I am looking for a graph-theoretic algorithm, that determines among all simple paths $\mathcal{P}_{ab}$ that connect vertex $a$ with vertex $b$ the one, that has minimal average edge-length, i.e. $$\ p_{ab}\in\mathcal{P}_{ab}:\quad \frac{\ell(p_{ab})}{\mathrm{card}(p_{ab})} \le \frac{\ell(q_{ab})}{\mathrm{card}(q_{ab})},\; \forall q_{ab}\in\mathcal{P}_{ab}$$

By "graph-theoretic" I mean algorithms in the vein of those that are likely to be found in publications about algorithmic graph-theory; on the contrary, mathematical programming is not what I am looking for.

programmingwould have been an option, if simplicity of the reported paths were guaranteed. It is however an option to filter out all non-simple paths to find an upper bound on the optimal solution. $\endgroup$