Random 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 eigenvalues we study spectral rigidity via the Delta_{3} statistic of RMT as well. It follows RMT prediction of linear behavior in semilogarithmic scale with the slope being approximately 1pi;{2} . Random and scale-free networks follow RMT prediction for very large scale. A small-world network follows it for sufficiently large scale, but much less than the random and scale-free networks.
Jalan
Sarika
S
Max-Planck Institute for the Physics of Complex Systems, Nöthnitzerstrasse 38, D-01187 Dresden, Germany. sarika@mpipks-dresden.mpg.de
Bandyopadhyay
Jayendra N
JN