Universality in Complex Networks: Random Matrix Analysis

Jayendra N. Bandyopadhyay; Sarika Jalan

doi:10.1103/physreve.76.026109

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arXiv · nlin/0608028

Universality in Complex Networks: Random Matrix Analysis

Jayendra N. Bandyopadhyay·Sarika Jalan

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Abstract

We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world and random networks follow universal Gaussian orthogonal ensemble statistics of random matrix theory. Secondly we show an analogy between the onset of small-world behavior, quantified by the structural properties of networks, and the transition from Poisson to Gaussian orthogonal ensemble statistics, quantified by Brody parameter characterizing a spectral property. We also present our analysis for a protein-protein interaction network in budding yeast.

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Jayendra N. Bandyopadhyay, Sarika Jalan. 2007-07-11. Universality in Complex Networks: Random Matrix Analysis. https://doi.org/10.1103/physreve.76.026109

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