Minimal Separator / Vertex disjoint Paths

I'm in need of implementing the algorithm to actually locate the minimal vertex separators set of the whole graph (not just s-t).

It is my understanding that this can be done by doing the s-t procedure for all possible vertex pairs and then looking at the minimal sets of vertex independent paths that arise from that.

Now, I get that all possible paths can be found easily by solving "max flow" s-t, and I do it with matlab, but I'm curious about getting the maximally vertex independent sets of paths.

I understand, from this that this can be acheived by doubling the vertices in some way, but I'm not able to figure it out on my own.

Question covering a similar issue: I'm specifically interested in case (a) that the first comment termed "network flow". Practical algorithms for the disjoint paths problem