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 non-ajacent 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 V-X, generates the cut that contains exactly the edges that go from X to V-X. |
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 Provan-Shier 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")