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GraphTheory[GeometricGraphs]

  

UnitDiskGraph

  

construct a unit disk graph

 

Calling Sequence

Parameters

Options

Description

Examples

Compatibility

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.

  

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.

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.

pointsLinearAlgebra:-RandomMatrix60,2,generator=0..100.,datatype=float8

(1)

withGraphTheory:

withGeometricGraphs:

GUnitDiskGraphpoints,10

GGraph 1: an undirected unweighted graph with 60 vertices and 54 edge(s)

(2)

DrawGraphG

Compatibility

• 

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

• 

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

See Also

GeometricGraphs

GraphTheory[RandomGraphs][RandomGeometricGraph]