多路复用网络中的链路持久性和条件距离
Link persistence and conditional distances in multiplex networks
摘要：
最近的进展解开隐藏的几何组织的真正的复用揭示了显着的相关性，在不同的网络层，这有利于跨层链接预测和相互导航等应用程序的双曲线节点坐标。但是，仅仅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，在真正的系统中的连接往往坚持从一层到另一个无关的双曲距离。这表明，除了纯粹的几何方面，一个层中的显式链路形成过程会影响其他层的拓扑结构。基于这一发现，我们提出了一个简单的修改最近开发的几何多重模型来解释这种影响，并表明扩展模型可以重现在真实系统中观察到的行为。我们还发现，链接持久性是显着的，在所有考虑的复用，可以解释他们的层的高边缘重叠，这不能单独用坐标相关性来解释。此外，通过考虑链路持久性和双曲线距离相关性，我们可以改进跨层链接预测。这些发现指导了多重嵌入方法的发展，这表明这种方法应该考虑到跨层的坐标相关性和链接持久性。
英文摘要：
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 trans-layer 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 irrespectively 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 trans-layer link prediction. These findings guide the development of multiplex embedding methods, suggesting that such methods should be accounting for both coordinate correlations and link persistence across layers.
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