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• W1960772788 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 $tau 3$. 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." @default.
• W1960772788 created "2016-06-24" @default.
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• W1960772788 date "2015-04-02" @default.
• W1960772788 modified "2023-09-26" @default.
• W1960772788 title "Robustness of scale-free spatial networks" @default.
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