Graph Convolutional Networks (GCNs) have shown remarkable performance in processing graph-structured data by leveraging neighborhood information for node representation learning. While most GCN models assume strong homophily within the networks they handle, some models can also handle heterophilous graphs. However, the selection of neighbors participating in the node representation learning process can significantly impact these models' performance. To address this, we investigate the influence of neighbor selection on GCN performance, focusing on the analysis of edge distribution through theoretical and empirical approaches. Based on our findings, we propose a novel GCN model called Graph Convolution Network with Improved Edge Distribution (GCN-IED). GCN-IED incorporates both direct edges, which rely on local neighborhood similarity, and hidden edges, obtained by aggregating information from multi-hop neighbors. We extensively evaluate GCN-IED on diverse graph benchmark datasets and observe its superior performance compared to other state-of-the-art GCN methods on heterophilous datasets. Our GCN-IED model, which considers the role of neighbors and optimizes edge distribution, provides valuable insights for enhancing graph representation learning and achieving superior performance on heterophilous graphs.
Keywords: Edge distribution; Graph Neural Networks; Heterophilous graphs; Neighbor selection; Node representation learning.
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