The edge-permutation procedure retains the number of edges and the degree distribution of the network.43 Two edges, A-B and X-Y, are chosen at random and reshuffled to create the edges A-Y and X-B. Reshuffling is skipped if the edges A-Y and X-B already exist. Reshuffling is performed 10,000 times, resulting is an edge-randomized version of CDN-o, which we call CDN-er and for which we can again compute the GEF. We constructed 1,000 versions of CDN-er and plotted the distribution of the resulting GEF values in Figure S4A. As one can see, the p value of the CDN is less than 0.001 because none of the edge-randomized CDNs achieved the same or a smaller GEF than the original CDN.