High-Order Knowledge Based Network Controllability Robustness Prediction: A Hypergraph Neural Network Approach

In order to evaluate the invulnerability of networks against various types of attacks and provide the guidance for potential performance enhancement as well as controllability maintenance, network controllability robustness (NCR) has attracted increasing attention in recent years. Traditionally, the controllability robustness is determined by attack simulations, which is computationally time consuming and only applicable for small-scale networks. Although some machine learning based methods for predicting network controllability robustness have been proposed lately, they only focus on pairwise interactions of complex networks and the underlying relationships between high-order structural information and network controllability robustness are not explored. In this paper, a dual hypergraph attention neural network model based on high-order knowledge (NCR-HoK) is proposed to accomplish the tasks of robustness learning and controllability robustness curve prediction. Through the proposed node feature encoder, the construction of hypergraph with high-order relation and dedicatedly designed dual hypergraph attention module, our method can effectively learn three types of network information simultaneously: the explicit structural information in the original graph, the high-order connection information in local neighborhoods and more hidden features in the embedding space. Notably, we explore for the first time the impact of high-order knowledge on the network's controllable robustness. Compared to the state-of-the-art methods for network robustness learning, our method has superior performance on both synthetic and real-world networks with low overheads.