Dismantling directed networks: A multi-temporal information field approach

While network robustness is often assessed via structural connectivity, this approach does not fully capture the performance of complex systems, which also depends on information flow among internal components. In this paper, we focus on the robustness of directed networks by proposing a framework to dismantle both their information flow and connectivity. Specifically, we develop a multi-temporal information field model for directed networks based on quantum mechanics, and construct the Directed Node Entanglement (DNE) centrality metric using a generalized network density matrix. We first investigate the impact of time scale on DNE and find that its dismantling performance is optimal at a smaller $\tau$. Consequently, we approximate DNE at these scales using mean-field theory and validate the accuracy of our approximation. Moreover, extensive targeted attack experiments on real-world networks show that DNE effectively disrupts both information flow and connectivity, achieving improvement rates of up to 21.34 % and 40.39 %, respectively. Finally, correlation analyses indicate that DNE accounts for both high outward connectivity and bridging potential, offering a distinct perspective on node importance in directed networks. In summary, our study extends the information field model to directed networks and investigates both their information flow and connectivity, providing valuable insights into network robustness.