Spectra of adjacency matrices of random geometric graphs

Abstract: We investigate the spectral properties of the adjacency matrices of random geometric graphs both theoretically and by simulation, concentrating on the thermodynamic limit. Our results show interesting differences from those previously found for other models of random graphs. In particular the spectra do not show the symmetry about $0$ found for classical and scale-free random graphs, and we find a striking singularity at $-1$.

Paper (PDF, 273KB).