Effect of Unfolding on the Spectral Statistics of Adjacency Matrices of Complex Networks

Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term correlation. We study the spectral fluctuations of the adjacency of networks using random-matrix theory. We consider the influence of the spectral unfolding, which is a necessary procedure to remove the secular properties of the spectrum, on different spectral statistics. We find that, while the spacing distribution of the eigenvalues shows little sensitivity to the unfolding method used, the spectral rigidity has greater sensitivity to unfolding.