Universality in Complex Networks: Random Matrix Analysis

Details Universality in Complex Networks: Random Matrix Analysis Universality in Complex Networks: Random Matrix Analysis

2006-08-13

arxiv.org/abs/nlin/0608028v2

Phys. Rev. E, Vol. 76, 026109 (2007)

Nonlinear Sciences

Adaptation and Self-Organizing Systems

4+ pages, 4 figures, to appear in PRE, major change in the paper including title

Scientific paper

10.1103/PhysRevE.76.026109

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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