# 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 nmin and nmax 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.

FindKClan[{vw,},]

uses rules vw to specify the graph g.

# Details • 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 & Context

• 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.
• In contrast, 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.

# Examples

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## Basic Examples(2)

Find a largest 2-clan in a graph:

 In:= In:= Out= Show the 2-clan:

 In:= Out= Find all 4-clans:

 In:= In:= Out= ## Properties & Relations(8)

Introduced in 2012
(9.0)
|
Updated in 2015
(10.3)