# FindKPlex

FindKPlex[g,k]

finds a largest k-plex in the graph g.

FindKPlex[g,k,n]

finds a k-plex containing at most n vertices.

FindKPlex[g,k,{n}]

finds a k-plex containing exactly n vertices.

FindKPlex[g,k,{nmin,nmax}]

finds a k-plex containing between nmin and nmax vertices.

FindKPlex[g,k,nspec,s]

finds at most s k-plexes.

FindKPlex[{g,v},k,]

finds k-plexes that include the vertex v only.

FindKPlex[{vw,},]

uses rules vw to specify the graph g.

# Details

• A k-plex is a maximal set of vertices such that each vertex is adjacent to all except k others.
• For a directed graph, the outgoing edges for each vertex connect to all except others.
• FindKPlex returns a list of k-plexes.
• FindKPlex will return an empty list if there is no k-plex.
• FindKPlex[,k,nspec,All] finds all the k-plexes.
• FindKPlex works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

# Examples

open allclose all

## Basic Examples(2)

Find a largest 2-plex in a graph:

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Show the 2-plex:

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Find all 4-plexes:

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