  A general analytical approach to the statistical description of quantum graph
spectra based on the exact periodic orbit expansions of quantum levels is
discussed. The exact and approximate expressions obtained in \cite{Anima} for
the probability distribution functions using the spectral hierarchy method are
analyzed. In addition, the mechanism of appearance of the universal statistical
properties of spectral fluctuations of quantum-chaotic systems is considered in
terms of the semiclassical theory of periodic orbits.
