# st_cuts

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

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

- Keywords
- graphs

##### 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:

A list of numeric vectors containing edge ids. Each vector is an \((s,t)\)-cut.

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 \(V-X\).

##### References

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

##### See Also

`st_min_cuts`

to list all minimum cuts.

##### Examples

```
# NOT RUN {
# 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")
# }
```

*Documentation reproduced from package igraph, version 1.2.2, License: GPL (>= 2)*