Scale-free networks resistant to intentional attacks

TL;DR

This paper investigates the robustness of certain scale-free networks with a modified degree distribution under intentional attacks, revealing they can withstand removal of up to 70% of nodes, contrary to typical expectations.

Contribution

It introduces a new model for scale-free networks with a specific degree distribution that explains their unexpected robustness to targeted attacks, supported by analytical and simulation results.

Findings

Networks with a constant degree distribution up to a critical point are highly resilient.

The model accurately describes real-world networks like IMDB and citation networks.

Such networks can survive removal of a large fraction of nodes without collapsing.

Abstract

We study the detailed mechanism of the failure of scale-free networks under intentional attacks. Although it is generally accepted that such networks are very sensitive to targeted attacks, we show that for a particular type of structure such networks surprisingly remain very robust even under removal of a large fraction of their nodes, which in some cases can be up to 70%. The degree distribution $P(k)$ of these structures is such that for small values of the degree $k$ the distribution is constant with $k$, up to a critical value $k_c$, and thereafter it decays with $k$ with the usual power law. We describe in detail a model for such a scale-free network with this modified degree distribution, and we show both analytically and via simulations, that this model can adequately describe all the features and breakdown characteristics of these attacks. We have found several experimental networks with such features, such as for example the IMDB actors collaboration network or the citations network, whose resilience to attacks can be accurately described by our model.