The Contract command contracts the specified edge of a graph. By default, all the loops and multiple edges are removed. By setting multi=true, the loops and multiple edges are preserved and the output is a weighted graph.

To contract multiple edges in a graph, use ContractSubgraph or use the foldl command.

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

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

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

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

$\mathrm{Contract}\left(G\,\left\{1\,3\right\}\right)$

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

$\mathrm{Contract}\left(G\,\left\{1\,3\right\}\,\mathrm{multi}=\mathrm{true}\right)$

$\mathrm{Graph\; 3:\; an\; undirected\; weighted\; graph\; with\; 3\; vertices,\; 3\; edge(s),\; and\; 1\; self-loop(s)}$

$P≔\mathrm{PetersenGraph}\left(\right)$

$P≔\mathrm{Graph\; 4:\; an\; undirected\; unweighted\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

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

$G≔\mathrm{foldl}\left(\mathrm{Contract}\,P\,\left\{1\,6\right\}\,\left\{2\,9\right\}\,\left\{3\,7\right\}\,\left\{4\,10\right\}\,\left\{5\,8\right\}\right)$

$G≔\mathrm{Graph\; 5:\; an\; undirected\; unweighted\; graph\; with\; 5\; vertices\; and\; 10\; edge(s)}$

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

$5$

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

$\mathrm{true}$