Impact of Random Failures and Attacks on Poisson and Power-Law Random Networks

TL;DR

This paper critically examines the robustness of Poisson and power-law networks under failures and attacks, revealing that differences are less pronounced than previously believed through detailed proofs and extensive experiments.

Contribution

It provides a unified framework for analyzing network robustness, offers new insights into the limitations of prior results, and presents rigorous experiments to evaluate analytic predictions.

Findings

Differences between failures and attacks are smaller than previously thought.

Power-law and Poisson networks show less contrasting robustness behaviors.

Analytic results are validated and their limitations clarified.

Abstract

It appeared recently that the underlying degree distribution of networks may play a crucial role concerning their robustness. Empiric and analytic results have been obtained, based on asymptotic and mean-field approximations. Previous work insisted on the fact that power-law degree distributions induce high resilience to random failure but high sensitivity to attack strategies, while Poisson degree distributions are quite sensitive in both cases. Then, much work has been done to extend these results. We aim here at studying in depth these results, their origin, and limitations. We review in detail previous contributions and give full proofs in a unified framework, and identify the approximations on which these results rely. We then present new results aimed at enlightening some important aspects. We also provide extensive rigorous experiments which help evaluate the relevance of the analytic results. We reach the conclusion that, even if the basic results of the field are clearly true and important, they are in practice much less striking than generally thought. The differences between random failures and attacks are not so huge and can be explained with simple facts. Likewise, the differences in the behaviors induced by power-law and Poisson distributions are not as striking as often claimed.