Abstract The two topological indices σ (recently proposed by Merrifield and Simmons) and Z (put forward by one of the present authors, Bull. Chem. Soc. Jpn., 44, 2332 (1971)) are shown to be both conceptually and numerically related. For alkanes, a linear correlation exists between ln σ and ln Z. For unbranched catacondensed benzenoid hydrocarbons σ and Z are linearly correlated. In any case σ and Z exhibit a reverse dependency on molecular structures: structural transformations having an increasing effect on Z decrease σ and vice versa.