# cliques

##### The functions find cliques, ie. complete subgraphs in a graph

These functions find all, the largest or all the maximal cliques in an undirected graph. The size of the largest clique can also be calculated.

- Keywords
- graphs

##### Usage

```
cliques(graph, min=NULL, max=NULL)
largest.cliques(graph)
maximal.cliques(graph)
clique.number(graph)
```

##### Arguments

- graph
- The input graph, directed graphs will be considered as undirected ones, multiple edges and loops are ignored.
- min
- Numeric constant, lower limit on the size of the cliques to
find.
`NULL`

means no limit, ie. it is the same as 0. - max
- Numeric constant, upper limit on the size of the cliques to
find.
`NULL`

means no limit.

##### Details

`cliques`

find all complete subgraphs in the input graph, obeying
the size limitations given in the `min`

and `max`

arguments.

`largest.cliques`

finds all largest cliques in the input graph. A
clique is largest if there is no other clique including more vertices.

`maximal.cliques`

finds all maximal cliques in the input graph.
A clique in maximal if it cannot be extended to a larger clique. The
largest cliques are always maximal, but a maximal clique is not
neccessarily the largest.

`clique.number`

calculates the size of the largest clique(s).

The current implementation of these functions searches
for maximal independent vertex sets (see
`independent.vertex.sets`

) in the complementer graph.

##### Value

`cliques`

,`largest.cliques`

and`clique.number`

return a list containing numeric vectors of vertex ids. Each list element is a clique.`clique.number`

returns an integer constant.

##### concept

- Clique
- Maximal clique
- Largest clique

##### See Also

##### Examples

```
# this usually contains cliques of size six
g <- erdos.renyi.game(100, 0.3)
clique.number(g)
cliques(g, min=6)
largest.cliques(g)
# To have a bit less maximal cliques, about 100-200 usually
g <- erdos.renyi.game(100, 0.03)
maximal.cliques(g)
```

*Documentation reproduced from package igraph, version 0.5.3, License: GPL (>= 2)*