MiS Preprint Repository

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MiS Preprint

Stochasticity in complex networks: a random matrix analysis

Jayendra Bandyopadhyay and Sarika Jalan


Following random matrix theory, we study nearest neighbor spacing distribution (NNSD) of the eigenvalues of the adjacency matrix of various model networks, namely scale-free, small-world and random networks.

Our analysis shows that, though spectral densities of these model networks are different, their eigenvalue fluctuations are same and follow Gaussian orthogonal ensemble (GOE) statistics. Secondly we show the analogy between the onset of small-world behavior (quantified by small diameter and large clustering coefficients) and the transition from Poisson to GOE statistics (quantified by Brody parameter).

We also present our analysis for a protein-protein interaction network in budding yeast.

Aug 14, 2006
Aug 14, 2006
Network, Random matrix theory, Order to chaos transition

Related publications

2007 Repository Open Access
Jayendra N. Bandyopadhyay and Sarika Jalan

Universality in complex networks : random matrix analysis

In: Physical review / E, 76 (2007) 2, p. 026109