Structural Robustness of Complex Networks: A Survey of A Posteriori Measures

TL;DR

This survey reviews a posteriori structural robustness measures for static complex networks, emphasizing their evaluation, attack strategies, estimation methods, and optimization, highlighting their advantages over a priori measures and suggesting future research directions.

Contribution

It provides a comprehensive overview of a posteriori robustness measures, comparing them with a priori measures, and introduces a practical destruction threshold for network robustness assessment.

Findings

A posteriori measures outperform a priori measures in robustness evaluation.

A practical destruction threshold for network robustness is proposed.

Experimental comparison validates the advantages of a posteriori measures.

Abstract

Network robustness is critical for various industrial and social networks against malicious attacks, which has various meanings in different research contexts and here it refers to the ability of a network to sustain its functionality when a fraction of the network fail to work due to attacks. The rapid development of complex networks research indicates special interest and great concern about the network robustness, which is essential for further analyzing and optimizing network structures towards engineering applications. This comprehensive survey distills the important findings and developments of network robustness research, focusing on the a posteriori structural robustness measures for single-layer static networks. Specifically, the a posteriori robustness measures are reviewed from four perspectives: 1) network functionality, including connectivity, controllability and communication ability, as well as their extensions; 2) malicious attacks, including conventional and computation-based attack strategies; 3) robustness estimation methods using either analytical approximation or machine learning-based prediction; 4) network robustness optimization. Based on the existing measures, a practical threshold of network destruction is introduced, with the suggestion that network robustness should be measured only before reaching the threshold of destruction. Then, a posteriori and a priori measures are compared experimentally, revealing the advantages of the a posteriori measures. Finally, prospective research directions with respect to a posteriori robustness measures are recommended.