Encoding Hyperuniformity in Geometric Networks: Structural Signatures and Diffusion Dynamics
Abstract
Disordered hyperuniformity is a recently discovered exotic state exhibiting anomalously suppressed density fluctuations at long wavelengths, and its generalization to network systems remains an important open question. Here, we show that, across a wide range of systems, geometric networks retain substantially more long-wavelength density information from the underlying point configurations than Delaunay triangulations. Within geometric networks, hyperuniformity manifests as suppressed vertex-to-vertex fluctuations in a range of network structural observables, including closeness centrality, vertex strength, and eigenvector centrality. These measures not only distinguish hyperuniform networks from non-hyperuniform ones, but also separate near-hyperuniform configurations from hyperuniform systems with strong local disorder, solving a central challenge in network hyperuniformity. We connect these structural signatures to network dynamics by introducing a relaxation-time centrality based on diffusion and demonstrate that hyperuniform geometric networks exhibit more homogeneous relaxation behavior than non-hyperuniform geometric networks. These results reveal how the suppression of large-scale density fluctuations manifests in both network structure and diffusion dynamics.
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BibTeX
@misc{wang2026encoding,
title = {{Encoding Hyperuniformity in Geometric Networks: Structural Signatures and Diffusion Dynamics}},
author = {Yongyi Wang and Eli Newby and Yang Jiao and Salvatore Torquato and Réka Albert},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24317},
eprint = {2610.24317},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24317},
}
RIS
TY - UNPB
TI - Encoding Hyperuniformity in Geometric Networks: Structural Signatures and Diffusion Dynamics
AU - Yongyi Wang
AU - Eli Newby
AU - Yang Jiao
AU - Salvatore Torquato
AU - Réka Albert
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24317
UR - https://arxiv.org/abs/2610.24317
AB - Disordered hyperuniformity is a recently discovered exotic state exhibiting anomalously suppressed density fluctuations at long wavelengths, and its generalization to network systems remains an important open question. Here, we show that, across a wide range of systems, geometric networks retain substantially more long-wavelength density information from the underlying point configurations than Delaunay triangulations. Within geometric networks, hyperuniformity manifests as suppressed vertex-to-vertex fluctuations in a range of network structural observables, including closeness centrality, vertex strength, and eigenvector centrality. These measures not only distinguish hyperuniform networks from non-hyperuniform ones, but also separate near-hyperuniform configurations from hyperuniform systems with strong local disorder, solving a central challenge in network hyperuniformity. We connect these structural signatures to network dynamics by introducing a relaxation-time centrality based on diffusion and demonstrate that hyperuniform geometric networks exhibit more homogeneous relaxation behavior than non-hyperuniform geometric networks. These results reveal how the suppression of large-scale density fluctuations manifests in both network structure and diffusion dynamics.
ER -