Multiplexity amplifies geometry in networks

TL;DR

This paper demonstrates that correlations across layers in multilayer networks significantly enhance their geometric structure, leading to higher mutual clustering than in individual layers, revealing a new dimension of multilayer network complexity.

Contribution

The study introduces a simple multiplex network model with latent geometry to explain how interlayer correlations amplify geometric features like clustering.

Findings

Mutual clustering is abnormally high in real-world multilayer networks.

Links consistent with latent geometry tend to persist across layers.

Multilayer networks exhibit a distinct geometric dimension from single layers.

Abstract

Many real-world network are multilayer, with nontrivial correlations across layers. Here we show that these correlations amplify geometry in networks. We focus on mutual clustering--a measure of the amount of triangles that are present in all layers among the same triplets of nodes--and find that this clustering is abnormally high in many real-world networks, even when clustering in each individual layer is weak. We explain this unexpected phenomenon using a simple multiplex network model with latent geometry: links that are most congruent with this geometry are the ones that persist across layers, amplifying the cross-layer triangle overlap. This result reveals a different dimension in which multilayer networks are radically distinct from their constituent layers.