connected = truefalse

If specified, indicates that the generated graph should be connected.

seed = integer or none

Seed for the random number generator. When an integer is specified, this is equivalent to calling randomize(seed).

RandomRegularGraph(n,d) creates a d-regular undirected unweighted graph on n vertices. n and d cannot both be odd and d must satisfy $d<n$.

If the option connected is specified, the graph created will be connected. n and d must then satisfy n = 1 and d = 0, or n = 2 and d = 1, or $n\&gt;2$ and $d\&gt;1$ as well as the above.

For RandomRegularGraph(n,d,connected), a random tree with maximum $\mathrm{degree}\le d$ is first created.

For generating weighted graphs use weights = f and see AssignEdgeWeights for details about f.

The random number generator used can be seeded using the seed option or the randomize function.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\&colon;$

$\mathrm{with}\left(\mathrm{RandomGraphs}\right)\&colon;$

$R≔\mathrm{RandomRegularGraph}\left(100\&comma;80\&comma;\mathrm{connected}\right)$

$R≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 100\; vertices\; and\; 4000\; edge(s)}$

$\mathrm{IsRegular}\left(R\right)$

$\mathrm{true}$

$\mathrm{IsConnected}\left(R\right)$

$\mathrm{true}$

$R≔\mathrm{RandomRegularGraph}\left(\left[\mathrm{seq}\left(''a''..''j''\right)\right]\&comma;3\&comma;\mathrm{weights}=-10..10\right)$

$R≔\mathrm{Graph\; 2:\; an\; undirected\; weighted\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

$\mathrm{WeightMatrix}\left(R\right)$

$\left[\begin{array}{cccccccccc}0& \mathrm{-1}& 0& 0& 0& 3& 0& 9& 0& 0\\ \mathrm{-1}& 0& 0& 9& 0& 0& 0& 0& \mathrm{-7}& 0\\ 0& 0& 0& 0& 0& 0& 7& \mathrm{-10}& 0& 6\\ 0& 9& 0& 0& 8& 0& 0& 0& \mathrm{-7}& 0\\ 0& 0& 0& 8& 0& \mathrm{-10}& \mathrm{-6}& 0& 0& 0\\ 3& 0& 0& 0& \mathrm{-10}& 0& 0& 0& \mathrm{-2}& 0\\ 0& 0& 7& 0& \mathrm{-6}& 0& 0& 0& 0& \mathrm{-7}\\ 9& 0& \mathrm{-10}& 0& 0& 0& 0& 0& 0& \mathrm{-6}\\ 0& \mathrm{-7}& 0& \mathrm{-7}& 0& \mathrm{-2}& 0& 0& 0& 0\\ 0& 0& 6& 0& 0& 0& \mathrm{-7}& \mathrm{-6}& 0& 0\end{array}\right]$

$f≔\mathrm{RandomTools}:-\mathrm{Generate}\left(\mathrm{float}\left(\mathrm{range}=0.1..1\&comma;\mathrm{digits}=2\right)\&comma;\mathrm{makeproc}=\mathrm{true}\right)\&colon;$

$R≔\mathrm{RandomRegularGraph}\left(10\&comma;3\&comma;\mathrm{weights}=f\right)$

$R≔\mathrm{Graph\; 3:\; an\; undirected\; weighted\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

$\mathrm{WeightMatrix}\left(R\right)$

$\left[\begin{array}{cccccccccc}0& 0& 0.33& 0& 0& 0& 0.42& 0& 0& 0.95\\ 0& 0& 0.33& 0& 0& 0& 0& 0& 0.27& 0.25\\ 0.33& 0.33& 0& 0& 0& 0& 0.64& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0.54& 0.74& 0.83\\ 0& 0& 0& 0& 0& 0.40& 0.54& 0.74& 0& 0\\ 0& 0& 0& 0& 0.40& 0& 0& 0.70& 0.47& 0\\ 0.42& 0& 0.64& 0& 0.54& 0& 0& 0& 0& 0\\ 0& 0& 0& 0.54& 0.74& 0.70& 0& 0& 0& 0\\ 0& 0.27& 0& 0.74& 0& 0.47& 0& 0& 0& 0\\ 0.95& 0.25& 0& 0.83& 0& 0& 0& 0& 0& 0\end{array}\right]$

$U≔\mathrm{rand}\left(1..4\right)\&colon;$

f := proc() local x; x := U(); if x=1 then 1 else 2 end if; end proc:

$H≔\mathrm{RandomRegularGraph}\left(10\&comma;3\&comma;\mathrm{connected}\&comma;\mathrm{weights}=f\right)$

$H≔\mathrm{Graph\; 4:\; an\; undirected\; weighted\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

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

$\left[\begin{array}{cccccccccc}0& 0& 2& 2& 1& 0& 0& 0& 0& 0\\ 0& 0& 2& 1& 0& 0& 1& 0& 0& 0\\ 2& 2& 0& 0& 0& 0& 0& 0& 2& 0\\ 2& 1& 0& 0& 0& 0& 1& 0& 0& 0\\ 1& 0& 0& 0& 0& 0& 0& 2& 2& 0\\ 0& 0& 0& 0& 0& 0& 0& 2& 2& 2\\ 0& 1& 0& 1& 0& 0& 0& 0& 0& 2\\ 0& 0& 0& 0& 2& 2& 0& 0& 0& 2\\ 0& 0& 2& 0& 2& 2& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 2& 2& 2& 0& 0\end{array}\right]$