A sprinkling of hybrid-signature discrete spacetimes in real-world networks

TL;DR

This paper investigates how real-world networks embedded in hybrid-signature spacetimes reveal information about their underlying dimensionality, using spectral dimension analysis to connect network properties with spacetime geometry.

Contribution

It introduces the use of hybrid-signature discrete spacetimes inspired by quantum gravity as models for real-world networks, linking network structure to spacetime geometry.

Findings

Hybrid-signature spacetimes match properties of small-world networks

Spectral dimension reveals embedding space characteristics

Models applicable to internet and neural networks

Abstract

Many real-world networks are embedded into a space or spacetime. The embedding space(time) constrains the properties of these real-world networks. We use the scale-dependent spectral dimension as a tool to probe whether real-world networks encode information on the dimensionality of the embedding space. We find that spacetime networks which are inspired by quantum gravity and based on a hybrid signature, following the Minkowski metric at small spatial distance and the Euclidean metric at large spatial distance, provide a template relevant for real-world networks of small-world type, including a representation of the internet's architecture and biological neural networks.