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arXiv · 2406.19104

Networks with many structural scales: a Renormalization Group perspective

Anna Poggialini·Pablo Villegas·Miguel A. Muñoz·Andrea Gabrielli
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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 socio-technological systems.

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Anna Poggialini, Pablo Villegas, Miguel A. Muñoz, Andrea Gabrielli. 2024-06-27. Networks with many structural scales: a Renormalization Group perspective. https://doi.org/10.1103/physrevlett.134.057401

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