<sod>Given a network ''N'' = (''V'',''E'') with a set of sources ''S'' = {''s''<sub>1</sub>, ..., ''s''<sub>n</sub>} and a set of sinks ''T'' = {''t''<sub>1</sub>, ..., ''t''<sub>m</sub>} instead of only one source and one sink, we are to find the maximum flow across ''N''. We can transform the multi-source multi-sink problem into a maximum flow problem by adding a ''consolidated source'' connecting to each vertex in ''S'' and a ''consolidated sink ''connected by each vertex in ''T'' (also known as ''supersource'' and ''supersink'') with infinite capacity on each edge (See Fig. 4.1.1.).<eod>
<sod>Given a network {{var|N}} = ({{var|V}},{{var|E}}) with a set of sources {{var|S}} = {{{var|s}}<sub>1</sub>, ..., {{var|s}}<sub>{{var|n}}</sub>} and a set of sinks {{var|T}} = {{{var|t}}<sub>1</sub>, ..., {{var|t}}<sub>{{var|m}}</sub>} instead of only one source and one sink, we are to find the maximum flow across {{var|N}}. We can transform the multi-source multi-sink problem into a maximum flow problem by adding a ''consolidated source'' connecting to each vertex in {{var|S}} and a ''consolidated sink ''connected by each vertex in {{var|T}} (also known as ''supersource'' and ''supersink'') with infinite capacity on each edge (See Fig. 4.1.1.).<eod>