construct a relative neighbor graph
RelativeNeighborhoodGraph( P, opts )
Matrix or list of lists representing set of points
(optional) one or more options as specified below
triangulation = list of three-element lists.
Supply a previously computed Delaunay triangulation of P. The input must be a valid Delaunay triangulation in the format returned by ComputationalGeometry[DelaunayTriangulation]: a list of three-element lists of integers, representing triangles in a triangulation of P.
vertices = list of integers, strings or symbols
Specifies the vertices to be used in the generated graph.
weighted = truefalse
If weighted=true, the result is a weighted graph whose edge weights correspond to the Euclidean distance between points. The default is false.
The RelativeNeighborhoodGraph(P,opts) command returns a relative neighbor graph for the point set P.
The parameter P must be a Matrix or list of lists representing a set of points.
Let P be a set of points in n dimensions, let p and q be arbitrary points from P, and let dist⁡p,q be the Euclidean distance between p and q.
The relative neighborhood graph is the undirected graph whose vertices correspond to the points in P and in which vertices p and q share an edge if there does not exist any r∈P such that dist⁡p,r<dist⁡p,q and dist⁡q,r<dist⁡p,q.
It has the following relationships with other graphs:
The Euclidean minimum spanning tree on P is a subgraph of the relative neighborhood graph on P.
The relative neighborhood graph on P is a subgraph of the Gabriel graph on P.
Generate a set of random two-dimensional points.
points ≔ LinearAlgebra:-RandomMatrix⁡60,2,generator=0..100.,datatype=float8
RNG ≔ RelativeNeighborhoodGraph⁡points
RNG≔Graph 1: an undirected graph with 60 vertices and 65 edge(s)
Supowit, K. J. (1983), "The relative neighborhood graph, with an application to minimum spanning trees", J. ACM, 30 (3): 428–448, doi:10.1145/2402.322386.
The GraphTheory[GeometricGraphs][RelativeNeighborhoodGraph] command was introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
Download Help Document
Relative Neighborhood Graph (RNG) ni orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha ya orodha. Ili kuunda mpangilio wa Delaunay wa P, lazima uingize mpangilio wa Delaunay halali katika muundo uliorudishwa na Geometry ya Kompyuta: orodha ya orodha ya nambari tatu za nambari kamili, zinazowakilisha pembe tatu katika mpangilio wa P. Nambari za nambari kamili, nyuzi au alama. uzito = kweli-mbaya Kama uzito = kweli, matokeo ni grafu uzito ambao makali uzito sambamba na umbali Euclidean kati ya pointi. default ni uongo. RelativeNeighborhoodGraph (P,opts) amri anarudi graph jamaa jirani kwa ajili ya kuweka pointi P. parameter P lazima Matrix au orodha ya orodha kuwakilisha seti ya pointi. Hebu P kuwa seti ya pointi katika n vipimo, hebu p na q kuwa pointi arbitrary kutoka P, na hebu dist<unk>p,q kuwa umbali Euclidean kati ya p na q. Grafu ya jirani ya jamaa ni grafu isiyoelekezwa ambayo ncha zake zinalingana na pointi katika P na ambayo ncha p na q zinashiriki ukingo ikiwa hakuna r < P kama vile dist < p, r < dist < p, q na dist < q, r < dist < p, q. Euclidean chini spanning mti juu ya P ni subgraph ya graph jamaa jirani juu ya P. graph jamaa jirani juu ya P ni subgraph ya graph Gabriel juu ya P. kuzalisha seti ya random mbili-dimensional pointi. "Kama ilivyoelezwa hapo juu, ""Random matrix"" ni moja ya matrix ya kawaida, ambayo inaonyesha ""Random matrix"" na ""Random matrix"" na ""Random matrix"" na ""Random matrix"" na ""Random matrix"" na ""Random matrix"" na ""Random matrix"" na ""Random matrix"" na ""Random matrix"" na ""Random matrix"" na ""Random matrix"" na ""Random matrix"" na ""Random matrix"" na ""Random matrix"" na ""Random matrix.""" "Kama ilivyoelezwa katika ""The Relative Neighborhood Graph: With an Application to Minimum Spanning Trees"" (J.A.M. 30 (3) 428-448; D.O.I. 1011-2402-3238) ni muhimu sana." GraphTheory [GeometricGraphs] [RelativeNeighborhoodGraph] amri ilianzishwa katika Maple 2020. Kwa maelezo zaidi juu ya mabadiliko ya Maple 2020, angalia Updates katika Maple 2020. Pakua Hati ya Msaada