Hidden geometric correlations in real multiplex networks

TL;DR

This paper reveals that real multiplex networks are organized by hidden geometric correlations across layers, enabling improved community detection, link prediction, and navigation within complex systems.

Contribution

It uncovers the presence of strong hidden geometric correlations in real multiplex networks and demonstrates their utility for community detection, link prediction, and navigation.

Findings

Strong geometric correlations exist across layers in real multiplex networks.

These correlations enable accurate trans-layer link prediction.

They facilitate efficient navigation using only local information.

Abstract

Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the individual layers. We find that these correlations are strong in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate: (i) the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers; (ii) accurate trans-layer link prediction, where connections in one layer can be predicted by observing the hidden geometric space of another layer; and (iii) efficient targeted navigation in the multilayer system using only local knowledge, which outperforms navigation in the single layers only if the geometric correlations are sufficiently strong. Our findings uncover fundamental organizing principles behind real multiplexes and can have important applications in diverse domains.