Network Robustness Revisited

TL;DR

This paper provides a clear, mathematically grounded overview of network robustness, addressing common computational issues and deriving simple formulas for attack impacts on complex networks.

Contribution

It offers a deep, didactic re-examination of network robustness, including formulas for attack effects on configuration model networks, filling gaps in accessible understanding.

Findings

Derived simple formulas for attack impacts on networks

Highlighted common computational complications in robustness analysis

Provided an accessible introduction to network robustness theory

Abstract

The robustness of complex networks was one of the first phenomena studied after the inception of network science. However, many contemporary presentations of this theory do not go beyond the original papers. Here we revisit this topic with the aim of providing a deep but didactic introduction. We pay particular attention to some complications in the computation of giant component sizes that are commonly ignored. Following an intuitive procedure, we derive simple formulas that capture the effect of common attack scenarios on arbitrary (configuration model) networks. We hope that this gentle but mathematically-grounded introduction will help new researchers discover this beautiful area of network science.