# girth

From igraph v0.5.5-3
by Gabor Csardi

##### Girth of a graph

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

- Keywords
- graphs

##### 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.

##### concept

Girth

##### 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 <- graph.tree(1000, 3)
girth(g)
# The worst case running time is for a ring
g <- graph.ring(100)
girth(g)
# What about a random graph?
g <- erdos.renyi.game(1000, 1/1000)
girth(g)
```

*Documentation reproduced from package igraph, version 0.5.5-3, License: GPL (>= 2)*

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