Link persistence and conditional distances in multiplex networks.

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.