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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56 Scopus citations


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 Erdos-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.

Original languageEnglish
Article number062302
JournalPhysical Review E
Issue number6
StatePublished - 6 Jun 2016

Bibliographical note

Publisher Copyright:
© 2016 American Physical Society.


We thank DTRA, NSF, the European MULTIPLEX, ONR, and the Israel Science Foundation for financial support. Y.D. acknowledges support from the NSFC (Grant No. 71201132) and the DFME (Grant No. 20120184120025).

FundersFunder number
National Science Foundation
Office of Naval Research
Defense Threat Reduction Agency
National Natural Science Foundation of China71201132
Israel Science Foundation


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