An edge cut is a set of edges that, if removed from a connected graph, will disconnect the graph.
A minimal edge cut is an edge cut such that if any edge is put back in the graph, the graph will be reconnected.
A minimum edge cut is an edge cut such that there is no other edge cut containing fewer edges.
Note that a minimum edge cut is always minimal, but a minimal edge cut is not always minimum.
Fig. 1 shows the original graph.
Fig. 2 shows a minimum (and therefore minimal) edge cut.
Fig. 3 shows a minimal edge cut (which is not minimum).
I'd like to find all (not one) minimal edge cuts of the following graph G.
G := GraphTheory:-ConvertGraph(g);
How to find its all minimal edge cuts? I have searched Literature  for the corresponding polynomial algorithm (which you can view). But I don't see any code implementation.
For the above graph (with 20 vertices and 72 edges), perhaps a violent search would be possible.
 Karzanov, A.V., Timofeev, E.A. Efficient algorithm for finding all minimal edge cuts of a nonoriented graph. Cybern Syst Anal 22, 156–162 (1986). https://doi.org/10.1007/BF01074775