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→Definitions and notations: Correction in the definition of the excess function |
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*{{math|''F'' {{=}} (''G'', ''c'', ''s'', ''t'')}} a ''flow network'', where {{math|''s'' ∈ ''V''}} and {{math|''t'' ∈ ''V''}} are chosen ''source'' and ''sink'' vertices respectively,
*{{math|''f'' : ''V'' × ''V'' → ℝ}} denote a [[Flow_network#Flows|''pre-flow'']] in {{mvar|F}},
*{{math|''x''<sub>''f''</sub> : ''V'' → ℝ}} denote the ''excess'' function with respect to the flow {{mvar|f}}, defined by {{math|''x''<sub>''f''</sub> (''u'') {{=}} ∑<sub>''v'' ∈ ''V''</sub> ''f'' (''v'', ''u'') − ∑<sub>''v'' ∈ ''V''</sub> ''f'' (''u'', ''v'')}},
*{{math|''c''<sub>''f''</sub> : ''V'' × ''V'' → ℝ<sub>∞</sub>}} denote the ''residual capacity function'' with respect to the flow {{mvar|f}}, defined by {{math|''c''<sub>''f''</sub> (''e'') {{=}} ''c''(''e'') − ''f'' (''e'')}},
and
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