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- Gabriel_graph abstract "In mathematics, the Gabriel graph of a set S of points in the Euclidean plane expresses one notion of proximity or nearness of those points. Formally, it is the graph with vertex set S in which any points P and Q in S are adjacent precisely if they are distinct and the closed disc of which line segment PQ is a diameter contains no other elements of S. Gabriel graphs naturally generalize to higher dimensions, with the empty disks replaced by empty closed balls. Gabriel graphs are named after K. R. Gabriel, who introduced them in a paper with R. R. Sokal in 1969.The Gabriel graph is a subgraph of the Delaunay triangulation; it can be found in linear time if the Delaunay triangulation is given (Matula & Sokal 1980). The Gabriel graph contains as a subgraph the Euclidean minimum spanning tree, the relative neighborhood graph, and the nearest neighbor graph. It is an instance of a beta-skeleton. Like beta-skeletons, and unlike Delaunay triangulations, it is not a geometric spanner: for some point sets, distances within the Gabriel graph can be much larger than the Euclidean distances between points (Bose et al. 2006).A finite site percolation threshold for Gabriel graphs has been proven to exist by Bertin, Billiot & Drouilhet (2002), and more precise values of both site and bond thresholds have been given by Norrenbrock (2014).".
- Gabriel_graph thumbnail Gabriel_graph.svg?width=300.
- Gabriel_graph wikiPageID "9312326".
- Gabriel_graph wikiPageLength "3846".
- Gabriel_graph wikiPageOutDegree "26".
- Gabriel_graph wikiPageRevisionID "679074677".
- Gabriel_graph wikiPageWikiLink Ball_(mathematics).
- Gabriel_graph wikiPageWikiLink Beta-skeleton.
- Gabriel_graph wikiPageWikiLink Beta_skeleton.
- Gabriel_graph wikiPageWikiLink Category:Euclidean_plane_geometry.
- Gabriel_graph wikiPageWikiLink Category:Geometric_graphs.
- Gabriel_graph wikiPageWikiLink Delaunay_triangulation.
- Gabriel_graph wikiPageWikiLink Diameter.
- Gabriel_graph wikiPageWikiLink Disc_(mathematics).
- Gabriel_graph wikiPageWikiLink Disk_(mathematics).
- Gabriel_graph wikiPageWikiLink Euclidean_minimum_spanning_tree.
- Gabriel_graph wikiPageWikiLink Euclidean_plane.
- Gabriel_graph wikiPageWikiLink Geometric_spanner.
- Gabriel_graph wikiPageWikiLink Glossary_of_graph_theory.
- Gabriel_graph wikiPageWikiLink Graph_(mathematics).
- Gabriel_graph wikiPageWikiLink K._Ruben_Gabriel.
- Gabriel_graph wikiPageWikiLink Line_segment.
- Gabriel_graph wikiPageWikiLink Linear_time.
- Gabriel_graph wikiPageWikiLink Mathematics.
- Gabriel_graph wikiPageWikiLink Nearest_neighbor_graph.
- Gabriel_graph wikiPageWikiLink Percolation_threshold.
- Gabriel_graph wikiPageWikiLink Relative_neighborhood_graph.
- Gabriel_graph wikiPageWikiLink Robert_R._Sokal.
- Gabriel_graph wikiPageWikiLink SIAM_Journal_on_Discrete_Mathematics.
- Gabriel_graph wikiPageWikiLink Set_(mathematics).
- Gabriel_graph wikiPageWikiLink Systematic_Biology.
- Gabriel_graph wikiPageWikiLink Systematic_Zoology.
- Gabriel_graph wikiPageWikiLink Time_complexity.
- Gabriel_graph wikiPageWikiLink Two-dimensional_space.
- Gabriel_graph wikiPageWikiLink File:Gabriel_Pairs.svg.
- Gabriel_graph wikiPageWikiLink File:Gabriel_graph.svg.
- Gabriel_graph wikiPageWikiLink File:Not_Gabriel_Pairs.svg.
- Gabriel_graph wikiPageWikiLinkText "Gabriel graph".
- Gabriel_graph hasPhotoCollection Gabriel_graph.
- Gabriel_graph wikiPageUsesTemplate Template:Citation.
- Gabriel_graph wikiPageUsesTemplate Template:Geometry-stub.
- Gabriel_graph wikiPageUsesTemplate Template:Harv.
- Gabriel_graph wikiPageUsesTemplate Template:Harvtxt.
- Gabriel_graph subject Category:Euclidean_plane_geometry.
- Gabriel_graph subject Category:Geometric_graphs.
- Gabriel_graph comment "In mathematics, the Gabriel graph of a set S of points in the Euclidean plane expresses one notion of proximity or nearness of those points. Formally, it is the graph with vertex set S in which any points P and Q in S are adjacent precisely if they are distinct and the closed disc of which line segment PQ is a diameter contains no other elements of S. Gabriel graphs naturally generalize to higher dimensions, with the empty disks replaced by empty closed balls.".
- Gabriel_graph label "Gabriel graph".
- Gabriel_graph sameAs Graphe_de_Gabriel.
- Gabriel_graph sameAs Gabrielgraaf.
- Gabriel_graph sameAs m.02843m1.
- Gabriel_graph sameAs Q2783524.
- Gabriel_graph sameAs Q2783524.
- Gabriel_graph wasDerivedFrom Gabriel_graph?oldid=679074677.
- Gabriel_graph depiction Gabriel_graph.svg.
- Gabriel_graph isPrimaryTopicOf Gabriel_graph.
