Department of Electrical Engineering, Computer Engineering and Informatics, Cyprus University of Technology, 33 Saripolou Street, 3036 Limassol, Cyprus.
Computational Social Science, ETH Zurich, Clausiusstrasse 50, 8092, Zurich, Switzerland.
Phys Rev E. 2019 Jan;99(1-1):012322. doi: 10.1103/PhysRevE.99.012322.
Recent progress towards unraveling the hidden geometric organization of real multiplexes revealed significant correlations across the hyperbolic node coordinates in different network layers, which facilitated applications like translayer link prediction and mutual navigation. But, are geometric correlations alone sufficient to explain the topological relation between the layers of real systems? Here, we provide the negative answer to this question. We show that connections in real systems tend to persist from one layer to another irrespective of their hyperbolic distances. This suggests that in addition to purely geometric aspects, the explicit link formation process in one layer impacts the topology of other layers. Based on this finding, we present a simple modification to the recently developed geometric multiplex model to account for this effect, and show that the extended model can reproduce the behavior observed in real systems. We also find that link persistence is significant in all considered multiplexes and can explain their layers' high edge overlap, which cannot be explained by coordinate correlations alone. Furthermore, by taking both link persistence and hyperbolic distance correlations into account, we can improve translayer link prediction. These findings guide the development of multiplex embedding methods, suggesting that such methods should account for both coordinate correlations and link persistence across layers.
最近在揭示真实多重网络隐藏的几何组织方面取得的进展表明，不同网络层中的双曲节点坐标之间存在显著的相关性，这使得跨层链路预测和相互导航等应用成为可能。但是，仅仅是几何相关性就足以解释真实系统各层之间的拓扑关系吗？在这里，我们对这个问题给出了否定的答案。我们表明，真实系统中的连接倾向于从一层传递到另一层，而与它们的双曲距离无关。这表明，除了纯粹的几何方面，一层中的显式链接形成过程会影响其他层的拓扑结构。基于这一发现，我们对最近提出的几何多重网络模型进行了简单的修改，以考虑到这一影响，并表明扩展模型可以再现真实系统中观察到的行为。我们还发现，链接持久性在所有考虑的多重网络中都很显著，可以解释它们的层之间的高边重叠，而这仅仅通过坐标相关性是无法解释的。此外，通过同时考虑链接持久性和双曲距离相关性，我们可以提高跨层链路预测的准确性。这些发现指导了多重网络嵌入方法的发展，表明这些方法应该同时考虑坐标相关性和跨层的链接持久性。
