An Asymmetric Popularity-Similarity Optimization Method for Embedding Directed Networks into Hyperbolic Space

Figure 3

Empirical versus theoretical connection probability. The hyperbolic embedding of directed networks is successful, as the empirical connection probability closely matches the geometric hidden model prediction. (a–d) The results of the C. elegans neural network, international trade network, email network, and international migration network, respectively. The black dashed lines are theoretical results of the connection probability, given by . Note that the parameters used in the theoretical simulation are the same as the corresponding empirical network. The pink dots are results of the empirical directed analysis. The whole range of hyperbolic distances and connection probabilities are binned, and each bin is the average of the values in it.

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