Laplacian Renormalization Group for heterogeneous networks: information core, entropic transitions and scale transformations

by Andrea Gabrielli (University of Roma Tre)

Tuesday 26 Mar 2024, 16:00 → 17:30 Europe/Rome

Aula Conversi (Dip. di Fisica - Edificio G. Marconi)

SEMINARIO DI MECCANICA STATISTICA

Complex networks often exhibit a rich architecture organized over multiple intertwined scales. Information pathways are expected to pervade these scales reflecting structural insights that are not manifest from analyses of the network topology. Moreover, small-world effects correlate the different network hierarchies making the identification of coexisting mesoscopic structures and functional cores a difficult task. We first present a thermodynamic interpretation of effective information pathways throughout complex networks based on information diffusion and statistical mechanics to shed light on these issues [1]. This directly lead us to a formulation of a new and general Renormalization Group scheme for heterogeneous networks that permits to change resolution scale in a physically motivated way. The Renormalization Group (RG) is the cornerstone of the modern theory of scale transformation, 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 and small world coupling between intertwined scales. Here, we propose a Laplacian Renormalization Group (LRG) diffusion-based approach to complex networks, defining the coarse-grained supernodes and superedges concept à la Kadanoff, the equivalent of the momentum space RG procedure à la Wilson for graphs, and applying this RG scheme to real networks in a natural and parsimonious way to define proper scale transformation at arbitrarily resolution scale, study the topological organisation of the network [2] and detect characteristic structures [3].

[1] P. Villegas, A. Gabrielli, G. Caldarelli, T. Gili, Laplacian paths in complex networks: Information core emerges from entropic transitions, Physical Review Research 4, 033196 (2022). 

[2] P. Villegas, T. Gili, G. Caldarelli, A. Gabrielli, Laplacian Renormalization Group for heterogeneous networks, Nature Physics 19, 445–450 (2023).

[3] P. Villegas, A. Gabrielli, A. Poggialini, T. Gili, Multi-scale Laplacian community detection in heterogeneous networks, https://arxiv.org/abs/2301.04514