ID: 2203.07230

Laplacian Renormalization Group for heterogeneous networks

March 14, 2022

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Pablo Villegas, Tommaso Gili, Guido Caldarelli, Andrea Gabrielli
Condensed Matter
Nonlinear Sciences
Physics
Statistical Mechanics
Disordered Systems and Neura...
Adaptation and Self-Organizi...
Biological Physics

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.

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