# FindKClub

FindKClub[g,k]

finds a largest k-club in the graph g.

# Details

• A k-club is a maximal set of vertices where the diameter of the corresponding subgraph is at most k.
• FindKClub returns a list of k-clubs.
• FindKClub will return an empty list if there is no k-club.
• FindKClub works with undirected graphs and multigraphs.

# Background & Context

• FindKClub finds one or more largest k-clubs in a graph, returning them as a list of vertices. Here, a k-club is a maximal set of vertices for which the 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-clubs 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).
• 1-clubs are cliques. While all k-clans are k-clubs, the converse is not always true. However, a k-club is always contained in a k-clique. Related functions include FindClique, FindKClan, FindKClique, and FindKPlex.

# Examples

open allclose all

## Basic Examples(1)

Find a largest 2-club in a graph:

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Show the 2-club:

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