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

This procedure generates various types of complete graphs.  The number of arguments indicates the number of parts.  Each part is specified by an integer indicating the number of vertices in that part.  For example a complete bipartite graph is specified as complete(m, n).

In the case of one argument a set vset of vertex names may be specified.

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

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

$G≔\mathrm{complete}\left(10\right)\:$

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

$\left\{\mathrm{e1}\,\mathrm{e10}\,\mathrm{e11}\,\mathrm{e12}\,\mathrm{e13}\,\mathrm{e14}\,\mathrm{e15}\,\mathrm{e16}\,\mathrm{e17}\,\mathrm{e18}\,\mathrm{e19}\,\mathrm{e2}\,\mathrm{e20}\,\mathrm{e21}\,\mathrm{e22}\,\mathrm{e23}\,\mathrm{e24}\,\mathrm{e25}\,\mathrm{e26}\,\mathrm{e27}\,\mathrm{e28}\,\mathrm{e29}\,\mathrm{e3}\,\mathrm{e30}\,\mathrm{e31}\,\mathrm{e32}\,\mathrm{e33}\,\mathrm{e34}\,\mathrm{e35}\,\mathrm{e36}\,\mathrm{e37}\,\mathrm{e38}\,\mathrm{e39}\,\mathrm{e4}\,\mathrm{e40}\,\mathrm{e41}\,\mathrm{e42}\,\mathrm{e43}\,\mathrm{e44}\,\mathrm{e45}\,\mathrm{e5}\,\mathrm{e6}\,\mathrm{e7}\,\mathrm{e8}\,\mathrm{e9}\right\}$

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

$\left\{\left\{1\,2\right\}\,\left\{1\,3\right\}\,\left\{1\,4\right\}\,\left\{1\,5\right\}\,\left\{1\,6\right\}\,\left\{1\,7\right\}\,\left\{1\,8\right\}\,\left\{1\,9\right\}\,\left\{1\,10\right\}\,\left\{2\,3\right\}\,\left\{2\,4\right\}\,\left\{2\,5\right\}\,\left\{2\,6\right\}\,\left\{2\,7\right\}\,\left\{2\,8\right\}\,\left\{2\,9\right\}\,\left\{2\,10\right\}\,\left\{3\,4\right\}\,\left\{3\,5\right\}\,\left\{3\,6\right\}\,\left\{3\,7\right\}\,\left\{3\,8\right\}\,\left\{3\,9\right\}\,\left\{3\,10\right\}\,\left\{4\,5\right\}\,\left\{4\,6\right\}\,\left\{4\,7\right\}\,\left\{4\,8\right\}\,\left\{4\,9\right\}\,\left\{4\,10\right\}\,\left\{5\,6\right\}\,\left\{5\,7\right\}\,\left\{5\,8\right\}\,\left\{5\,9\right\}\,\left\{5\,10\right\}\,\left\{6\,7\right\}\,\left\{6\,8\right\}\,\left\{6\,9\right\}\,\left\{6\,10\right\}\,\left\{7\,8\right\}\,\left\{7\,9\right\}\,\left\{7\,10\right\}\,\left\{8\,9\right\}\,\left\{8\,10\right\}\,\left\{9\,10\right\}\right\}$

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

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

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

$K≔\mathrm{complete}\left(\left\{\mathrm{ETH}\,\mathrm{SFU}\,\mathrm{UofS}\,\mathrm{UofW}\right\}\right)\:$

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

$\left\{\left\{\mathrm{ETH}\,\mathrm{SFU}\right\}\,\left\{\mathrm{ETH}\,\mathrm{UofS}\right\}\,\left\{\mathrm{ETH}\,\mathrm{UofW}\right\}\,\left\{\mathrm{SFU}\,\mathrm{UofS}\right\}\,\left\{\mathrm{SFU}\,\mathrm{UofW}\right\}\,\left\{\mathrm{UofS}\,\mathrm{UofW}\right\}\right\}$