DND: Deep Learning-Based Directed Network Disintegrator

Network disintegration is a fundamental problem in network science, the core of which is how to determine the smallest set of nodes whose removal can weaken the function of the network and quickly paralyze it. It is computationally NP-hard and usually cannot be solved in polynomial time complexity. Many network disintegration methods have been proposed, but they mainly focus on undirected networks. Due to the complex structure of directed networks and the fact that it is necessary to consider the direction of edges to aggregate neighbor node information, solving the disintegration problem of directed networks is a challenge. Inspired by machine learning technology to solve the network disintegration problem, this paper studies feasible disintegration methods in directed networks and proposes a deep learning-based framework, DND (directed network disintegrator), for directed network disintegration, which has a small time complexity when dismantling large directed networks. DND can be trained in small, artificially generated synthetic directed networks and then applied to real-world, complex application scenarios. To test the disintegration effect of DND, we conducted extensive experiments on different types of synthetic directed networks and compared them with other methods. The experimental results show that the disintegration effect of DND is weaker than the CoreHD method, and better than the disintegration method based on local structural features, but the disintegration speed is the fastest with the increase in network size. We also disintegrate directed networks in the real world, and DND achieves a better disintegration effect, providing new insights into solving complex network-related problems and enabling us to design more robust networks to withstand attacks and failures.