Networks with Many Structural Scales: A Renormalization Group Perspective
Anna Poggialini1,2, Pablo Villegas2,3, Miguel A Muñoz3,4
1Dipartimento di Fisica Università "Sapienza, ," Piazzale Aldo Moro, 2, I-00185 Rome, Italy.
Abstract:
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 entropy-loss 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, e.g., that the human connectome exhibits notable features of scale invariance. Our findings open new avenues for exploring the scale-invariant structural properties crucial in biological and sociotechnological systems.
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