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Connectivity of soft random geometric graphs | | Mathew D. Penrose
; | | Date: |
15 Nov 2013 | | Abstract: | Consider a graph on $n$ uniform random points in the unit square, each pair
being connected by an edge with probability $p$ if the inter-point distance is
at most $r$. We show that as $n o infty$ the probability of full
connectivity is governed by that of having no isolated vertices, itself
governed by a Poisson approximation for the number of isolated vertices,
uniformly over all choices of $p,r$. We determine the asymptotic probability of
connectivity for all $(p_n,r_n)$ subject to $r_n = O(n^{-epsilon}),$ some
$epsilon >0$. We generalize the first result to higher dimensions, and to a
larger class of connection probability functions in $d=2$. | | Source: | arXiv, 1311.3897 | | Services: | Forum | Review | PDF | Favorites | |
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