Laplacian Renormalization Group for heterogeneous networks

TL;DR

This paper introduces a Laplacian-based renormalization group method for complex networks, enabling analysis of their hierarchical structures and scales without relying on hidden geometry assumptions.

Contribution

It proposes a novel diffusion-based RG scheme for heterogeneous networks, including definitions of supernodes and momentum space procedures inspired by Wilson's approach.

Findings

Successfully applied to real networks

Provides a natural and parsimonious RG framework

Advances understanding of network hierarchies

Abstract

The renormalization group is the cornerstone of the modern theory of universality and phase transitions, a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its network counterpart is particularly challenging due to correlations between intertwined scales. To date, the explorations are based on hidden geometries hypotheses. Here, we propose a Laplacian RG diffusion-based picture in complex networks, defining both the Kadanoff supernodes' concept, the momentum space procedure, \emph{\'a la Wilson}, and applying this RG scheme to real networks in a natural and parsimonious way.