  Several spectral fluctuation measures of random matrix theory (RMT) have been
applied in the study of spectral properties of networks. However, the
calculation of those statistics requires performing an unfolding procedure,
which may not be an easy task. In this work, network spectra are interpreted as
time series, and we show how their short and long-range correlations can be
characterized without implementing any previous unfolding. In particular, we
consider three different representations of Erd\"os-R\'enyi (ER) random
networks: standard ER networks, ER networks with random-weighted self-edges,
and fully random-weighted ER networks. In each case, we apply singular value
decomposition (SVD) such that the spectra are decomposed in trend and
fluctuation normal modes. We obtain that the fluctuation modes exhibit a clear
crossover between the Poisson and the Gaussian orthogonal ensemble statistics
when increasing the average degree of ER networks. Moreover, by using the trend
modes, we perform a data-adaptive unfolding to calculate, for comparison
purposes, traditional fluctuation measures such as the nearest neighbor spacing
distribution, number variance $\Sigma$2, as well as $\Delta$3 and {\delta}n
statistics. The thorough comparison of RMT short and long-range correlation
measures make us identify the SVD method as a robust tool for characterizing
random network spectra.
