Fig. 7: Greedy routing performance on directed real networks.

For the networks in panels a–f, the task was to perform greedy routing between each node pair connected by at least one directed path, whereas for the larger networks in panels g–l, the task was to perform greedy routing in five samples of 500,000 node pairs connected by at least one directed path. 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. The colours indicate the used geometric measure as listed in the common legend at the bottom of the figure. We plotted in each panel for each method only the result of the parameter setting that turned out to be the best according to the GR-score. The bars were created considering all the tested number of dimensions, whereas the horizontal lines show the best two-dimensional average performances achieved among all the embedding methods. Each row of panels refers to a real network named in the row title, and the different columns correspond to different quality measures: the 1st column shows the greedy routing score (the higher the better), the 2nd column corresponds to the success rate of greedy routing (the higher the better), and the 3rd column depicts the average hop-length of the successful greedy paths (the smaller the better), where the grey bars indicate the average of the hop-length of the shortest paths connecting the node pairs for which the greedy routing was successful.