Random matrix analysis of network Laplacians

Sarika Jalan and Jayendra N. Bandyopadhyay

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 2, 667-674

Abstract: We analyse the eigenvalue fluctuations of the Laplacian of various networks under the random matrix theory framework. Analyses of random networks, scale-free networks and small-world networks show that the nearest neighbor spacing distribution of the Laplacian of these networks follow Gaussian orthogonal ensemble statistics of the random matrix theory. Furthermore, we study the nearest neighbor spacing distribution as a function of the random connections and find that the transition to the Gaussian orthogonal ensemble statistics occurs at the small-world transition.

Keywords: Network; Graph Laplacian; Random matrix theory (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:2:p:667-674

DOI: 10.1016/j.physa.2007.09.026

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