A quant. measure of the polarity of a bond can be obtained through combining the two complementary topol. partitionings of the electron d. obtained from the atoms in mols. theory, on the one hand, and the electron localization function, on the other. This requires an integration of the electron d. in the at. subbasins of a common bond electron localization basin. We present the first numerical application of the resulting topol. definition of bond polarity to a set of small linear systems consisting of the FCN, HF, HCl, HBr, and NaCl mols. and the NeAr van der Waals dimer. It is shown that the findings are essentially in line with common expectation for these simple mols., thus confirming the potential value of the novel bond polarity index for the anal. of controversial bonding situations. Addnl. insight is provided through the detailed investigation of fluctuations in the basin populations.