Fig. 2: Validation of D-Mercator on synthetic networks.

Relationship between coordinates of the synthetic \({{\mathbb{S}}}^{2}\) networks (original) and its embeddings (inferred) with parameters: a, c, e \(\beta=3,\gamma=2.5,N=2000,\, \langle k \rangle=8\) and b, d, f \(\beta=5,\, \gamma=2.7,\, N=2000,\, \langle k \rangle=9\). In the top left corner of each figure, the value of the Pearson correlation coefficient between the inferred and original coordinates is reported. Since the coordinates from the embedding might be rotated, we transform them to minimize the average angular distance between the original and inferred coordinates (see Section III in Supplementary Information).