Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2603.29611 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
Tabla de Contenidos:
- We compare the spectrum and the localisation properties of the eigenmodes of the Laplacian and the adjacency matrix of 2D random geometric graphs, using numerical diagonalization of these matrices for different system sizes and connectivities. For sufficiently large ensembles of systems, we evaluate the spectrum, the probability distribution of the participation ratio and the relation between participation ratios and eigenvalues. While all eigenmodes of the adjacency matrix are localised for sufficiently large system sizes, the Laplacian matrix always leads to a small proportion of system-spanning modes due to a conservation law, and therefore to power-law tails in the probability distribution of the participation ratio and its relation to the eigenvalues. By disentangling the effects of finite system size, of mean degree, of component size distribution, and of network motifs, we provide a thorough understanding of the data.