A Graph Transformer-Driven Approach for Network Robustness Learning

TL;DR

This paper tackles the computational burden of assessing network robustness by introducing NRL-GT, a graph-transformer-based framework that jointly learns controllability and connectivity robustness from multiple viewpoints (robustness curves, overall robustness, and synthetic-network classification). The core innovation is a graph transformer backbone enhanced with degree-centrality encoding and a dual-head attention mechanism that captures local topology and edge dependencies, enabling high-precision, scalable robustness predictions across networks of varying sizes and distributions. The authors demonstrate strong generalization, transferable backbones, and substantial speedups over traditional attack simulations and competing learning methods, with clear benefits for real-world networks such as circuits and power systems. They also show that the backbone can transfer to different downstream tasks and sizes, and provide thorough ablations and comparisons to justify architectural choices. Overall, NRL-GT offers a practical, efficient, and extensible tool for rapid robustness assessment in complex networks, with potential extensions to hypergraphs and broader feature sets.

Abstract

Learning and analysis of network robustness, including controllability robustness and connectivity robustness, is critical for various networked systems against attacks. Traditionally, network robustness is determined by attack simulations, which is very time-consuming and even incapable for large-scale networks. Network Robustness Learning, which is dedicated to learning network robustness with high precision and high speed, provides a powerful tool to analyze network robustness by replacing simulations. In this paper, a novel versatile and unified robustness learning approach via graph transformer (NRL-GT) is proposed, which accomplishes the task of controllability robustness learning and connectivity robustness learning from multiple aspects including robustness curve learning, overall robustness learning, and synthetic network classification. Numerous experiments show that: 1) NRL-GT is a unified learning framework for controllability robustness and connectivity robustness, demonstrating a strong generalization ability to ensure high precision when training and test sets are distributed differently; 2) Compared to the cutting-edge methods, NRL-GT can simultaneously perform network robustness learning from multiple aspects and obtains superior results in less time. NRL-GT is also able to deal with complex networks of different size with low learning error and high efficiency; 3) It is worth mentioning that the backbone of NRL-GT can serve as a transferable feature learning module for complex networks of different size and different downstream tasks.

Figures (6)

• Figure 1: The overall architecture of NRL-GT. There is a backbone and three downstream modules in NRL-GT including robustness curve learning, overall robustness learning, and synthetic network classification.
• Figure 2: The architecture of the proposed Graph Transformer Layer, which generates robustness-related node representations.
• Figure 3: Precision comparison and generalization ability evaluation of NRL-GT, PCR 31, iPCR 32 for controllability robustness learning under RA. The experimental datasets include BA, ER, NW, QSN, and SF networks. In the title of each figure, D, UD, W, and UW indicate that the network is directed, undirected, weighted, and unweighted respectively. ${P_N}$ represents the number of nodes in the network that have been removed.
• Figure 4: Precision comparison and generalization ability evaluation of NRL-GT, CNN-RP 68, and mCNN-RP 77 for connectivity robustness learning under RA and TBA. The experimental datasets include directed and undirected, weighted and unweighted BA, ER, NW, QSN, and SF networks.
• Figure 5: Comparison of controllability robustness curve learning results of NRL-GT, PCR 31, and iPCR 32 on real-world networks, including circuit networks, power networks, brain networks, and so on. The details of real-world networks are displayed in Table S2.

Theorems & Definitions (3)

• Remark 1
• Theorem 1
• proof