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arXiv · 1605.06386

$k$-core percolation on complex networks: Comparing random, localized and targeted attacks

Xin Yuan·Yang Dai·H. Eugene Stanley·Shlomo Havlin
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Abstract

The type of malicious attack inflicting on networks greatly influences their stability under ordinary percolation in which a node fails when it becomes disconnected from the giant component. Here we study its generalization, $k$-core percolation, in which a node fails when it loses connection to a threshold $k$ number of neighbors. We study and compare analytically and by numerical simulations of $k$-core percolation the stability of networks under random attacks (RA), localized attacks (LA) and targeted attacks (TA), respectively. By mapping a network under LA or TA into an equivalent network under RA, we find that in both single and interdependent networks, TA exerts the greatest damage to the core structure of a network. We also find that for Erdős-Rényi (ER) networks, LA and RA exert equal damage to the core structure whereas for scale-free (SF) networks, LA exerts much more damage than RA does to the core structure.

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Xin Yuan, Yang Dai, H. Eugene Stanley, Shlomo Havlin. 2016-05-20. $k$-core percolation on complex networks: Comparing random, localized and targeted attacks. https://doi.org/10.1103/physreve.93.062302

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