Network Controllability Robustness Learning via Spatial Graph Neural Networks

Controllability of complex networks refers to the ability of a networked system to steer from any initial state to any desired state in a finite time under feasible control inputs. Its robustness reflects the ability of a network to maintain controllability under various attacks, which records a series of controllability values under continuous attacks and can be directly determined by attack simulations. However, such simulation experiments are very time-consuming. It is necessary to design a model to replace simulation experiments to learn network controllability robustness with high precision and high speed, which is the objective of Network Controllability Robustness Learning . In this paper, given the superiority of spatial graph neural networks in generating network embedding, a novel controllability robustness learning approach via spatial graph neural networks (CRL-SGNN) is proposed by taking into account both generalization and high precision. In this scheme, controllability robustness related complex network representations that contain network topology information and degree-based node attribute information are first generated through the introduced graph convolutional layer and then sent to the prediction module consisting of multiple branches. A large number of experiments show that: 1) CRL-SGNN can overcome the issue of different distributions between training and test sets with satisfactory performance, implying strong generalization ability of CRL-SGNN; 2) Compared to the cutting-edge methods, CRL-SGNN can obtain superior results in less time; 3) A highlight which cannot be ignored is that the embedding generation module of CRL-SGNN can serve as a transferable feature learning module to deal with complex networks of any size with low prediction error and high efficiency.