Random-walk-based or Similarity-based Methods, Which is Better for Directed Graph Embedding?

Graph embedding methods map nodes in a graph into low-dimensional latent vectors that preserve the underlying semantic information in the graph and can be used for graph inference and analysis. Graph embedding is applicable to both directed and undirected graphs; however, it is more challenging for the former ones due to their asymmetric nature. Single-vector embedding methods have limitations in preserving the asymmetric information in directed graphs since they provide a single latent vector for each node in the graph. To alleviate this problem, double-vector embedding methods provide two latent vectors, i.e., source and target, for any nodes; in this paper, we first divide these methods into two following categories based on their graph embedding mechanism: random-walk-based methods (RWM) and similarity-based methods (SBM). Although the effectiveness of the double-vector and single-vector embedding methods are widely studied in the literature, there are no comprehensive studies to evaluate and compare the effectiveness of the state-of-the-art RWM and SBM in directed graph embedding. This paper provides such a study by conducting extensive experiments with seven real-world datasets. Our experimental results demonstrate that 1) the double-vector embedding methods are not always superior to the single-vector ones in directed graph embedding, and 2) superiority of random-walk-based or similarity-based double-vector embedding methods over the others depends on different factors such as the machine learning tasks, datasets, and even evaluation metrics.