Spectra of adjacency matrices of random geometric graphs

Paul Blackwell, Mark Edmondson-Jones and Jonathan Jordan

Submitted to Internet Mathematics.

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 $-1$.

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Last updated 22 February 2007.