Stimulated by recent experimental and theoretical interest in coronoids, a class of polycyclic aromatic compounds, we have developed graph-theoretically based topological indices for the characterization of a number of coronoid compounds. Coronoids have been the focus of several studies due to superaromaticity and other electronic and geometric properties exhibited by these polycyclics that make them also suitable for many applications due to the presence of cavities of different sizes. We have computed various topological indices for coronoid polycyclic aromatic hydrocarbons with cavities that vary topologically. Exact analytical expressions of a series of coronoid compounds have been computed by means of strength-weighted graphs based on the transitive closure of Djoković-Winkler relation. © 2018, © 2018 Taylor & Francis Group, LLC.