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Random Geometric Graphs$
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Mathew Penrose

Print publication date: 2003

Print ISBN-13: 9780198506263

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198506263.001.0001

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CONNECTIVITY AND THE NUMBER OF COMPONENTS

CONNECTIVITY AND THE NUMBER OF COMPONENTS

Chapter:
(p.281) 13 CONNECTIVITY AND THE NUMBER OF COMPONENTS
Source:
Random Geometric Graphs
Author(s):

Mathew Penrose (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198506263.003.0013

This chapter is mainly concerned with the connectivity threshold T on n random points (i.e., the smallest r at which G(n,r) is connected). The results for this threshold are similar to those for the threshold M at which G(n,r) has no isolated points. For uniformly distributed points, these two thresholds are equal with high probability, and more generally the asymptotics for T are similar to those for M discussed in Chapters 7 and 8. Extensions to k-connectivity are considered, and a central limit theorem for the number of components of G(n,r) in the thermodynamic limit is presented.

Keywords:   connectivity threshold, isolated points, k-connectivity, components, central limit theorem

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