Approaches related to graph theory are investigated which allow a better understanding and yield routes for systematic enlargement and improvement of experimental spectroscopic line lists of molecules. The proposed protocols are based on the fact that quantum mechanics builds, in a simple and natural way, large-scale, weighted, undirected graphs, whereby the vertices are discrete energy levels, the edges are transitions, and the weights are transition intensities. A small part of molecular quantum mechanical graphs can be probed experimentally via high-resolution spectroscopic techniques, while the complete graph encompassing the full line list information for a given molecule can be obtained through sophisticated variational nuclear motion computations. Both approaches yield what one may call spectroscopic networks (SNs). It is shown on the example of the HD 16O isotopologue of the water molecule that both the measured and the computed one-photon absorption SNs have a scale-free behavior with all of the usual consequences, including appearance of hubs, robustness, error tolerance, and the "small-world" property. For the complete computed "deterministic" network the scale-free property holds if a realistic intensity cut-off is employed during its build-up, thus introducing "stochasticity". The graph-theoretical view of molecular spectra offers several new ideas for improving the accuracy and robustness of the information systems containing high-resolution spectroscopic data.