The opts argument can contain one or more of the options shown below.

directed=true or false

This option specifies whether the resulting graph should be directed. The default is false.

layout=true or false

This option specifies whether a default coordinate assignment for the vertices of the graph should be made. The default is true.

selfloops=true or false

This option specifies whether the generated graph should include a self-loop for each vertex. The default is false.

vertexpositions=p

Specifies coordinate positions for the vertices for use with DrawGraph.

CompleteGraph(n) returns the complete graph on n vertices. CompleteGraph(V) does the same thing except the vertices are labeled using the entries of V.

CompleteGraph(n, m) returns the complete bipartite graph with bipartitions of size n and m.

CompleteGraph(n1,...,nk) returns the complete multipartite graph with partitions of size n1,..., nk.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{K4}≔\mathrm{CompleteGraph}\left(4\right)$

$\mathrm{K4}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 4\; vertices\; and\; 6\; edge(s)}$

$\mathrm{Edges}\left(\mathrm{K4}\right)$

$\left\{\left\{1\,2\right\}\,\left\{1\,3\right\}\,\left\{1\,4\right\}\,\left\{2\,3\right\}\,\left\{2\,4\right\}\,\left\{3\,4\right\}\right\}$

$\mathrm{DrawGraph}\left(\mathrm{K4}\right)$

$G≔\mathrm{CompleteGraph}\left(\left[a\,b\,c\right]\right)$

$G≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 3\; vertices\; and\; 3\; edge(s)}$

$\mathrm{Edges}\left(G\right)$

$\left\{\left\{a\,b\right\}\,\left\{a\,c\right\}\,\left\{b\,c\right\}\right\}$

$\mathrm{K23}≔\mathrm{CompleteGraph}\left(2\,3\right)$

$\mathrm{K23}≔\mathrm{Graph\; 3:\; an\; undirected\; graph\; with\; 5\; vertices\; and\; 6\; edge(s)}$

$\mathrm{Edges}\left(\mathrm{K23}\right)$

$\left\{\left\{1\,3\right\}\,\left\{1\,4\right\}\,\left\{1\,5\right\}\,\left\{2\,3\right\}\,\left\{2\,4\right\}\,\left\{2\,5\right\}\right\}$

$\mathrm{DrawGraph}\left(\mathrm{K23}\,\mathrm{style}=\mathrm{bipartite}\right)$

The directed and layout options were introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.

The selfloops option was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.

The GraphTheory[CompleteGraph] command was updated in Maple 2023.

The vertexpositions option was introduced in Maple 2023.

For more information on Maple 2023 changes, see Updates in Maple 2023.