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Flow network
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==Definition== A '''network''' is a directed graph {{math|''G'' {{=}} (''V'', ''E'')}} with a non-negative '''capacity''' [[function (mathematics)|function]] {{math|''c''}} for each edge, and without multiple arcs (i.e. edges with the same source and target nodes). [[Without loss of generality]], we may assume that if {{math|(''u'', ''v'') β ''E''}}, then {{math|(''v'', ''u'')}} is also a member of {{mvar|E}}. Additionally, if {{math|(''v'', ''u'') β ''E''}} then we may add {{math|(''v'', ''u'')}} to ''E'' and then set the {{math|''c''(''v'', ''u'') {{=}} 0}}. If two nodes in {{mvar|G}} are distinguished β one as the source {{mvar|s}} and the other as the sink {{mvar|t}} β then {{math|(''G'', ''c'', ''s'', ''t'')}} is called a '''flow network'''.<ref>A.V. Goldberg, Γ. Tardos and R.E. Tarjan, Network flow algorithms, Tech. Report STAN-CS-89-1252, Stanford University CS Dept., 1989</ref>
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