# R igraph manual pages

Use this if you are using igraph from R

## List all (s,t)-cuts of a graph

### Description

List all (s,t)-cuts in a directed graph.

### Usage

```st_cuts(graph, source, target)
```

### Arguments

 `graph` The input graph. It must be directed. `source` The source vertex. `target` The target vertex.

### Details

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.

### Value

A list with entries:

 `cuts` A list of numeric vectors containing edge ids. Each vector is an (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.

### Author(s)

Gabor Csardi csardi.gabor@gmail.com

### References

JS Provan and DR Shier: A Paradigm for listing (s,t)-cuts in graphs, Algorithmica 15, 351–372, 1996.

`st_min_cuts` to list all minimum cuts.

### Examples

```
# A very simple graph
g <- graph_from_literal(a -+ b -+ c -+ d -+ e)
st_cuts(g, source="a", target="e")

# A somewhat more difficult graph
g2 <- graph_from_literal(s --+ a:b, a:b --+ t,
a --+ 1:2:3, 1:2:3 --+ b)
st_cuts(g2, source="s", target="t")
```

[Package igraph version 1.2.7 Index]