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An arc {{math|(''u'', ''v'') ∈ ''E''<sub>''f''</sub>}} is called '''admissible''' if {{math|𝓁(''u'') {{=}} 𝓁(''v'') + 1}}. The '''admissible network''' {{math|''G̃''<sub>''f''</sub> (''V'', ''Ẽ''<sub>''f''</sub> )}} is composed of the set of arcs {{math|''e'' ∈ ''E''<sub>''f''</sub>}} that are admissible. The admissible network is acyclic.
For a fixed flow {{math|''f''}}, a vertex {{math|''v''}} is called '''active''' if it has positive excess with respect to {{math|''f''}}, i.e., {{math|''x''<sub>''f''(''v'')</sub> > 0}}.
===Operations===
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