@defgroup min_cut Minimum Cut algorithms

 @defgroup min_cut Minimum Cut algorithms 

 @ingroup algs

 @ingroup algs 

 \brief This group describes the algorithms

 for finding minimum cut in graphs.

 \brief This group describes the algorithms for finding minimum cut in

 graphs.

 This group describes the algorithms

 for finding minimum cut in graphs.

 This group describes the algorithms for finding minimum cut in graphs.

 The minimum cut problem is to find a non-empty and non-complete

 \f$X\f$ subset of the vertices with minimum overall capacity on

 outgoing arcs. Formally, there is \f$G=(V,A)\f$ directed graph, an

 \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum

 cut is the solution of the next optimization problem:

 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}\sum_{uv\in A, u\in X, v\not\in X}c_{uv}\f]

 The lemon contains several algorithms related to minimum cut problems:

 - \ref lemon::HaoOrlin "Hao-Orlin algorithm" for calculate minimum cut

   in directed graphs  

 - \ref lemon::NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for

   calculate minimum cut in undirected graphs

 - \ref lemon::GomoryHuTree "Gomory-Hu tree computation" for calculate all

   pairs minimum cut in undirected graphs

 If you want to find minimum cut just between two distinict nodes,

 please see the \ref max_flow "Maximum Flow page".