Frequency combs and cavity-enhanced optical techniques have revolutionized molecular spectroscopy: their combination allows recording saturated Doppler-free lines with ultrahigh precision. Network theory, based on the generalized Ritz principle, offers a powerful tool for the intelligent design and validation of such precision-spectroscopy experiments and the subsequent derivation of accurate energy differences. As a proof of concept, 156 carefullyselected near-infrared transitions are detected for H 2 16 O, a benchmark system of molecular spectroscopy, at kHz accuracy. These measurements, augmented with 28 extremelyaccurate literature lines to ensure overall connectivity, allow the precise determination of the lowest ortho-H 2 16 O energy, now set at 23.794 361 22(25) cm −1 , and 160 energy levels with similarly high accuracy. Based on the limited number of observed transitions, 1219 calibrationquality lines are obtained in a wide wavenumber interval, which can be used to improve spectroscopic databases and applied to frequency metrology, astrophysics, atmospheric sensing, and combustion chemistry.