The connectivity of a graph on uniform points on [0,1]d

Martin J. B. Appel and Ralph P. Russo

Statistics & Probability Letters, 2002, vol. 60, issue 4, 351-357

Abstract: A random graph Gn(x) is constructed on independent random points U1,...,Un distributed uniformly on [0,1]d, d[greater-or-equal, slanted]1, in which two distinct such points are joined by an edge if the l[infinity]-distance between them is at most some prescribed value 0 1, a.s., as n-->[infinity], where dn is the largest nearest-neighbor link, the smallest x for which Gn(x) has no isolated vertices.

Keywords: Random; graph; Connectivity; Connectivity; distance; Largest; nearest-neighbor; link; Random; minimal; spanning; tree; Geometric; probability (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (1)

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