Editing Max-flow min-cut theorem (section)

==Example==
[[File:Max_flow.svg|thumb|right|A maximal flow in a network. Each edge is labeled with ''f/c'', where ''f'' is the flow over the edge and ''c'' is the edge's capacity. The flow value is 5. There are several minimal ''s''-''t'' cuts with capacity 5; one is ''S''={''s'',''p''} and ''T''={''o'', ''q'', ''r'', ''t''}.]]
The figure on the right shows a flow in a network. The numerical annotation on each arrow, in the form ''f''/''c'', indicates the flow (''f'') and the capacity (''c'') of the arrow. The flows emanating from the source total five (2+3=5), as do the flows into the sink (2+3=5), establishing that the flow's value is 5. 

One ''s''-''t'' cut with value 5 is given by ''S''={''s'',''p''} and ''T''={''o'', ''q'', ''r'', ''t''}. The capacities of the edges that cross this cut are 3 and 2, giving a cut capacity of 3+2=5. (The arrow from ''o'' to ''p'' is not considered, as it points from ''T'' back to ''S''.) 

The value of the flow is equal to the capacity of the cut, showing that the flow is a maximal flow and the cut is a minimal cut.

Note that the flow through each of the two arrows that connect ''S'' to ''T'' is at full capacity; this is always the case: a minimal cut represents a 'bottleneck' of the system.