A quantitative method for determining the robustness of complex networks

TL;DR

This paper introduces a new quantitative method to measure the robustness of complex networks by calculating an invulnerability index based on normalized network efficiency, providing a clearer assessment of network resilience.

Contribution

It proposes a novel quantitative approach for evaluating network robustness using an invulnerability index, improving upon qualitative methods.

Findings

The invulnerability index effectively quantifies network resilience.

The method accurately distinguishes robustness levels under different attack scenarios.

Validation on small-world networks confirms the index's reliability.

Abstract

Most current studies estimate the invulnerability of complex networks using a qualitative method that analyzes the inaccurate decay rate of network efficiency. This method results in confusion over the invulnerability of various types of complex networks. By normalizing network efficiency and defining a baseline, this paper defines the invulnerability index as the integral of the difference between the normalized network efficiency curve and the baseline. This quantitative method seeks to establish a benchmark for the robustness and fragility of networks and to measure network invulnerability under both edge and node attacks. To validate the reliability of the proposed method, three small-world networks were selected as test beds. The simulation results indicate that the proposed invulnerability index can effectively and accurately quantify network resilience. The index should provide a valuable reference for determining network invulnerability in future research.