Source: J. Appl. Probab.
Volume 43, Number 3
We consider a family of long-range percolation models
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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