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

Figure 1

Flow diagram of the directed network embedding algorithm. The algorithm steps and intermediate input/output are illustrated. (a, b) An illustration of transforming directed networks (a) to directed networks with a bipartite structure (b). Specifically, an asymmetric link in (a) can be expressed as a link between any pair of nodes from set A and set B in (b). (c) The main principle of our embedding method. The hidden metric model with the asymmetric popularity-similarity method is used to construct the embedding process, where the estimation and optimization methods (MLE and LMH) obtain the metric space coordinates of nodes. (d) The mapping achieves the representation and visualization of directed networks in the hyperbolic plane.