norm : integer or one of Euclidean 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].

vertices : list of integers, strings or symbols

Specifies the vertices to be used in the generated graph.

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.

The UnitDiskGraph(P, threshold, opts) command returns a graph whose vertices correspond to points from P and in which two vertices share an edge if the distance between their corresponding points is less than or equal to threshold.

The optional threshold must be a nonnegative real number or infinity. If not specified, a threshold of 1 is used.

A value of infinity for threshold will produce a complete weighted graph on the point set P.

$\mathrm{points}≔\mathrm{LinearAlgebra}:-\mathrm{RandomMatrix}\left(60\,2\,\mathrm{generator}=0..100.\,\mathrm{datatype}=\mathrm{float}\left[8\right]\right)$

$\mathrm{points}≔\begin{array}{c}\left[\begin{array}{cc}9.85017697341803& 82.9750304386195\\ 86.0670183749663& 83.3188659363996\\ 64.3746795546741& 73.8671607639673\\ 57.3670557294666& 2.34399775883031\\ 23.6234264844933& 52.6873367387328\\ 47.0027547350003& 22.2459488367552\\ 74.9213491558963& 62.0471820220718\\ 92.1513434709073& 96.3107262637080\\ 48.2319624355944& 63.7563267144141\\ 90.9441877431805& 33.8527464913022\\ ⋮& ⋮\end{array}\right]\\ \hfill \text{60 × 2 Matrix}\end{array}$

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

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

$G≔\mathrm{UnitDiskGraph}\left(\mathrm{points}\,10\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 60\; vertices\; and\; 54\; edge(s)}$

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

The GraphTheory[GeometricGraphs][UnitDiskGraph] command was introduced in Maple 2020.

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