Universality in complex networks: Random matrix analysis
نویسندگان
چکیده
منابع مشابه
Universality in complex networks: random matrix analysis.
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 s...
متن کاملRandom matrix analysis of complex networks.
We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of the adjacency matrix of various model networks, namely, random, scale-free, and small-world networks. These distributions follow the Gaussian orthogonal ensemble statistic of RMT. To probe long-range correlations in the eigenv...
متن کاملUniversality in Random Matrix Theory
which is the Central Limit Theorem. In principle, all the random variables X1, X2, · · · , XN can be of order 1, hence SN ∼ 1 as well, but the probability of having such a rare event is incredibly small. We can even estimate the bound on the probability for the rare event from the large deviation principle. A similar phenomenon happens when we form a large matrix from i.i.d. random variables an...
متن کاملStochasticity in Complex Networks: A random matrix analysis
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. Se...
متن کاملBreakdown of Universality in Random Matrix Models
We calculate smoothed correlators for a large random matrix model with a potential containing products of two traces trW1(M) ·trW2(M) in addition to a single trace trV (M). Connected correlation function of density eigenvalues receives corrections besides the universal part derived by Brézin and Zee and it is no longer universal in a strong sense. On leave of absence from National Laboratory fo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review E
سال: 2007
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.76.026109