  The explicit solution to the spectral problem of quantum graphs found
recently in \cite{Anima}, is used to produce the exact periodic orbit theory
description for the probability distributions of spectral statistics, including
the distribution for the nearest neighbor separations, $s_{n}=k_{n}-k_{n-1}$,
and the distribution of the spectral oscillations around the average, $\delta
k_{n}=k_{n}-\bar k_{n}$.
