Rough rock fractures have complex geometries which result in highly heterogeneous aperture fields. To accurately estimate the permeability of such fractures, heterogeneity of the aperture fields must be quantified. In this study heterogeneity of single rough rock fractures is for the first time parametrized by connectivity metrics, which quantify how connected the bounds of a heterogeneous field are. We use 3000 individual realizations of synthetic aperture fields with different statistical parameters and compute three connectivity metrics based on percolation theory for each realization. The sensitivity of the connectivity metrics with respect to the determining parameter, i.e the cutoff threshold, is studied and the correlation between permeability of the fractures and the computed connectivity metrics is presented. The results show that the Θ connectivity metric predicts the permeability with higher accuracy. All three studied connectivity metrics provide better permeability estimations when a larger aperture value is chosen as the cutoff threshold. Overall, this study elucidates that using connectivity metrics provides a less expensive alternative to fluid flow simulations when an estimation of fracture permeability is desired.