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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.