triangulation = list of three-element lists.

Supply a previously computed Delaunay triangulation of P. The input must be a valid Delaunay triangulation in the format returned by ComputationalGeometry[DelaunayTriangulation]: a list of three-element lists of integers, representing triangles in a triangulation of P.

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 Euclidean distance between points. The default is false.

The DelaunayGraph(P, opts) command returns a Delaunay graph for the point set P.

The parameter P must be a Matrix or list of lists representing a set of points.

Let $P$ be a set of points in $n$ dimensions.

A Delaunay graph is a undirected graph corresponding to a Delaunay triangulation on P. Its vertices correspond to the points in $P$ and an edge exists between points $p$ and $q$ from $P$ whenever $p$ and $q$ form the corners of a triangle in a Delaunay triangulation.

The Delaunay graph is an example of geometric spanner, a graph for which the weighted graph distance connecting any two vertices $p$ and $q$ is a bounded multiple of the Euclidean distance between $p$ and $q$.

The Gabriel graph on $P$ is a subgraph of the Delaunay graph on $P$.

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

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

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

$\mathrm{DG}≔\mathrm{DelaunayGraph}\left(\mathrm{points}\right)$

$\mathrm{DG}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 60\; vertices\; and\; 167\; edge(s)}$

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

Chew, L. Paul (1986), "There is a planar graph almost as good as the complete graph", Proc. 2nd Annual Symposium on Computational Geometry, pp. 169–177. doi:10.1145/10515.10534

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

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