Robustness of onion-like correlated networks against targeted attacks

TL;DR

This paper proposes an analytically derived onion-like network structure that enhances robustness against both random failures and targeted attacks, outperforming traditional scale-free networks.

Contribution

It introduces a nearly optimal, analytically characterized onion-like network structure with high assortativity, improving robustness against targeted attacks while maintaining resilience to random failures.

Findings

The onion-like structure significantly reduces vulnerability to targeted high-degree node removal.

Analytical expressions for percolation thresholds and giant component sizes are derived.

Numerical simulations confirm the robustness improvements of the proposed network design.

Abstract

Recently, it was found by Schneider et al. [Proc. Natl. Acad. Sci. USA, 108, 3838 (2011)], using simulations, that scale-free networks with "onion structure" are very robust against targeted high degree attacks. The onion structure is a network where nodes with almost the same degree are connected. Motivated by this work, we propose and analyze, based on analytical considerations, an onion-like candidate for a nearly optimal structure against simultaneous random and targeted high degree node attacks. The nearly optimal structure can be viewed as a hierarchically interconnected random regular graphs, the degrees and populations of which are specified by the degree distribution. This network structure exhibits an extremely assortative degree-degree correlation and has a close relationship to the "onion structure." After deriving a set of exact expressions that enable us to calculate the critical percolation threshold and the giant component of a correlated network for an arbitrary type of node removal, we apply the theory to the cases of random scale-free networks that are highly vulnerable against targeted high degree node removal. Our results show that this vulnerability can be significantly reduced by implementing this onion-like type of degree-degree correlation without much undermining the almost complete robustness against random node removal. We also investigate in detail the robustness enhancement due to assortative degree-degree correlation by introducing a joint degree-degree probability matrix that interpolates between an uncorrelated network structure and the onion-like structure proposed here by tuning a single control parameter. The optimal values of the control parameter that maximize the robustness against simultaneous random and targeted attacks are also determined. Our analytical calculations are supported by numerical simulations.