Networks with many structural scales: a Renormalization Group perspective

TL;DR

This paper defines and characterizes scale-invariant networks using a renormalization-group approach, distinguishing them from scale-free networks and analyzing natural examples like the human connectome.

Contribution

It introduces a rigorous framework for identifying and classifying scale-invariant networks, expanding understanding of their structural properties across various systems.

Findings

Human connectome shows features of scale invariance

Distinct characteristics differentiate scale-invariant from scale-free networks

Framework enables exploration of scale-invariant properties in biological and social systems

Abstract

Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a constant entropy-loss rate across scales in a renormalization-group coarse-graining setting. This framework enables us to differentiate between scale-free and scale-invariant networks, revealing distinct characteristics within each class. Furthermore, we offer a comprehensive inventory of genuinely scale-invariant networks, both natural and artificially constructed, demonstrating, e.g., that the human connectome exhibits notable features of scale invariance. Our findings open new avenues for exploring the scale-invariant structural properties crucial in biological and socio-technological systems.