标题： 一维随机几何图上的局域和非局域模式 显示英文标题

标题： Localized and delocalized modes on random geometric graphs in 1D

摘要： 我们对一维随机几何图的拉普拉斯矩阵和邻接矩阵的本征模的局域化特性进行了广泛的研究。 我们评估了态密度、参与比的概率分布及其与本征值的关系。 通过分离系统大小、图组件大小分布、节点平均度、网络基序和简并性的影响，我们提供了对该系统的全面理解。 我们将我们的发现与具有相同平均度的有序图以及一维紧束缚模型进行比较。 显示英文摘要

摘要： 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.