Correction to: Nature https://www.nature.com/articles/nature16948, published online 17 February 2016.

In this Letter, in Fig. 3c and f the Saccharomyces cerevisiae and Escherichia coli networks were subject to both weight loss and node deletion, a combination of two types of perturbation, as opposed to weight loss only (as the labelling incorrectly indicated). The collapse in Fig. 3h was also obtained from this combined perturbation, and therefore the results displayed in Fig. 3h remain fully consistent with the theoretical framework presented in this Letter. Figure 1 to this Amendment shows the corrected Fig. 3c, f and h, in which Fig. 3c and f have been generated with weight-loss perturbations only, as originally reported, together with the originally published panels, for completeness and transparency. The codes used to generate the original and the corrected Fig. 3 are available at https://github.com/jianxigao/NuRsE. We thank Travis A. Gibson for alerting us to this error. The original Letter has not been corrected.

Fig. 1
figure 1

This figure shows the originally published Fig. 3c, f and h and the corrected Fig. 3c, f and h.

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