Diffusion Graph Transformer for Learning Controllability Robustness in Large-Scale Networks

Network controllability robustness refers to the ability of networks to maintain controllability in the face of various attacks, which is typically determined by recording a series of controllability values under sustained attacks in simulations. However, conducting such simulation experiments is often extremely time-consuming. Particularly, for large-scale networks, such simulation experiments are even infeasible. Therefore, in order to replace the traditional simulations, we propose a method named diffusion graph transformer (DGT) in this work for learning controllability robustness of complex networks under batch attacks by leveraging the descriptive capability of the graph attention mechanism in node feature representation and the effectiveness of the diffusion principle in feature propagation. DGT first generates embeddings based on node degree attributes, then adaptively propagates the transformed features through a specially designed diffusion strategy, followed by a fully connected layer for the final prediction. Extensive experimental results demonstrate that: 1) DGT exhibits excellent accuracy and significant speed advantages in the task of controllability robustness learning of complex networks; 2) compared to current related research on complex network robustness learning tasks, DGT is the first to address the controllability robustness learning task under batch attacks on large-scale networks, and it demonstrates strong generalization performance in terms of network scale, being applicable to networks with hundreds of thousands of nodes; and 3) the DGT model excels in transferability in terms of attack batch sizes, offering flexibility in predicting network controllability robustness toward various attack batches.