  We analyze, in general terms, the evolution of energy levels in quantum
mechanics, as a function of a coupling parameter, and demonstrate the
possibility of level crossings in systems described by irreducible matrices. In
long-range interactions, the coupling parameter is the interatomic distance. We
demonstrate the utility of adjacency matrices and adjacency graphs in the
analysis of "hidden" symmetries of a problem; these allow us to break reducible
matrices into irreducible subcomponents. A possible breakdown of the
no-crossing theorem for higher-dimensional irreducible matrices is indicated,
and an application to the 2S-2S interaction in hydrogen is briefly described.
The analysis of interatomic interactions in this system is important for
further progress on optical measurements of the 2S hyperfine splitting.
