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