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

This procedure creates a graph whose vertex set is the usual set-theoretic union of the vertex sets of G and H, and which has an edge for each edge of G and for each edge of H.

Multiple edges that have the same endpoints are retained unless 'SIMPLE' is specified, in which case multiple edges are reduced to a single edge.

This routine is normally loaded by using the command with(networks), but it may also be referenced by using the full name networks[gunion](...).

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

$G≔\mathrm{complete}\left(\left\{\mathrm{a1}\,\mathrm{a2}\,\mathrm{a3}\,\mathrm{a4}\right\}\right)\:$

$H≔\mathrm{complete}\left(2\,3\right)\:$

$J≔\mathrm{void}\left(\left\{2\,4\,\mathrm{a1}\,\mathrm{a2}\right\}\right)\:$

$\mathrm{addedge}\left(\mathrm{Cycle}\left(\mathrm{a1}\,\mathrm{a2}\,2\,4\right)\,J\right)\:$

$U≔\mathrm{gunion}\left(G\,J\right)\:$

$\mathrm{ends}\left(\left[\mathrm{op}\left(\mathrm{edges}\left(U\right)\right)\right]\,U\right)$

$\left[\left\{\mathrm{a1}\,\mathrm{a2}\right\}\,\left\{4\,\mathrm{a1}\right\}\,\left\{\mathrm{a1}\,\mathrm{a3}\right\}\,\left\{\mathrm{a1}\,\mathrm{a4}\right\}\,\left\{\mathrm{a2}\,\mathrm{a3}\right\}\,\left\{\mathrm{a2}\,\mathrm{a4}\right\}\,\left\{\mathrm{a3}\,\mathrm{a4}\right\}\,\left\{\mathrm{a1}\,\mathrm{a2}\right\}\,\left\{2\,\mathrm{a2}\right\}\,\left\{2\,4\right\}\right]$

$U≔\mathrm{gunion}\left(U\,H\,'\mathrm{SIMPLE}'\right)\:$

$\mathrm{vertices}\left(U\right)$

$\left\{1\,2\,3\,4\,5\,\mathrm{a1}\,\mathrm{a2}\,\mathrm{a3}\,\mathrm{a4}\right\}$

$\mathrm{ends}\left(\left[\mathrm{op}\left(\mathrm{edges}\left(U\right)\right)\right]\,U\right)$

$\left[\left\{1\,3\right\}\,\left\{\mathrm{a1}\,\mathrm{a3}\right\}\,\left\{\mathrm{a1}\,\mathrm{a4}\right\}\,\left\{\mathrm{a2}\,\mathrm{a3}\right\}\,\left\{\mathrm{a2}\,\mathrm{a4}\right\}\,\left\{\mathrm{a3}\,\mathrm{a4}\right\}\,\left\{1\,4\right\}\,\left\{1\,5\right\}\,\left\{2\,3\right\}\,\left\{2\,4\right\}\,\left\{2\,5\right\}\,\left\{2\,\mathrm{a2}\right\}\,\left\{4\,\mathrm{a1}\right\}\,\left\{\mathrm{a1}\,\mathrm{a2}\right\}\right]$