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On the Connectivity of Random k-th Nearest Neighbour Graphs

Published online by Cambridge University Press:  12 September 2008

Colin Cooper  and
Alan Frieze
Colin Cooper
Affiliation:
School of Mathematical Sciences, University of North London, London N7 8DB, UK
Alan Frieze
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
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Abstract

Model 1. Consider the complete graph Kn, with vertex set [n] = {1, 2,…, n}, in which each edge e is assigned a length Xe. Colour the k shortest edges incident with each vertex green and the remaining edges blue. The graph made up of the green edges only, will be referred to as the k-th nearest neighbour graph. This graph has been studied in a variety of contexts both computational and statistical.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 4 , Issue 4 , December 1995 , pp. 343 - 362
Copyright
Copyright © Cambridge University Press 1995

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