Ultra-small scale-free geometric networks
J. E. Yukich
Source: J. Appl. Probab. Volume 43, Number 3
(2006), 665-677.
Abstract
We consider a family of long-range percolation models (Gp)p>0 on Zd that allow dependence between edges and have the following connectivity properties for p ∈ (1/d, ∞): (i) the degree distribution of vertices in Gp has a power-law distribution; (ii) the graph distance between points x and y is bounded by a multiple of logpdlogpd|x - y| with probability 1 - o(1); and (iii) an adversary can delete a relatively small number of nodes from Gp(Zd ∩ [0, n]d), resulting in two large, disconnected subgraphs.
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Permanent link to this document: http://projecteuclid.org/euclid.jap/1158784937
Digital Object Identifier: doi:10.1239/jap/1158784937
Mathematical Reviews number (MathSciNet): MR2274791
Zentralblatt MATH identifier: 1120.60095
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