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Transportation networks are used to model the flow of Commodity , Information , or Traffic (see Transport Network ).


DEFINITIONS


A transportation network ''G'' is a graph with
  • Exactly one Vertex of in-degree 0 (no incoming Edges or '''arcs'''), called the '''source''';

  • Exactly one vertex of out-degree 0 (no outgoing arcs), called the '''sink''';

  • Non-negative weight, called capacity assigned to each arc.


Flows represent commodity flowing along arcs from the source to the sink. The amount of flow along each arc may not exceed the arc's capacity, and none of the commodity may be 'lost' along the way (that is, the total flow out of the source must equal the total flow into the sink).

A cut in a network is a Partition of its vertices into two sets, ''S'' and ''T'', such that the source is in ''S'' and the sink is in ''T''.

The cut set is the Set of all arcs that connect some vertex in ''S'' with some vertex in ''T''.


SEE ALSO