A hyperbolic embedding for scale-free networks

Graph neural network, with its powerful learning ability, has become a cutting-edge method of processing ultra-large-scale network data. In order to polished up the representation accuracy of embedding, the key is to find the intrinsic geometric metric of the complex network. Since the real data is mostly scale-free network, the embedding accuracy of traditional models is still limited by the dimensionality of the euclidean space and computational complexity. Therefore, the hyperbolic embedding, whose metric properties conform to the power-law distribution and tree-like hierarchical structure of the complex network, will effectively approximates the latent lowdimensional manifold of the data distribution. This paper proposes an auto-encoder in hyperbolic space (HVGAE), taking full use of hyperbolic graph convolutional (HGCN) and the idea of variational autoencoder. Under the optimal combination of the encoder module, competitive results have been achieved in different real scenarios.