The Huckel-London-Pople-McWeeny (HLPM) (topological) approach for calculating pi-electron ring-currents and bond-currents in conjugated systems is applied to coronene and the 17 nonalternant isomers of it for which Balaban, Bean, and Fowler recently published ab initio ipso-centric pi-electron current-density maps. In a parallel investigation to that conducted by Balaban et al., the key findings of their quantum-mechanical study are confirmed by this topological one: (a) all seven rings in all of the 18 structures studied are found to bear substantial diamagnetic ring-currents, greater than the benzene value; (b) all 18 conjugated systems have a pronounced, overall London diamagnetic-susceptibility, perpendicular to their respective molecular-planes; (c) a substantial diamagnetic current runs around the periphery of each of these structures; and (d) there is general agreement between the two studies as to which structures, of those treated, respect the annulene-within-an-annulene model for conjugated systems of this sort. The same ideas are also tested against ring-current and bond-current intensities recently calculated by Randic et al. using purely graph-theoretical methods that are based on circuits of conjugation. Considerable qualitative agreement is found, and when there is disagreement, arguments are offered as to why the HLPM topological ring-currents and bond-currents are to be preferred.