GraphComplement returns the complement of a graph G, that is the graph with the same vertex set as G, but whose edge (arc) set consists of the edges (arcs) not present in G.

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

$C≔\mathrm{CycleGraph}\left(5\right)$

$C≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 5\; vertices\; and\; 5\; edge(s)}$

$G≔\mathrm{GraphComplement}\left(C\right)$

$G≔\mathrm{Graph\; 2:\; an\; undirected\; unweighted\; graph\; with\; 5\; vertices\; and\; 5\; edge(s)}$

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

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

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

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

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

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