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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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References

[1]Alon, N. and Spencer, J. H. (1991) The Probabilistic Method. John Wiley, Chichester.Google Scholar
[2]Bollobás, B. (1985) Random Graphs. Academic Press, New York.Google Scholar
[3]Erdős, P. and Rényi, A. (1961) On the strength of connectedness of a random graph. Acta Math. Acad. Sci. Hungar. 12 261–267.CrossRefGoogle Scholar
[4]Holst, L. (1992) On the number of vertices in the complete graph with a given vertex as nearest neighbour, in Frieze, A. M. and Luczak, T., eds., Random Graphs, Volume 2, John Wiley, Chichester, 91–99.Google Scholar
[5]McDiarmid, C. (1989) On the method of bounded differences. LMS Surveys in Combinatorics. Cambridge University Press, 148–184.Google Scholar
[6]Newman, C. M., Rinott, Y. and Tversky, A. (1983) Nearest neighbours and Voronoi regions in certain point processes. Advances in Applied Probability 15 726–751.CrossRefGoogle Scholar