Calculate Maximum Flows Between Vertices
maxflow calculates a matrix of maximum pairwise flows within a (possibly valued) input network.
maxflow(dat, src = NULL, sink = NULL, ignore.eval = FALSE)
dat |
one or more input graphs. |
src |
optionally, a vector of source vertices; by default, all vertices are selected. |
sink |
optionally, a vector of sink (or target) vertices; by default, all vertices are selected. |
ignore.eval |
logical; ignore edge values (i.e., assume unit capacities) when computing flow? |
maxflow computes the maximum flow from each source vertex to each sink vertex, assuming infinite vertex capacities and limited edge capacities. If ignore.eval==FALSE, supplied edge values are assumed to contain capacity information; otherwise, all non-zero edges are assumed to have unit capacity.
Note that all flows computed here are pairwise – i.e., when computing the flow from v to v', we ignore any other flows which could also be taking place within the network. As a result, it should not be assumed that these flows can be realized simultaneously. (For the latter purpose, the values returned by maxflow can be treated as upper bounds.)
A matrix of pairwise maximum flows (if multiple sources/sinks selected), or a single maximum flow value (otherwise).
Carter T. Butts buttsc@uci.edu
Edmonds, J. and Karp, R.M. (1972). “Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems.” Journal of the ACM, 19(2), 248-264.
g<-rgraph(10,tp=2/9) #Generate a sparse random graph maxflow(g) #Compute all-pairs max flow
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