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CREF Talk – Laplacian Renormalization Group for heterogeneous networks

Wednesday, 12 April, 3 pm
Speaker Andrea Gabrielli
Title: Laplacian Renormalization Group for heterogeneous networks: information core and entropic transitions

Abstract:

Complex networks usually 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 tie in the different network hierarchies making it more complicated to identify coexisting mesoscopic structures and functional cores.

We present a communicability analysis of effective information pathways throughout complex networks based on information diffusion to shed further light on these issues [1].

This will lead us to formulate a new and general renormalization group scheme for heterogeneous networks.

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 geometrical hypotheses.

Here, we propose a Laplacian RG diffusion-based picture for complex networks, defining both the supernodes concept à la Kadanoff, the equivalent momentum space procedure à la Wilson for graphs, and applying this RG scheme to real networks in a natural and parsimonious way [2].

[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, pages445–450 (2023).

This paper was featured on the March Issue of Nature Physics’s cover