Important: The networks package has been deprecated.  Use the superseding command GraphTheory[GraphComplement] instead.

The complement of a graph is computed and returned as a new graph.  If one argument is used, then the complement is relative to the complete graph on the same number of vertices.  If a second argument is given then the complement is relative to the given graph.

This routine is normally loaded via the command with(networks) but can also be referenced using the full name networks[complement](...).

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

$G≔\mathrm{cycle}\left(5\right)\:$

$H≔\mathrm{complement}\left(G\right)\:$

$\mathrm{ends}\left(H\right)$

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

$K≔\mathrm{complete}\left(5\right)\:$

$\mathrm{delete}\left(\mathrm{edges}\left(\left\{1\,3\right\}\,K\right)\,K\right)\:$

$\mathrm{Kc}≔\mathrm{complement}\left(G\,K\right)\:$

$\mathrm{ends}\left(\mathrm{Kc}\right)$

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