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出典:Wikipedia
出典:『Wikipedia』 (2011/03/18 05:37 UTC 版)
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 generalize to higher dimensions trivially, 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.