Andrea Gabrielli — Università di Roma Tre e Centro Ricerche Enrico Fermi #
Networks with many scales of length and the Laplacian Renormalization Group #
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 diffusion entropy production 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 that the human connectome exhibits notable features of scale invariance. Our findings pave the way for novel avenues to investigate the scale-invariant structural properties crucial in biological and socio-technological systems.