Fig. 6: Graph reconstruction performance on directed real networks.
From: Model-independent embedding of directed networks into Euclidean and hyperbolic spaces
For the networks in panels a–f, the task was to reconstruct all the links (Esampled = E), whereas for the network of political blogs in panels g–j and for the word association network in panels j–l, due to the large network size, the task was to reconstruct five samples of Esampled = 5000 and Esampled = 500 number of links, respectively. In the case of the larger networks, we always considered the average of the quality scores over the five samples and depicted the corresponding standard deviations with (usually very small) grey error bars. Each row of panels refers to a real network indicated in the row title, while the different columns show the different quality measures that we studied, given by the precision obtained when reconstructing the first Esampled most probable links (1st column), the area under the precision-recall (PR) curve (2nd column), and the area under the ROC curve (3rd column). The colours indicate the applied geometric measure, as listed in the common legend at the bottom of the figure. Using the bars, we plotted only the best results regarding all the performance measures, considering all the tested number of dimensions. The horizontal lines in colour show the best two-dimensional performances achieved among all the embedding methods, whereas the grey horizontal lines correspond to the baselines provided by the random predictor and the best local method.
