Max Flow

Abstract

Suppose we are given a tuple G = (V, c, s, t), where V is a set of vertices, s, t ∈ V are distinguished vertices called the source and sink respectively, and c is a function $c\::{V^{2}}\: \to {R_{ + }}$ assigning a nonnegative real capacity to each pair of vertices. We make G into a directed graph by defining the set of directed edges

$$ E{\rm{ = }}\left\{ {\left( {u,\;\upsilon } \right)|c\left( {u,\;\upsilon } \right) > 0} \right\}.$$