# Local Clustering Graph Neural Networks

Graph Neural Networks (GNNs), which benefit various real-world problems and applications, have emerged as a powerful technique for learning graph representations. The depth of a GNN model, denoted by $K$, restricts the receptive field of a node to its $K$-hop neighbors and plays a subtle role in the performance of GNNs. Recent works demonstrate how different choices of $K$ produce a trade-off between increasing representation capacity and avoiding over-smoothing. We establish a theoretical connection between GNNs and local clustering, showing that short random-walks in GNNs have a high probability to be stuck at a local cluster. Based on the theoretical analysis, we propose Local Clustering Graph Neural Networks (LCGNN), a GNN learning paradigm that utilizes local clustering to efficiently search for small but compact subgraphs for GNN training and inference. Compared to full-batch GNNs, sampling-based GNNs and graph partition-based GNNs, LCGNN performs comparably or even better, achieving state-of-the-art results on four Open Graph Benchmark (OGB) datasets. The locality of LCGNN allows it to scale to graphs with 100M nodes and 1B edges on a single GPU.

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