Use this if you are using igraph from R
st_min_cuts {igraph}  R Documentation 
(s,t)
cuts of a graphListing 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 unweighted (=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 
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

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")