distribution=function

This option can take any value understood by the RandomTools distribution generator. See RandomTools/flavor/distribution. This method will generate $n+n^{\frac{1}{d}}$ points and check if there were $n$ unique points generated.  If not, it will try again. If both distribution and generator options are given, only generator will be used.

generator=function

This option can take a custom procedure that generates points (as lists) of the appropriate dimension. This method will generate $n+n^{\frac{1}{d}}$ points and check if there were $n$ unique points generated.  If not, it will try again. If both distribution and generator options are given, only generator will be used.

seed=posint

Specify a seed to send to randomize before generating the random points.

The random layout method uses RandomTools:-Generate to generate random positions for the vertices of the graph. By default, this method randomly populates a ${\left[2n^{\frac{1}{d}}\right]}^d$ grid with the graph vertices (with an additional small random perturbation added to reduce the likelihood of overlapping edges).

This layout method works in two and three dimensions.

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

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

$G≔\mathrm{Graph}\left(\mathrm{undirected}\,\left\{\left\{1\,2\right\}\,\left\{1\,4\right\}\,\left\{2\,3\right\}\,\left\{3\,4\right\}\right\}\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 4\; vertices\; and\; 4\; edge(s)}$

$\mathrm{DrawGraph}\left(G\,\mathrm{layout}=\mathrm{random}\right)$

$\mathrm{DrawGraph}\left(G\,\mathrm{layout}=\mathrm{random}\,\mathrm{layoutoptions}=\left[\mathrm{distribution}=\mathrm{Normal}\left(0\,0.5\right)\right]\right)$

$R≔\mathrm{RandomTools}:-\mathrm{Generate}\left(\mathrm{list}\left(\mathrm{distribution}\left(\mathrm{Uniform}\left(-0.97\,0.97\right)\right)\,2\right)\,\mathrm{makeproc}\right)\:$

$\mathrm{DrawGraph}\left(G\,\mathrm{layout}=\mathrm{random}\,\mathrm{layoutoptions}=\left[\mathrm{generator}=R\right]\right)$

$H≔\mathrm{HypercubeGraph}\left(3\right)$

$H≔\mathrm{Graph\; 2:\; an\; undirected\; unweighted\; graph\; with\; 8\; vertices\; and\; 12\; edge(s)}$

$\mathrm{DrawGraph}\left(H\,\mathrm{layout}=\mathrm{random}\,\mathrm{dimension}=3\right)$