In graph theory, 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>.