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

arXiv: https://arxiv.org/abs/2302.03745 · HTML: https://mlsanity.com/paper/2302.03745/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2023.

## Built on by (most cited first, 3 of 3)

- [SPP-CNN: An Efficient Framework for Network Robustness Prediction](https://mlsanity.com/paper/2305.07872/) (2023)
- [Comprehensive Analysis of Network Robustness Evaluation Based on Convolutional Neural Networks with Spatial Pyramid Pooling](https://mlsanity.com/paper/2308.08012/) (2023)
- [HWL-HIN: A Hypergraph-Level Hypergraph Isomorphism Network as Powerful as the Hypergraph Weisfeiler-Lehman Test with Application to Higher-Order Network Robustness](https://mlsanity.com/paper/2512.22014/) (2025)

## Abstract (arXiv)

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.