We provide a physical interpretation of the Kirchhoff index of any molecules as well as of the Wiener index of acyclic ones. For the purpose, we use a local vertex invariant that is obtained from first principles and describes the atomic displacements due to small vibrations/oscillations of atoms from their equilibrium positions. In addition, we show that the topological atomic displacements correlate with the temperature factors (B-factors) of atoms obtained by X-ray crystallography for both organic molecules and biological macromolecules.
Estrada, E., Hatano, N., & University of Strathclyde, New Professors Fund (Funder) (2010). Topological atomic displacements, Kirchhoff and Wiener indices of molecules. Chemical Physics Letters, 486(4-6), 166-170. https://doi.org/10.1016/j.cplett.2009.12.090