Unsupervised graph representation learning aims to distill various graph information into a downstream task-agnostic dense vector embedding. However, existing graph representation learning approaches are designed mainly under the node homophily assumption: connected nodes tend to have similar labels and optimize performance on node-centric downstream tasks. Their design is apparently against the task-agnostic principle and generally suffers poor performance in tasks, e.g., edge classification, that demands feature signals beyond the node-view and homophily assumption. To condense different feature signals into the embeddings, this paper proposes PairE, a novel unsupervised graph embedding method using two paired nodes as the basic unit of embedding to retain the high-frequency signals between nodes to support node-related and edge-related tasks. Accordingly, a multi-self-supervised autoencoder is designed to fulfill two pretext tasks: one retains the high-frequency signal better, and another enhances the representation of commonality. Our extensive experiments on a diversity of benchmark datasets clearly show that PairE outperforms the unsupervised state-of-the-art baselines, with up to 101.1\% relative improvement on the edge classification tasks that rely on both the high and low-frequency signals in the pair and up to 82.5\% relative performance gain on the node classification tasks.
Low-dimension graph embeddings have proved extremely useful in various downstream tasks in large graphs, e.g., link-related content recommendation and node classification tasks, etc. Most existing embedding approaches take nodes as the basic unit for information aggregation, e.g., node perception fields in GNN or con-textual nodes in random walks. The main drawback raised by such node-view is its lack of support for expressing the compound relationships between nodes, which results in the loss of a certain degree of graph information during embedding. To this end, this paper pro-poses PairE(Pair Embedding), a solution to use "pair", a higher level unit than a "node" as the core for graph embeddings. Accordingly, a multi-self-supervised auto-encoder is designed to fulfill two pretext tasks, to reconstruct the feature distribution for respective pairs and their surrounding context. PairE has three major advantages: 1) Informative, embedding beyond node-view are capable to preserve richer information of the graph; 2) Simple, the solutions provided by PairE are time-saving, storage-efficient, and require the fewer hyper-parameters; 3) High adaptability, with the introduced translator operator to map pair embeddings to the node embeddings, PairE can be effectively used in both the link-based and the node-based graph analysis. Experiment results show that PairE consistently outperforms the state of baselines in all four downstream tasks, especially with significant edges in the link-prediction and multi-label node classification tasks.