MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Stochasticity in complex networks: a random matrix analysis
Jayendra Bandyopadhyay and Sarika JalanAbstract
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.
- Received:
- 14.08.06
- Published:
- 14.08.06
- Keywords:
- Network, Random matrix theory, Order to chaos transition