DESCRIPTION
v.net.flow computes the maximum flow and minimum cut 
between two sets of nodes.
NOTES
The two sets of nodes are called sources and sink 
and v.net.flow finds the maximum flow from the former to 
the latter ones. Edge capacities can be specified by arc_column 
for forward direction and arc_backward_column for backward direction. If 
the latter parameter is omitted then the same capacity is used in 
either direction. The sets are given by the respective cats, 
layer and where parameters. Maximum flow corresponds 
to the maximum amount of water possibly flowing through the network 
preserving the capacity constraints and minimum cut to the set of edges 
of minimum total capacity completely separating sources from sinks. 
The cut produced by this module corresponds to the first fully 
saturated edges from sources to sinks. An attribute table containing 
the flow information is linked to the output map. The table 
consists of two columns: cat and flow and stores 
the flow along each line. Negative flow means that "water" is 
flowing in the backward direction. Cut map contains the edges 
in the minimum cut.
A famous result 
says that the total amount of water flowing is equal to the minimum 
cut.
EXAMPLES
Find maximum flow from factories to stores using SPEED for the capacities.
v.net.flow input=roads output=roads_flow cut=roads_cut arc_column=SPEED \
           source_where="type=factory" sink_where="type=store"
If all the capacties are one then the minimum cut corresponds to the 
minimum number of edges separating sources from sinks. 
v.net.flow input=network output=flow cut=cut arc_column=ones \
           source_cats=1-10 sink_cats=100-100
SEE ALSO
v.net,
v.net.connectivity
AUTHORS
Daniel Bundala, Google Summer of Code 2009, Student
Wolf Bergenheim, Mentor
Last changed: $Date: 2016-08-30 15:30:47 +0200 (Tue, 30 Aug 2016) $