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)max_cliques(graph, min = NULL, max = NULL, subset = NULL, file = NULL)
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.
NULLmeans no limit, ie. it is the same as 0.- max
Numeric constant, upper limit on the size of the cliques to find.
NULLmeans no limit.- subset
If not
NULL, then it must be a vector of vertex ids, numeric or symbolic if the graph is named. The algorithm is run from these vertices only, so only a subset of all maximal cliques is returned. See the Eppstein paper for details. This argument makes it possible to easily parallelize the finding of maximal cliques.- file
If not
NULL, then it must be a file name, i.e. a character scalar. The output of the algorithm is written to this file. (If it exists, then it will be overwritten.) Each clique will be a separate line in the file, given with the numeric ids of its vertices, separated by whitespace.
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.
max_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.
count_max_cliques counts the maximal cliques.
clique_num calculates the size of the largest clique(s).
The current implementation of these functions searches for maximal
independent vertex sets (see ivs) in the
complementer graph.
Value
cliques, largest_cliques and clique_num
return a list containing numeric vectors of vertex ids. Each list element is
a clique.
max_cliques returns NULL, invisibly, if its file
argument is not NULL. The output is written to the specified file in
this case.
clique_num and count_max_cliques return an integer
scalar.
References
For maximal cliques the following algorithm is implemented: David Eppstein, Maarten Loffler, Darren Strash: Listing All Maximal Cliques in Sparse Graphs in Near-optimal Time. http://arxiv.org/abs/1006.5440
See Also
Examples
# NOT RUN {
# this usually contains cliques of size six
g <- sample_gnp(100, 0.3)
clique_num(g)
cliques(g, min=6)
largest_cliques(g)
# To have a bit less maximal cliques, about 100-200 usually
g <- sample_gnp(100, 0.03)
max_cliques(g)
# }