# R igraph manual pages

Use this if you are using igraph from R

## Girth of a graph

### Description

The girth of a graph is the length of the shortest circle in it.

### Usage

```girth(graph, circle = TRUE)
```

### Arguments

 `graph` The input graph. It may be directed, but the algorithm searches for undirected circles anyway. `circle` Logical scalar, whether to return the shortest circle itself.

### Details

The current implementation works for undirected graphs only, directed graphs are treated as undirected graphs. Loop edges and multiple edges are ignored. If the graph is a forest (ie. acyclic), then zero is returned.

This implementation is based on Alon Itai and Michael Rodeh: Finding a minimum circuit in a graph Proceedings of the ninth annual ACM symposium on Theory of computing, 1-10, 1977. The first implementation of this function was done by Keith Briggs, thanks Keith.

### Value

A named list with two components:

 `girth` Integer constant, the girth of the graph, or 0 if the graph is acyclic. `circle` Numeric vector with the vertex ids in the shortest circle.

### Author(s)

Gabor Csardi csardi.gabor@gmail.com

### References

Alon Itai and Michael Rodeh: Finding a minimum circuit in a graph Proceedings of the ninth annual ACM symposium on Theory of computing, 1-10, 1977

### Examples

```
# No circle in a tree
g <- make_tree(1000, 3)
girth(g)

# The worst case running time is for a ring
g <- make_ring(100)
girth(g)

# What about a random graph?
g <- sample_gnp(1000, 1/1000)
girth(g)

```

[Package igraph version 1.2.5 Index]