Department of Physics

Permanent URI for this collectionhttp://localhost:4000/handle/123456789/1932

Browse

Filters

2006 - 20093

Settings

Subject: search.filters.subject.Matrix analysis

Search Results

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    Stochasticity in Complex Networks: A random matrix analysis
    (2006-08) Bandyopadhyay, Jayendra N.
    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.
  • No Thumbnail Available
    Item
    Randomness of random networks: A random matrix analysis
    (Sci Egngine, 2009-08) Bandyopadhyay, Jayendra N.
    We analyze complex networks under the random matrix theory framework. Particularly, we show that statistics, which gives information about the long-range correlations among eigenvalues, provides a measure of randomness in networks. As networks deviate from the regular structure, follows the random matrix prediction of logarithmic behavior (i.e., ) for longer scale.
  • No Thumbnail Available
    Item
    Universality in complex networks: Random matrix analysis
    (APS, 2007-08) Bandyopadhyay, Jayendra N.
    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. Second, 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.