# kCliques

0th

Percentile

##### Find all the k-cliques in an undirected graph

Find all the k-cliques in an undirected graph

Keywords
models
##### Usage
kCliques(g)
##### Arguments
g
an instance of the graph class
##### Details

Notice that there are different definitions of k-clique in different context.

In computer science, a k-clique of a graph is a clique, i.e., a complete subgraph, of k nodes.

In Social Network Analysis, a k-clique in a graph is a subgraph where the distance between any two nodes is no greater than k.

Here we take the definition in Social Network Analysis.

Let D be a matrix, D[i][j] is the shortest path from node i to node j. Algorithm is outlined as following: (1) use Johnson's algorithm to fill D; let N = max(D[i][j]) for all i, j; (2) each edge is a 1-clique by itself; (3) for k = 2, ..., N, try to expand each (k-1)-clique to k-clique: (3.1) consider a (k-1)-clique the current k-clique KC; (3.2) repeat the following: if for all nodes j in KC, D[v][j]

##### Value

A list of length N; k-th entry (k = 1, ..., N) is a list of all the k-cliques in graph g.

##### References

Social Network Analysis: Methods and Applications. By S. Wasserman and K. Faust, pp. 258.

• kCliques
##### Examples
con <- file(system.file("XML/snacliqueex.gxl",package="RBGL"))
coex <- fromGXL(con)
close(con)

kCliques(coex)

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

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