<p>This paper addresses the detection of high-impedance faults with low-cost and efficient algorithms in distribution networks. A graph theory approach is used in the sequence and phase domains to analyze the sensitivity of a current phase difference criterion under steady-state fault conditions, including more realistic unbalanced conditions. Single-phase-to-ground faults with fault impedance varying from zero to typically high levels were simulated along distribution systems adapted from the IEEE 34-bus feeder. The results obtained in the balanced and unbalanced systems through the sequence-domain and phase-domain methods, respectively, were compared. Regarding shunt faults, grounding significantly attenuated the post-fault phase difference of the healhy-phase currents, and the sensor location was shown to be critical for effective sensitization. On the other hand, in the case of downed conductors, the sensitivity to the fault impedance variation was satisfactorily reduced, indicating the suitability of the evaluated criterion for ungrounded faults in ungrounded branches, as a complementary protection function. For future research, it is intended to incrementally adapt this phase-domain graph theory approach to simulate electromagnetic transient phenomena using the inverse Fourier transform.</p>