Random matrix analysis of network Laplacians

Details Random matrix analysis of network Laplacians Random matrix analysis of network Laplacians

2006-11-29

arxiv.org/abs/cond-mat/0611735v2

Physica A, 387, Issues 2-3, 667 (2008)

Physics

Condensed Matter

Statistical Mechanics

14 pages, 5 figures, replaced with the final version

Scientific paper

10.1016/j.physa.2007.09.026

We analyze eigenvalues 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 nearest neighbor spacing distribution of the Laplacian of these networks follow Gaussian orthogonal ensemble statistics of random matrix theory. Furthermore, we study nearest neighbor spacing distribution as a function of the random connections and find that transition to the Gaussian orthogonal ensemble statistics occurs at the small-world transition.

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