maxClique: Find all the cliques in a graph

In RBGL: An interface to the BOOST graph library

Description

Find all the cliques in a graph

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

Author(s)

Li Long <[e-mail]>

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)

Example output

Loading required package: graph
Loading required package: BiocGenerics
Loading required package: parallel

Attaching package: 'BiocGenerics'

The following objects are masked from 'package:parallel':

    clusterApply, clusterApplyLB, clusterCall, clusterEvalQ,
    clusterExport, clusterMap, parApply, parCapply, parLapply,
    parLapplyLB, parRapply, parSapply, parSapplyLB

The following objects are masked from 'package:stats':

    IQR, mad, sd, var, xtabs

The following objects are masked from 'package:base':

    Filter, Find, Map, Position, Reduce, anyDuplicated, append,
    as.data.frame, basename, cbind, colMeans, colSums, colnames,
    dirname, do.call, duplicated, eval, evalq, get, grep, grepl,
    intersect, is.unsorted, lapply, lengths, mapply, match, mget,
    order, paste, pmax, pmax.int, pmin, pmin.int, rank, rbind,
    rowMeans, rowSums, rownames, sapply, setdiff, sort, table, tapply,
    union, unique, unsplit, which, which.max, which.min

$maxCliques
$maxCliques[[1]]
[1] "D" "B" "C" "A"

$maxCliques[[2]]
[1] "D" "E" "H"

$maxCliques[[3]]
[1] "F" "E" "H" "G"


$maxCliques
$maxCliques[[1]]
[1] "B1" "B2" "B3" "B4"

$maxCliques[[2]]
[1] "B1" "Y" 

$maxCliques[[3]]
[1] "B1" "A5"

$maxCliques[[4]]
[1] "A2" "A4" "A3"

$maxCliques[[5]]
[1] "A2" "A4" "A1"

$maxCliques[[6]]
[1] "A4" "A5" "A3"

$maxCliques[[7]]
[1] "A4" "A5" "A1"

$maxCliques[[8]]
[1] "A1" "Y" 

$maxCliques[[9]]
[1] "Z" "Y" "X"

$maxCliques[[10]]
[1] "Z"  "B4"

RBGL documentation built on Nov. 8, 2020, 5 p.m.