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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 $B\left(p\right)$ 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 $B\left(p\right)\cap B\left(q\right)$ 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.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{GeometricGraphs}\right)\:$

$\mathrm{points}≔\mathrm{LinearAlgebra}:-\mathrm{RandomMatrix}\left(60\,2\,\mathrm{generator}=0..100.\,\mathrm{datatype}=\mathrm{float}\left[8\right]\right)$

$\mathrm{points}≔\begin{array}{c}\left[\begin{array}{cc}9.85017697341803& 82.9750304386195\\ 86.0670183749663& 83.3188659363996\\ 64.3746795546741& 73.8671607639673\\ 57.3670557294666& 2.34399775883031\\ 23.6234264844933& 52.6873367387328\\ 47.0027547350003& 22.2459488367552\\ 74.9213491558963& 62.0471820220718\\ 92.1513434709073& 96.3107262637080\\ 48.2319624355944& 63.7563267144141\\ 90.9441877431805& 33.8527464913022\\ ⋮& ⋮\end{array}\right]\\ \text{60 × 2 Matrix}\end{array}$

$\mathrm{SOIG}≔\mathrm{SphereOfInfluenceGraph}\left(\mathrm{points}\right)$

$\mathrm{SOIG}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 60\; vertices\; and\; 97\; edges}$

$\mathrm{DrawGraph}\left(\mathrm{SOIG}\right)$

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

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