2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122234The 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, $δk_{n}=k_{n}-\bar k_{n}$.24 pages, 5 figuresQuantum Physicstext