Gauge-origin independent current density susceptibility tensors have been computed using the gauge-including magnetically induced current (GIMIC) method. The anisotropy of the magnetically induced current density (ACID) functions constructed from the current density susceptibility tensors are therefore gauge-origin independent. The ability of the gauge-origin independent ACID function to provide quantitative information about the current flow along chemical bonds has been assessed by integrating the cross-section area of the ACID function in the middle of chemical bonds. Analogously, the current strength susceptibility passing a given plane through the molecule is obtained by numerical integration of the current flow parallel to the normal vector of the integration plane. The cross-section area of the ACID function is found to be strongly dependent on the exact location of the integration plane, which is in sheer contrast to the calculated ring-current strength susceptibilities that are practically independent of the chosen position of the integration plane. The gauge-origin independent ACID functions plotted for different isosurface values show that a visual assessment of the current flow and degree of aromaticity depends on the chosen isosurface. The present study shows that ACID functions are not an unambiguous means to estimate the degree of molecular aromaticity according to the magnetic criterion and to determine the current pathway of complex molecular rings.