By theoretical simulations the relationship between the quantum transport current and magnetic field induced current in triangular nanographene molecules is investigated. In both cases the time-reversal symmetry between the doubly degenerate states of the isolated molecule is broken, which results in incomplete cancellation of the two equivalent circulating current patterns with opposite flow directions. This shows that the source-drain driven current loop and the diamagnetic circulating current can be understood on the same theoretical footing. [DOI: 10.1380/ejssnt.2004.205]