Before revision:  Interestingly, in this case the annealed approximation fails to predict the dynamical behavior for sparse connectivities , suggesting that even weak topological correlations can strongly limit its applicability for finite N .
After revision:  Interestingly, in this case the annealed approximation fails to predict the dynamical behavior for sparse connectivities It is shown that the naive mean-field assumption typical for the annealed approximation leads to false predictions in this case, since correlations between thresholds and out-degree that emerge as a side-effect strongly modify damage propagation behavior .