Overview of the GraphTheory[GeometricGraphs] Subpackage - Maple Programming Help

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Overview of the GraphTheory[GeometricGraphs] Subpackage

 

Description

List of GraphTheory[GeometricGraphs] Subpackage Commands

Gallery of GraphTheory[GeometricGraphs]

Description

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The GraphTheory[GeometricGraphs] subpackage collects routines for generating graphs from geometric data, typically sets of points in 2 or 3 dimensions.

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Some of these geometric graphs have well-known relationships with one another:

  

The Euclidean minimum spanning tree on P is a subgraph of the relative neighborhood graph on P.

  

The nearest neighbor graph on P is a subgraph of the Gabriel graph and the sphere of influence graph on P.

  

The relative neighborhood graph on P is a subgraph of the Urquhart graph on P.

  

The Urquhart graph on P is a subgraph of the Gabriel graph on P.

  

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

List of GraphTheory[GeometricGraphs] Subpackage Commands

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The following is a list of geometric graphs that can be generated.

DelaunayGraph

EuclideanMinimumSpanningTree

FarthestNeighborGraph

GabrielGraph

GeometricMinimumSpanningTree

NearestNeighborGraph

RelativeNeighborhoodGraph

SphereOfInfluenceGraph

UnitDiskGraph

UrquhartGraph

VisibilityGraph

 

Gallery of GraphTheory[GeometricGraphs]

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The following is a gallery of geometric graphs that can be generated.

Delaunay graph

Euclidean minimum spanning tree

Farthest neighbor graph

Gabriel graph

Geometric minimum spanning tree

Nearest neighbor graph

Relative neighborhood graph

Sphere of influence graph

Unit disk graph

Urquhart graph

Visibility graph

 

 

See Also

ComputationalGeometry

GraphTheory

GraphTheory[RandomGraphs][RandomGeometricGraph]