The spectroscopic network of a molecule is a large graph: the vertices are the rotationalvibrational quantum states of the molecule, and the edges are the allowed transitions between the states. Physical attributes, such as transition wavenumber and intensity, correspond to weight functions on the graph. Spectroscopic networks offer a novel way to analyse and improve the large amount of data acquired about the nuclear dynamics of molecules via various spectroscopic techniques. Spectroscopic networks can be used to detect errors in databases containing measured data, to help the assignment of new experiments, and to aid the planning of future measurements with certain aims. In the talk various problems and methods involving spectroscopic networks will be presented from a mathematical point of view.

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