Optimization of Network Robustness to Waves of Targeted and Random Attack

TL;DR

This paper investigates how to design networks that are most robust against both targeted and random attacks, revealing that a bimodal degree distribution with specific parameters maximizes resilience.

Contribution

It introduces an optimal network design with a bimodal degree distribution that enhances robustness against combined attack types, a novel approach in network resilience.

Findings

Optimal network robustness is achieved with a bimodal degree distribution.

The fraction of high-degree nodes relates to attack ratios as r ~ p_t/p_r.

The network design significantly improves resilience against simultaneous attacks.

Abstract

We study the robustness of complex networks to multiple waves of simultaneous (i) targeted attacks in which the highest degree nodes are removed and (ii) random attacks (or failures) in which fractions $p_t$ and $p_r$ respectively of the nodes are removed until the network collapses. We find that the network design which optimizes network robustness has a bimodal degree distribution, with a fraction $r$ of the nodes having degree $k_2= (\kav - 1 +r)/r$ and the remainder of the nodes having degree $k_1=1$, where $\kav$ is the average degree of all the nodes. We find that the optimal value of $r$ is of the order of $p_t/p_r$ for $p_t/p_r\ll 1$.