Simplifying Graph Convolutional Networks with Redundancy-Free Neighbors

--In recent years, Graph Convolutional Networks (GCNs) have gained popularity for their exceptional ability to process graph-structured data. Existing GCN-based approaches typically employ a shallow model architecture due to the over-smoothing phenomenon. Current approaches to mitigating over-smoothing primarily involve adding supplementary components to GCN architectures, such as residual connections and random edge-dropping strategies. However, these improvements toward deep GCNs have achieved only limited success. In this work, we analyze the intrinsic message passing mechanism of GCNs and identify a critical issue: messages originating from high-order neighbors must traverse through low-order neighbors to reach the target node. This repeated reliance on low-order neighbors leads to redundant information aggregation, a phenomenon we term over-aggregation. Our analysis demonstrates that over-aggregation not only introduces significant redundancy but also serves as the fundamental cause of over-smoothing in GCNs. Motivated by this discovery, we introduce a novel framework named redundancy-free graph convolutional network, where the neighbors of the graph are hierarchically organized so that the multi-order neighbor sets of a specific node do not intersect. This organizational structure enables high-order neighbors to directly propagate their messages to the target node, thereby effectively avoiding duplicate aggregation. The layer number of the proposed method adapts according to the graph structure, eliminating the need for manual adjustments to capture node information at specific distances. The experimental results on sixteen real-world datasets demonstrate the superior performance of the proposed method on node-and graph-level tasks.