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.

st_min_cuts() to list all minimum cuts.

Other flow: dominator_tree(), edge_connectivity(), is_min_separator(), is_separator(), max_flow(), min_cut(), min_separators(), min_st_separators(), st_min_cuts(), vertex_connectivity()

### 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 1.5.1 Index]