Generalized k-cores of networks under attack with limited knowledge

Yilun Shang

Chaos, Solitons & Fractals, 2021, vol. 152, issue C

Abstract: Network theory has been used as an effective approach for understanding and controlling many real-world large-scale systems. A significant aspect of network operation is its robustness against failures and attacks. Here, we develop a theoretical framework for two classes of network attack with limited knowledge, namely, min−n and max−n attacks, where only n nodes are observed and a node with smallest or largest degree is removed at a time until a fraction 1−p of nodes are attacked. We study the effect of these attacks on the generalized k-core (Gk-core) of the network, which is obtained by implementing a k-leaf pruning process, removing progressively nodes with degree smaller than k alongside their nearest neighbors. This removal process can be viewed as a generation of the ordinary k-core decomposition. It is found that the G2-core undergoes a continuous phase transition with respect to p while Gk-core shows a first-order percolation transition for k≥3 under both types of attacks for all n. We reveal that knowing one more node during attacks, improving from n=1 to n=2, turns out to be most beneficial in terms of changing the robustness of Gk-core in both directions. Moreover, it is shown that degree heterogeneity plays a role in robustness as prioritizing attack on small-degree nodes in heterogeneous networks may help consolidate the Gk-core, but also in stability where hub nodes act like anchors stabilizing the Gk-core structure. Our results offer insight into the design of resilient complex systems and evaluation of network robustness and stability.

Keywords: Network; Core; Percolation; Attack; Robustness; Stability (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006597

DOI: 10.1016/j.chaos.2021.111305

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