Abstract
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.
Highlights
In the past few decades, increasing studies had proved that most real-world networks are multilayered by dependency connectivity to interact with one another, and such structures are of great interest in the aspect of the robustness [1,2,3,4,5,6]
The geometric correlation contains two parts: one, the radial correlation is equal to degree correlation, which has been widely discussed on its contribution to systems robustness; and two, the angular correlation is a novel statistical property
The hidden geometric structures of real-world networks provide a new perspective in revealing a relationship between topology and dynamical processes
Summary
In the past few decades, increasing studies had proved that most real-world networks are multilayered by dependency connectivity to interact with one another, and such structures are of great interest in the aspect of the robustness [1,2,3,4,5,6]. The correlated structures affect the structural robustness in diverse fashions: strong degree correlations across layers suppress susceptibility to a social cascade process [17] and be robust against targeted attacks [18]. For another branch of studies, attentions have shifted to understanding the dynamical process of interdependent networks by hidden geometric correlations [19,20,21]. Angular correlations across layers can produce the lower outbreak threshold [21] and mitigate the breakdown of mutual connectivity under targeted attacks [20]
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