We propose a novel positional encoding for learning graph on Transformer architecture. Existing approaches either linearize a graph to encode absolute position in the sequence of nodes, or encode relative position with another node using bias terms. The former loses preciseness of relative position from linearization, while the latter loses a tight integration of node-edge and node-topology interaction. To overcome the weakness of the previous approaches, our method encodes a graph without linearization and considers both node-topology and node-edge interaction. We name our method Graph Relative Positional Encoding dedicated to graph representation learning. Experiments conducted on various graph datasets show that the proposed method outperforms previous approaches significantly. Our code is publicly available at https://github.com/lenscloth/GRPE.
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