) \f$ be a directed graph and let \f$ F \f$ be a 

 //   ///Let \f$ G=(V, A) \f$ be a directed graph and let \f$ F \f$ be a 

   ///number type. Let moreover 

 //   ///number type. Let moreover 

   ///\f$ f,c:A\to F \f$, be functions on the edge-set. 

 //   ///\f$ f,c:A\to F \f$, be functions on the edge-set. 

   ///In the appications of ResGraphAdaptor, \f$ f \f$ usually stands for a flow 

 //   ///In the appications of ResGraphAdaptor, \f$ f \f$ usually stands for a 

   ///and \f$ c \f$ for a capacity function.   

 //   ///flow and \f$ c \f$ for a capacity function.   

   ///Suppose that a graph instange \c g of type 

 //   ///Suppose that a graph instange \c g of type 

   ///\c ListGraph implements \f$ G \f$.

 //   ///\c ListGraph implements \f$ G \f$.

   ///\code

 //   ///\code

   ///  ListGraph g;

 //   /// ListGraph g;

   ///\endcode

 //   ///\endcode

   ///Then RevGraphAdaptor implements the graph structure with node-set 

 //   ///Then RevGraphAdaptor implements the graph structure with node-set 

   ///\f$ V \f$ and edge-set \f$ A_{forward}\cup A_{backward} \f$, where 

 //   ///\f$ V \f$ and edge-set \f$ A_{forward}\cup A_{backward} \f$, where 

   ///\f$ A_{forward}=\{uv : uv\in A, f(uv)<c(uv)\} \f$ and 

 //   ///\f$ A_{forward}=\{uv : uv\in A, f(uv)<c(uv)\} \f$ and 

   ///\f$ A_{backward}=\{vu : uv\in A, f(uv)>0\} \f$, 

 //   ///\f$ A_{backward}=\{vu : uv\in A, f(uv)>0\} \f$, 

   ///i.e. the so called residual graph. 

 //   ///i.e. the so called residual graph. 

   ///When we take the union \f$ A_{forward}\cup A_{backward} \f$, 

 //   ///When we take the union \f$ A_{forward}\cup A_{backward} \f$, 

   ///multilicities are counted, i.e. if an edge is in both 

 //   ///multilicities are counted, i.e. if an edge is in both 

   ///\f$ A_{forward} \f$ and \f$ A_{backward} \f$, then in the adaptor it 

 //   ///\f$ A_{forward} \f$ and \f$ A_{backward} \f$, then in the adaptor it 

   ///appears twice. 

 //   ///appears twice. The following code shows how such an instance can be 

   ///The following code shows how 

 //   ///constructed.

   ///such an instance can be constructed.

 //   ///\code

   ///\code

 //   /// typedef ListGraph Graph;

   ///typedef ListGraph Graph;

 //   /// Graph::EdgeMap<int> f(g);

   ///Graph::EdgeMap<int> f(g);

 //   /// Graph::EdgeMap<int> c(g);

   ///Graph::EdgeMap<int> c(g);

 //   /// ResGraphAdaptor<Graph, int, Graph::EdgeMap<int>, Graph::EdgeMap<int> > ga(g);

   ///ResGraphAdaptor<Graph, int, Graph::EdgeMap<int>, Graph::EdgeMap<int> > ga(g);

 //   ///\endcode

   ///\endcode

 //   ///\author Marton Makai

   ///\author Marton Makai

 //   ///

   ///