Detecting the ultra low dimensionality of real networks

TL;DR

This paper introduces a method to determine the intrinsic low dimensionality of real-world networks using hyperbolic geometry, revealing surprising regularities across various domains without requiring prior embeddings.

Contribution

The authors propose a novel approach to infer network dimensionality directly, uncovering ultra low dimensionality in diverse real networks and advancing understanding of their structural properties.

Findings

Tissue-specific biomolecular networks are extremely low dimensional.

Brain connectomes are close to three dimensions, matching their anatomical structure.

Social networks and the Internet require slightly higher dimensions.

Abstract

Reducing dimension redundancy to find simplifying patterns in high-dimensional datasets and complex networks has become a major endeavor in many scientific fields. However, detecting the dimensionality of their latent space is challenging but necessary to generate efficient embeddings to be used in a multitude of downstream tasks. Here, we propose a method to infer the dimensionality of networks without the need for any a priori spatial embedding. Due to the ability of hyperbolic geometry to capture the complex connectivity of real networks, we detect ultra low dimensionality far below values reported using other approaches. We applied our method to real networks from different domains and found unexpected regularities, including: tissue-specific biomolecular networks being extremely low dimensional; brain connectomes being close to the three dimensions of their anatomical embedding; and social networks and the Internet requiring slightly higher dimensionality. Beyond paving the way towards an ultra efficient dimensional reduction, our findings help address fundamental issues that hinge on dimensionality, such as universality in critical behavior.