 GraphTheory[GeometricGraphs] - Maple Programming Help

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GraphTheory[GeometricGraphs]

 UnitDiskGraph
 construct a unit disk graph

 Calling Sequence UnitDiskGraph( P, f, opts )

Parameters

 P - Matrix or list of lists representing set of points threshold - (optional) positive real number opts - (optional) one or more options as specified below

Options

 • norm : integer or one of Euclidean or infinity.
 Specifies the norm to be used in computing distances. The default is 2, the Euclidean 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.

Description

 • 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.

Examples

Generate a set of random two-dimensional points and connect edges when the Euclidean distance between them is less than or equal to 10.

 > $\mathrm{points}≔\mathrm{LinearAlgebra}:-\mathrm{RandomMatrix}\left(60,2,\mathrm{generator}=0..100.,\mathrm{datatype}=\mathrm{float}\left[8\right]\right)$
  (1)
 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{GeometricGraphs}\right):$
 > $G≔\mathrm{UnitDiskGraph}\left(\mathrm{points},10\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 60 vertices and 54 edge\left(s\right)}}$ (2)
 > $\mathrm{DrawGraph}\left(G\right)$ Compatibility

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