  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.
