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Abstract
A growing family of random graphs is called robust if it retains a giant
component after percolation with arbitrary positive retention probability. We
study robustness for graphs, in which new vertices are given a spatial position
on the d-dimensional torus and are connected to existing vertices with a
probability favouring short spatial distances and high degrees. In this model
of a scale-free network with clustering we can independently tune the power law exponent tau of the degree distribution and the rate delta d at which the connection probability decreases with the distance of two vertices. We show
that the network is robust if tau<2+1/delta, but fails to be robust if
tau>3. In the case of one-dimensional space we also show that the network is not robust if tau<2+1/(delta-1). This implies that robustness of a
scale-free network depends not only on its power-law exponent but also on its
clustering features. Other than the classical models of scale-free networks our
model is not locally tree-like, and hence we need to develop novel methods for
its study, including, for example, a surprising application of the BK-inequality.
Original language | English |
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Pages (from-to) | 1680-1722 |
Number of pages | 35 |
Journal | Annals of Probability |
Volume | 45 |
Issue number | 3 |
Early online date | 15 May 2017 |
DOIs | |
Publication status | Published - 31 May 2017 |
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Dive into the research topics of 'Robustness of scale-free spatial networks'. Together they form a unique fingerprint.Projects
- 1 Finished
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Emergence of Condensation in Stochastic Systems
Morters, P.
Engineering and Physical Sciences Research Council
1/08/13 → 31/08/16
Project: Research council