distribution = algebraic or list(algebraic)

A continuous distribution as supported by the Statistics package, or list of such distributions. The default is the uniform distribution between 0 and 1.

norm = integer or one of Frobenius or infinity.

Specifies the norm to be used in computing distances. The default is 2, the Euclidean norm.

For more information on norms, see LinearAlgebra[Norm].

seed = integer or none

Seed for the random number generator. Equivalent to calling randomize(seed) immediately before invoking this function.

weighted = true or false

If weighted=true, the result is a weighted graph whose edge weights correspond to the distance between points using the specified norm. Default is false.

RandomGeometricGraph(n,t,dims,opts) creates a random geometric graph on n vertices. A random geometric graph is a graph whose vertices correspond to a set of randomly generated points, and whose edges correspond with those pairs of points whose distance falls under a specified threshold t.

If omitted, the parameter dims is assumed to be 2 unless a multidimensional distribution was specified with the distribution option, in which case dims is taken to be numelems(distribution).

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

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

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

$\mathrm{G1}≔\mathrm{RandomGeometricGraph}\left(100\,1\right)$

$\mathrm{G1}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 100\; vertices\; and\; 4795\; edges}$

$\mathrm{G2}≔\mathrm{RandomGeometricGraph}\left(100\,1\,\mathrm{weighted}\right)$

$\mathrm{G2}≔\mathrm{Graph\; 2:\; an\; undirected\; weighted\; graph\; with\; 100\; vertices\; and\; 4837\; edges}$

$\mathrm{interface}\left(\mathrm{rtablesize}=4\right)\:$

$\mathrm{WeightMatrix}\left(\mathrm{G2}\right)$

$\begin{array}{c}\left[\begin{array}{ccccc}0.& 0.676701145737883& 0.168143107093171& 0.112118041294177& \dots \\ 0.676701145737883& 0.& 0.772318810162342& 0.629702446893480& \dots \\ 0.168143107093171& 0.772318810162342& 0.& 0.280260786478517& \dots \\ 0.112118041294177& 0.629702446893480& 0.280260786478517& 0.& \dots \\ ⋮& ⋮& ⋮& ⋮& \end{array}\right]\\ \hfill \text{100 × 100 Matrix}\end{array}$

$\mathrm{G3}≔\mathrm{RandomGeometricGraph}\left(200\,\frac{1}{2}\,\mathrm{norm}=\mathrm{\infty }\,\mathrm{distribution}=\left[\mathrm{`\$`}\left(\mathrm{Normal}\left(0\,1\right)\,3\right)\right]\right)$

$\mathrm{G3}≔\mathrm{Graph\; 3:\; an\; undirected\; graph\; with\; 200\; vertices\; and\; 441\; edges}$

The GraphTheory[RandomGraphs][RandomGeometricGraph] command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.