Learning node representation that incorporating information from graph structure benefits wide range of tasks on graph. Majority of existing graph neural networks (GNNs) have limited power in capturing position information for a given node. The idea of positioning nodes with selected anchors has been exploit , yet mainly rely on explicit labeling of distance information. Here we propose Graph Inference Representation (GIR), an anchor based GNN  encoding path information related to  anchors for each node. Abilities to get position-aware embedding are theoretically and experimentally investigated on GIRs and its core variants. Further, the complementary characteristic of GIRs and typical GNNs embeddings are demonstrated. We show that GIRs get outperformed results on position-aware scenario, and could improve GNNs results by fuse GIRs embedding .
Learning node representations that incorporate information from graph structure benefits wide range of tasks on graph. The majority of existing graph neural networks (GNNs) have limited power in capturing position information for a given node. The idea of positioning nodes with selected anchors has been exploited , yet mainly relying on explicit labeling of distance information. Here we propose Graph Inference Representation (GIR), an anchor based GNN model encoding path information related to pre-selected anchors for each node. Abilities to get position-aware embeddings are theoretically and experimentally investigated on GIR and its core variants. Further, the complementarity between GIRs and typical GNNs is demonstrated. We show that GIRs get outperformed results in position-aware scenarios, and performances on typical GNNs could be improved by fusing GIR embeddings .
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