Applying a magnetic field to a molecule induces a current density vector field J(x) : R 3 → R 3 . The stagnation graph of J is the subset of R 3 where |J(x)| = 0 and in general consists of isolated stagnation points and extended stagnation lines . These stagnation graphs form a compact representation of the topology of the vector field and have significance in ring-current models and NMR spectra . The stagnation graph can be obtained as the critical network of -|J|, as can be seen for a C 2 H 2 molecule in Fig. . This stagnation graph exhibits the same features as a more detailed analysis at signifi- cantly reduced cost . The graph is known to contain a stagnation line that bisects the molecule -this can be seen in Fig. , but is quite ragged due to the decreasing density of DFT grid points as we move further from the nuclei. In combination with this, the single-valued (|J| = 0) and line-like (and therefore weakly-connected) nature of stagnation graphs make for a challenging test case for topological analysis. In any case, the approximate stagnation points determined via the present analysis on DFT grids can be used as a starting point for the derivative based optimization and refinement of the stagnation graph presented in Ref. . Utilising the starting points from the algorithms in the present work can significantly reduce the cost of determining detailed stagnation graphs using the derivative based approaches.