Localized and delocalized modes on random geometric graphs in one dimension.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 41560252.
- Also identified by DOI 10.1103/bp8s-pf4s.
- No licence information is recorded for this record.
- Because redistribution is not established, this page shows the abstract only. Follow the links below for the full text.
Abstract
We perform an extensive investigation of the localization properties of the eigenmodes of the Laplace and adjacency matrices for one-dimensional random geometric graphs. We evaluate the density of states, the probability distribution of the participation ratio, and its relation to the eigenvalues. 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.