Find all the k-cliques in an undirected graph
Find all the k-cliques in an undirected graph
kCliques(g)
g |
an instance of the |
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] <= k, add node v to KC; (3.3) eliminate duplicates; (4) the whole graph is N-clique.
A list of length N; k-th entry (k = 1, ..., N) is a list of all the k-cliques in graph g.
Li Long <li.long@isb-sib.ch>
Social Network Analysis: Methods and Applications. By S. Wasserman and K. Faust, pp. 258.
con <- file(system.file("XML/snacliqueex.gxl",package="RBGL"))
coex <- fromGXL(con)
close(con)
kCliques(coex)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.