  Assessing and improving the robustness of a graph $G$ are critical steps in
network design and analysis. To this end, we consider the optimisation problem
of removing $k$ edges from $G$ such that the resulting graph has minimal
robustness, simulating attacks or failures. In this paper, we propose total
harmonic resistance as a new robustness measure for this purpose - and compare
it to the recently proposed forest index [Zhu et al., IEEE Trans.\ Inf.\
Forensics and Security, 2023]. Both measures are related to the established
total effective resistance measure, but their advantage is that they can handle
disconnected graphs. This is also important for originally connected graphs due
to the removal of the $k$ edges. To compare our measure with the forest index,
we first investigate exact solutions for small examples. The best $k$ edges to
select when optimizing for the forest index lie at the periphery. Our proposed
measure, in turn, prioritizes more central edges, which should be beneficial
for most applications. Furthermore, we adapt a generic greedy algorithm to our
optimization problem with the total harmonic resistance. With this algorithm,
we perform a case study on the Berlin road network and also apply the algorithm
to established benchmark graphs. The results are similar as for the small
example graphs above and indicate the higher suitability of the new measure.
