construct a sphere of influence graph
SphereOfInfluenceGraph( P, opts )
Matrix or list of lists representing set of points
(optional) one or more options as specified below
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.
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.
Given a set P of points, center a ball B⁡p 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 B⁡p∩B⁡q 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.
Generate a set of random two-dimensional points amd draw a sphere of influence graph.
points≔9.8501769734180382.975030438619586.067018374966383.318865936399664.374679554674173.867160763967357.36705572946662.3439977588303123.623426484493352.687336738732847.002754735000322.245948836755274.921349155896362.047182022071892.151343470907396.310726263708048.231962435594463.756326714414190.944187743180533.8527464913022⋮⋮60 × 2 Matrix
SOIG≔Graph 1: an undirected unweighted graph with 60 vertices and 97 edge(s)
The GraphTheory[GeometricGraphs][SphereOfInfluenceGraph] command was introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
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