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The Graph <math> G_f = (V,E_f) <math> is defined as the residual graph relative to f, where <math> E_f <math> is the set of residual edges. A path <math> P \in G_f <math> from the source <math> s<math> to the sink <math> t<math> is called an augmented path of <math> f<math>. This path can be used to increase the flow from <math> s<math> to <math> t<math>.
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