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GraphTheory[GeometricGraphs]

  

SphereOfInfluenceGraph

  

construct a sphere of influence graph

 

Calling Sequence

Parameters

Options

Description

Definition

Examples

Compatibility

Calling Sequence

SphereOfInfluenceGraph( P, opts )

Parameters

P

-

Matrix or list of lists representing set of points

opts

-

(optional) one or more options as specified below

Options

• 

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 SphereOfInfluenceGraph(P, opts) command returns the sphere of influence graph for the point set P.

• 

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

Definition

• 

Given a set P of points, center a ball Bp at each point p with radius equal to the distance between p and its nearest neighbor in P.

• 

The sphere of influence graph is the graph whose vertices correspond to points in P and in which an edge between p and q exists if BpBq contains more than one point.

• 

The sphere of influence graph is not guaranteed to be connected.

• 

The undirected nearest neighbor graph is a subgraph of the sphere of influence graph.

Examples

Generate a set of random two-dimensional points amd draw a sphere of influence graph.

withGraphTheory:

withGeometricGraphs:

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

(1)

SOIGSphereOfInfluenceGraphpoints

SOIGGraph 1: an undirected unweighted graph with 60 vertices and 97 edge(s)

(2)

DrawGraphSOIG

Compatibility

• 

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

• 

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

See Also

GeometricGraphs

GraphTheory[GeometricGraphs][NearestNeighborGraph]