Quantum mechanics builds large-scale graphs (networks): the  vertices are the discrete energy levels the quantum system possesses,  while the edges are the (quantum-mechanically allowed) transitions.  Parts of the complete quantum mechanical networks can be probed  experimentally via high-resolution, energy-resolved spectroscopic  techniques, while the complete rovibronic line list information for a  given molecule can only be obtained through sophisticated  quantum-chemical computations. Experiments as well as computations  yield what we call spectroscopic networks (SN).  First-principles SNs  of even small, 3- to 5-atomic molecules can be huge, including  billions of transitions and millions of enery levels. Besides helping  to interpret high-resolution spectra, the network-theoretical view  offers several ideas for improving the accuracy and robustness of the  increasingly important information systems containing line-by-line  spectroscopic data. A present-day application of spectroscopic  networks is within the MARVEL (Measured Active Rotational-Vibrational  Energy Levels) approach, whereby the transitions information of a  measured SN is turned into experimental energy levels via a weighted  linear least-squares refinement.