Use this if you are using igraph from R
Listing all minimum (s,t)cuts of a directed graph, for given s and t.
st_min_cuts(graph, source, target, capacity = NULL)
graph 
The input graph. It must be directed. 
source 
The id of the source vertex. 
target 
The id of the target vertex. 
capacity 
Numeric vector giving the edge capacities. If this is

Given a G directed graph and two, different and nonajacent vertices, s and t, an (s,t)cut is a set of edges, such that after removing these edges from G there is no directed path from s to t.
The size of an (s,t)cut is defined as the sum of the capacities (or weights) in the cut. For unweighed (=equally weighted) graphs, this is simply the number of edges.
An (s,t)cut is minimum if it is of the smallest possible size.
A list with entries:
value 
Numeric scalar, the size of the minimum cut(s). 
cuts 
A list of numeric vectors containing edge ids. Each vector is a minimum (s,t)cut. 
partition1s 
A list of numeric vectors containing vertex ids, they correspond to the edge cuts. Each vertex set is a generator of the corresponding cut, i.e. in the graph G=(V,E), the vertex set X and its complementer VX, generates the cut that contains exactly the edges that go from X to VX. 
Gabor Csardi csardi.gabor@gmail.com
JS Provan and DR Shier: A Paradigm for listing (s,t)cuts in graphs, Algorithmica 15, 351–372, 1996.
# A difficult graph, from the ProvanShier paper g < graph_from_literal(s + a:b, a:b + t, a + 1:2:3:4:5, 1:2:3:4:5 + b) st_min_cuts(g, source="s", target="t")