Fig. 4.

Angular coordinates comparison and C-score on popularity-similarity-optimization synthetic networks. a–i For all the combinations of the PSO parameters N (size) and m (half of average degree), we chose among the synthetic networks embedded with RA-MCE-EA the ones with the best C-score, which had always temperature T = 0. For these networks, we plotted the aligned inferred angular coordinates against the original angular coordinates (θ). The alignment was done in the following manner: we applied 360 rotations of one degree both to the inferred coordinates as they are and to the inferred coordinates obtained arranging the nodes in the opposite clock direction. Then from these resulting 720 alternatives of the inferred angular coordinates, we chose the one that maximizes the correlation with the original angular coordinates, in order to guarantee the best alignment. The alignment does not change the C-score, which represents the percentage of node pairs in the same circular order in the original and inferred networks (see “Methods” section for details). Similar plots for the other coalescent embedding methods and temperature values can be found in Supplementary Figs. 8–17. j–r The plots report the average C-score and the standard error over the 100 synthetic networks that have been generated for each different parameter combination. There are no separate plots for the methods with and without EA since this adjustment affects the distances but not the circular ordering, therefore it does not change the C-score. For each subplot, the value of HyperMap-CN for T = 0 is missing because the original code assumes T > 0