FindKClan

FindKClan[g,k]
finds a largest k-clan in the graph g.

FindKClan[g,k,n]
finds a k-clan containing at most n vertices.

FindKClan[g,k,{n}]
finds a k-clan containing exactly n vertices.

FindKClan[g,k,{nmin,nmax}]
finds a k-clan containing between and vertices.

FindKClan[g,k,nspec,s]
finds at most s k-clans.

FindKClan[{g,v},k,]
finds k-clans that include the vertex v only.

DetailsDetails

  • A k-clan is a k-clique where the diameter of the corresponding subgraph is at most k.
  • FindKClan returns a list of k-clans.
  • FindKClan will return an empty list if there is no k-clan.
  • FindKClan[,k,nspec,All] finds all the k-clans.
  • FindKClan works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

Background
Background

  • FindKClan finds one or more k-clans in a graph, returning them as a list of vertices. Here, a k-clan is a k-clique such that the graph diameter (i.e. the length of the longest possible path between two vertices) of the subgraph induced by the vertices is at most k. k-clans are used in project selection, pattern matching, finance, and network analysis.
  • FindKClique can be used to find k-cliques of different subgraph diameter, 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 subgraph diameter, a specified number of cliques, or all.
  • 1-clans are cliques. All k-clans are k-clubs and k-cliques, but the converse is not always true. Related functions include FindClique, FindKClique, FindKClub, and FindKPlex.
Introduced in 2012
(9.0)
| Updated in 2014
(10.0)