The Robustness of Interdependent Directed Networks With Intra-layer Angular Correlations - Wu, Zongning; Di, Zengru; Fan, Ying (Frontiers in Physics, 2021)
The robustness of interdependent networks is a frontier topic in current network science. A line of studies has so far been investigated in the perspective of correlated structures on robustness, such as degree correlations and geometric correlations in interdependent networks, in-out degree correlations in interdependent directed networks, and so on. Advances in network geometry point that hyperbolic properties are also hidden in directed structures, but few studies link those features to the dynamical process in interdependent directed networks. In this paper, we discuss the impact of intra-layer angular correlations on robustness from the perspective of embedding interdependent directed networks into hyperbolic space. We find that the robustness declines as increasing intra-layer angular correlations under targeted attacks. Interdependent directed networks without intra-layer angular correlations are always robust than those with intra-layer angular correlations. Moreover, empirical networks also support our findings: the significant intra-layer angular correlations are hidden in real interdependent directed networks and contribute to the prediction of robustness. Our work sheds light that the impact of intra-layer angular correlations should be attention, although in-out degree correlations play a positive role in robustness. In particular, it provides an early warning indicator by which the system decoded the intrinsic rules for designing efficient and robust interacting directed networks.