finds a largest k-clique in the graph g.
finds a k-clique containing at most n vertices.
finds a k-clique containing exactly n vertices.
finds a k-clique containing between nmin and nmax vertices.
finds at most s k-cliques.
finds k-cliques that include the vertex v only.
uses rules vw to specify the graph g.
- A k-clique is a maximal set of vertices that are at a distance no greater than k from each other.
- FindKClique returns a list of k-cliques.
- FindKClique will return an empty list if there is no k-clique.
- FindKClique[…,k,nspec,All] finds all the k-cliques.
- FindKClique works with undirected graphs, directed graphs, multigraphs, and mixed graphs.
Background & Context
- FindKClique finds one or more k-cliques in a graph, returning them as a list of vertices. Here, a k-clique is a maximal set of vertices that are at a distance no greater than k from each other. k-cliques are used in project selection, pattern matching, finance, and network analysis.
- FindKClique can be used to find k-cliques of different sizes, from 1 to the largest possible size (in general n for a graph on n vertices). FindKClique can be used to find a single k-clique of specified size, a specified number of cliques, or all.
- 1-cliques are cliques. All k-clans are k-cliques, but the converse is not always true. Related functions include FindClique, FindKClan, FindKClub, and FindKPlex.
Examplesopen allclose all
FindKClique gives an empty list if there is no k-clique:
To prevent data packets from circulating indefinitely in a mobile ad hoc network, a time to live (TTL—the maximum number of edges traversed) value is set to 3. Find all devices that can be reached from device 1: