Percolation of partially interdependent networks under targeted attack

TL;DR

This paper analyzes the percolation behavior of partially interdependent networks under targeted attack, revealing phase transition characteristics and critical lines that inform the design of more robust network systems.

Contribution

It introduces a comprehensive framework for understanding percolation in partially interdependent networks under targeted attacks, including phase transition laws and critical line behaviors.

Findings

Percolation laws derived for extreme cases of interdependence.

Critical line between phase transitions decreases with attack probability.

Monotonic increase of critical line with interdependence parameter .

Abstract

The study of interdependent networks, and in particular the robustness on networks, has attracted considerable attention. Recent studies mainly assume that the dependence is fully interdependent. However, targeted attack for partially interdependent networks simultaneously has the characteristics of generality in real world. In this letter, the comprehensive percolation of generalized framework of partially interdependent networks under targeted attack is analyzed. As $\alpha=0$ and $\alpha=1$, the percolation law is presented. Especially, when $a=b=k$, $p_{1}=p_{2}=p$, $q_{A}=q_{B}=q$, the first and second lines of phase transition coincide with each other. The corresponding phase transition diagram and the critical line between the first and the second phase transition are found. We find that the tendency of critical line is monotone decreasing with parameter $p_{1}$. However, for different $\alpha$, the tendency of critical line is monotone increasing with $\alpha$. In a larger sense, our findings have potential application for designing networks with strong robustness and can regulate the robustness of some current networks.