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

st_cuts {igraph} | R Documentation

## 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.

### See Also

`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 1.3.1 Index]