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, spectroscopic networks offer a practical framework to assess data in line-by-line spectroscopic databases and to help detect flawed transition entries. Existing validation methods based on cycle testing work only for transitions taking part in at least one cycle in a measured spectroscopic network and do not work for bridges. Introducing two-edge-connectivity from graph theory to high-resolution spectroscopy offers an approach to put the maximum number of bridges, if not all, into at least one cycle. An algorithmic solution is shown to augment an existing spectroscopic network with a minimum number of new spectroscopic measurements selected according to well-defined guidelines. Two metrics rank measurements based on their utility toward achieving two-edge-connectivity. The utility of these concepts is demonstrated on spectroscopic data of 14NH3.