Localized and delocalized modes on random geometric graphs in 1D

Fuente: arXiv
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Main Authors: Schaefer, Luca, Drossel, Barbara
Format: Preprint
Published: 2025
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author Schaefer, Luca
Drossel, Barbara
author_facet Schaefer, Luca
Drossel, Barbara
contents We perform an extensive investigation of the localization properties of the eigenmodes of the Laplace and adjacency matrix for one-dimensional random geometric graphs. We evaluate the density of states, the probability distribution of the participation ratio and its relation to the eigenvalue. By disentangling the influence of system size, graph component size distribution, mean degree of nodes, network motifs, and degeneracy, we provide a comprehensive understanding of this system. We compare our findings to ordered graphs with the same mean degree and to one-dimensional tight-binding models.
format Preprint
id arxiv_https___arxiv_org_abs_2508_18936
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Localized and delocalized modes on random geometric graphs in 1D
Schaefer, Luca
Drossel, Barbara
Disordered Systems and Neural Networks
Statistical Mechanics
We perform an extensive investigation of the localization properties of the eigenmodes of the Laplace and adjacency matrix for one-dimensional random geometric graphs. We evaluate the density of states, the probability distribution of the participation ratio and its relation to the eigenvalue. By disentangling the influence of system size, graph component size distribution, mean degree of nodes, network motifs, and degeneracy, we provide a comprehensive understanding of this system. We compare our findings to ordered graphs with the same mean degree and to one-dimensional tight-binding models.
title Localized and delocalized modes on random geometric graphs in 1D
topic Disordered Systems and Neural Networks
Statistical Mechanics
url https://arxiv.org/abs/2508.18936