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.)