# maxClique

##### Find all the cliques in a graph

Find all the cliques in a graph

- Keywords
- models

##### Usage

`maxClique(g, nodes=NULL, edgeMat=NULL)`

##### Arguments

- g
- an instance of the
`graph`

class - nodes
- vector of node names, to be supplied if
`g`

is not - edgeMat
- 2 x p matrix with indices of edges in nodes, one-based, only to be supplied if codeg is not

##### Details

Notice the maximum clique problem is NP-complete, which means it cannot be solved by any known polynomial algorithm.

We implemented the algorithm by C. Bron and J. Kerbosch,

It is an error to supply both `g`

and either of the other arguments.

If `g`

is not supplied, no checking of the consistency of
`nodes`

and `edgeMat`

is performed.

##### Value

- maxClique
- list of all cliques in
`g`

##### References

Finding all cliques of an undirected graph, by C. Bron and J. Kerbosch, Communication of ACM, Sept 1973, Vol 16, No. 9.

##### Examples

```
con1 <- file(system.file("XML/conn.gxl",package="RBGL"), open="r")
coex <- fromGXL(con1)
close(con1)
maxClique(coex)
con2 <- file(system.file("XML/hcs.gxl",package="RBGL"), open="r")
coex <- fromGXL(con2)
close(con2)
maxClique(coex)
```

*Documentation reproduced from package RBGL, version 1.48.1, License: Artistic-2.0*

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