Spectral statistics for scaling quantum graphs
  The explicit solution to the spectral problem of quantum graphs is used to obtain the exact distributions of several spectral statistics, such as the oscillations of the quantum momentum eigenvalues around the average, $\delta k_{n}=k_{n}-\bar k_{n}$, and the nearest neighbor separations, $s_{n}=k_{n}-k_{n-1}$. 
Yu. Dabaghian