Wolfram Language & System 10.3 (2015)|Legacy Documentation

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finds a largest k-club in the graph g.


  • 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
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.
Introduced in 2012
| Updated in 2014