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

TL;DR

This paper investigates how different attack strategies—random, localized, and targeted—affect the stability of complex networks under $k$-core percolation, revealing that targeted attacks are most damaging, especially in scale-free networks.

Contribution

It provides a comparative analysis of attack impacts on $k$-core percolation in networks, including analytical mapping and numerical simulations, highlighting the greater damage caused by targeted attacks.

Findings

Targeted attacks cause the most damage to network cores.

Localized and random attacks have similar effects in Erdős-Rényi networks.

Localized attacks are more damaging than random attacks in scale-free networks.

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 Erd\H{o}s-R\'{e}nyi (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.