Important: The networks package has been deprecated.  Use the superseding package GraphTheory instead.

This procedure tests whether intlist is the degree sequence of a simple graph (or multigraph with no loops if 'MULTI' is specified).

If intlist is graphical (multigraphical) the procedure call returns a list of edges for one realization of intlist as a graph. Otherwise it returns FAIL.

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

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

$\mathrm{new}\left(G\right)\:$

$\mathrm{addvertex}\left(1\,2\,3\,4\,5\,6\,7\,G\right)\:$

$\mathrm{graphical}\left(\left[6\,4\,6\,4\,4\,4\,6\right]\right)$

$\left[\left\{1\,7\right\}\,\left\{1\,3\right\}\,\left\{1\,5\right\}\,\left\{1\,4\right\}\,\left\{1\,6\right\}\,\left\{1\,2\right\}\,\left\{3\,7\right\}\,\left\{6\,7\right\}\,\left\{4\,7\right\}\,\left\{5\,7\right\}\,\left\{2\,7\right\}\,\left\{2\,3\right\}\,\left\{3\,5\right\}\,\left\{3\,4\right\}\,\left\{3\,6\right\}\,\left\{2\,6\right\}\,\left\{4\,5\right\}\right]$

$\mathrm{addedge}\left(\,G\right)\:$

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

$\left[4\,4\,4\,4\,6\,6\,6\right]$

$\mathrm{new}\left(H\right)\:$

$\mathrm{addvertex}\left(1\,2\,3\,4\,5\,6\,7\,H\right)\:$

$\mathrm{graphical}\left(\left[3\,3\,6\,6\,6\,3\,3\right]\,'\mathrm{MULTI}'\right)$

$\left[\left\{3\,4\right\}\,\left\{3\,5\right\}\,\left\{3\,4\right\}\,\left\{3\,5\right\}\,\left\{3\,4\right\}\,\left\{3\,5\right\}\,\left\{4\,5\right\}\,\left\{4\,7\right\}\,\left\{4\,6\right\}\,\left\{1\,2\right\}\,\left\{2\,5\right\}\,\left\{1\,2\right\}\,\left\{6\,7\right\}\,\left\{1\,7\right\}\,\left\{5\,6\right\}\right]$

$\mathrm{addedge}\left(\,H\right)\:$

$\mathrm{vdegree}\left(3\,H\right)$

$6$

$\mathrm{graphical}\left(\left[5\,4\,3\,2\,1\,1\right]\right)$

$\mathrm{FAIL}$