We consider calculation of induced currents of pi-electrons over the molecular network when molecules are placed in a magnetic field. The approach is based on consideration of current contributions arising from conjugated circuits within each individual Kekule valence structure. The calculation is illustrated for an isomer of coronene C24H12 for which ab initio computations of pi-electron current densities are available. Agreement is found between the quantum chemical ab initio computations that make no assumptions on ring contributions and the graph theoretical models based on conjugated circuit currents. (C) 2010 Elsevier B.V. All rights reserved.