  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.
