From bridges to cycles in spectroscopic networks

Spectroscopic networks provide a particularly useful representation of observed rovibronic transitions of molecules, as well as of related quantum states, whereby the states form a set of vertices connected by the measured transitions forming a set of edges. Among their several uses, SNs offer a practical framework to assess data in line-by-line spectroscopic databases. They can be utilized to help detect flawed transition entries. Methods which achieve this validation work for transitions taking part in at least one cycle in a measured spectroscopic network but they do not work for bridges. The concept of two-edge-connectivity of graph theory, introduced here to high-resolution spectroscopy, offers an elegant approach that facilitates putting the maximum number of bridges, if not all, into at least one cycle. An algorithmic solution is shown how to augment an existing spectroscopic network with a minimum number of new spectroscopic measurements selected according to well-defined guidelines. In relation to this, two metrics are introduced, ranking measurements based on their utility toward achieving the goal of two-edge-connectivity. Utility of the new concepts are demonstrated on spectroscopic data of [Formula: see text].