# R igraph manual pages

Use this if you are using igraph from R

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

### Description

Listing all minimum (s,t)-cuts of a directed graph, for given s and t.

### Usage

```st_min_cuts(graph, source, target, capacity = NULL)
```

### Arguments

 `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 `NULL` and the graph has a `weight` edge attribute, then this attribute defines the edge capacities. For forcing unit edge capacities, even for graphs that have a `weight` edge attribute, supply `NA` here.

### 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.

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.

### Value

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.

### 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_cuts`, `min_separators`
```