Network permutation for negative controls of paths.

The five-layer network built using Pearson correlation is used as the base network. For each of the 100 repetitions, the network was permuted by swapping the edges between pairs of nodes. In permutation 1, the edge between B and C was swapped with the edge between D and E. In the permutation 2, the edge between A and E was swapped with the edge between B and C. In permutation 3, first the edge swap from the top network was applied, followed by the edge swap from the middle network. In each case, the edge swap can only be done if it does not result in two edges between the same pair of nodes. Making the permutation in this way keeps the original degree distribution of the network. The weights for each of the edges are permuted as well. This edge swapping technique is applied 10 times for each edge in the original network. After they are permuted, the top paths for each network are identified in the same manner as before. There are three possibilities for considering whether the paths from the original network appear in the paths from the permuted networks. In permutation 1, the path exists in the permuted network and furthermore was identified as a top path. In permutation 2, the original path does exist in the permuted network but was not identified as a top path. In permutation 3, the original path doesn’t exist in the permuted network at all.