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Description
A cut set of a digraph D
is any set of edges whose removal disconnects it. The edge connectivity of D
is the minimum size of any cut set of D
. It would be nice to have an edge-based counterpart to VertexConnectivity
(see #94 , if we ever get it merged :D). Using the DigraphMaximumFlow
function, as a consequence of the max-flow min cut theorem, we could naively compute the edge connectivity as the minimum of Sum(DigraphMaximumFlow(D, u, v)[u])
where u, v
range over all pairs of vertices of D
, but this might be a bit too slow (because the maximum flow computation already takes O(V^2 * E)
time, where V
is the number of vertices and E
is the number of edges).
The notes by Abdol-Hossein Esfahanian [1] have quite a detailed exposition detailing various optimizations on top of this to reduce the number of max-flow calls and also covers arc-connectivity (strong edge-connectivity), so could be a good starting point.
1: "Connectivity Algorithms" by Abdol-Hossein Esfahanian's
https://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
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