We present the first quantum system where Anderson localization is complete
ly described within periodic-orbit theory. The model isa quantum graph anal
ogous to an aperiodic Kronig-Penney model in one dimension. The exact expre
ssion for the probability to return to an initially localized state is comp
uted in terms of classical trajectories. It saturates to a finite value due
to localization, while the diagonal approximation decays diffusively. Our
theory is based on the identification of families of isometric orbits. The
coherent periodic-orbit sums within these families, and the summation over
ail families, are performed analytically using advanced combinatorial metho
ds.