Networks with many structural scales: a Renormalization Group perspective

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.

6 pages, 3 figures and Supplemental Material

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Cited by in corpus (8)

• Network Renormalization
• Strange Attractors in Complex Networks
• Topological protection breakdown: a route to frustrated ferroelectricity
• Global decomposition of networks into multiple cores formed by local hubs
• From Spatial to Spectral: Network Renormalization via Dynamical Correlations
• Higher-order contagion processes in 3.99 dimensions
• Geometric Criticality in Scale-Invariant Networks
• Asymptotic versus mesoscopic spectral dimensions in networks and inhomogeneous structures