Spectral statistics of random geometric graphs

Carl Dettmann, Orestis Georgiou, Georgie Knight

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)
270 Downloads (Pure)

Abstract

We study the spectrum of random geometric graphs using random matrix theory. We look at short range correlations in the level spacings via the nearest neighbour and next nearest neighbour spacing distribution and long range correlations via the spectral rigidity Δ3 statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find that the spectral statistics of random geometric graphs fits the universality of random matrix theory. In particular, the short range correlations are very close to those found in the Gaussian orthogonal ensemble of random matrix theory. For long range correlations we find deviations from Gaussian orthogonal ensemble statistics towards Poisson. We compare with previous results for Erdös-Rényi, Barabási-Albert and Watts-Strogatz random graphs where similar random matrix theory universality has been found.
Original languageEnglish
Article number18003
Number of pages7
JournalEPL
Volume118
Early online date30 May 2017
DOIs
Publication statusPublished - 2017

Keywords

  • Networks and genealogical trees
  • Matrix theory
  • Combinatorics
  • Graph theory

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