cliques: Functions to find cliques, i.e. complete subgraphs in a graph

In igraph: Network Analysis and Visualization

Functions to find cliques, i.e. complete subgraphs in a graph

Description

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.

Usage

cliques(graph, min = 0, max = 0)

largest_cliques(graph)

max_cliques(graph, min = NULL, max = NULL, subset = NULL, file = NULL)

count_max_cliques(graph, min = NULL, max = NULL, subset = NULL)

clique_num(graph)

largest_weighted_cliques(graph, vertex.weights = NULL)

weighted_clique_num(graph, vertex.weights = NULL)

clique_size_counts(graph, min = 0, max = 0, maximal = FALSE)

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, i.e. it is the same as 0.
max	Numeric constant, upper limit on the size of the cliques to find. NULL means 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.
vertex.weights	Vertex weight vector. If the graph has a weight vertex attribute, then this is used by default. If the graph does not have a weight vertex attribute and this argument is NULL, then every vertex is assumed to have a weight of 1. Note that the current implementation of the weighted clique finder supports positive integer weights only.
maximal	Specifies whether to look for all weighted cliques (FALSE) or only the maximal ones (TRUE).

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 is maximal if it cannot be extended to a larger clique. The largest cliques are always maximal, but a maximal clique is not necessarily the largest.

count_max_cliques() counts the maximal cliques.

clique_num() calculates the size of the largest clique(s).

clique_size_counts() returns a numeric vector representing a histogram of clique sizes, between the given minimum and maximum clique size.

Value

cliques(), largest_cliques() and clique_num() return a list containing numeric vectors of vertex ids. Each list element is a clique, i.e. a vertex sequence of class igraph.vs().

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.

clique_size_counts() returns a numeric vector with the clique sizes such that the i-th item belongs to cliques of size i. Trailing zeros are currently truncated, but this might change in future versions.

Related documentation in the C library

igraph_cliques(), igraph_largest_cliques(), igraph_clique_number(), igraph_largest_weighted_cliques(), igraph_weighted_clique_number(), igraph_maximal_cliques_hist(), igraph_clique_size_hist().

Author(s)

Tamas Nepusz [e-mail] and Gabor Csardi [e-mail]

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. https://arxiv.org/abs/1006.5440

See Also

Other cliques: ivs(), weighted_cliques()

Examples

# 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)

igraph documentation built on Oct. 20, 2024, 1:06 a.m.