EGNN: Exploring Structure-Level Neighborhoods in Graphs With Varying Homophily Ratios

Abstract

Graph neural networks (GNNs) have garnered significant attention for their competitive performance on graph-structured data. However, many existing methods are commonly constrained by the homophily assumption, making them overly reliant on the uniform neighbor propagation, which limits their ability to generalize to heterophilous graphs. Although some approaches extend aggregation to multi-hop neighbors, adapting neighborhood sizes on a per-node basis remains a significant challenge. In view of this, we propose an Evolutionary Graph Neural Network (EGNN) with adaptive structure-level aggregation and label smoothing, offering a novel solution to the aforementioned drawback. The core innovation of EGNN lies in assigning each node a personalized neighborhood structure utilizing behavior-level crossover and mutation. Specifically, we first adaptively search for the optimal structure-level neighborhoods for nodes within the solution space, leveraging the exploratory capabilities of evolutionary computation. This approach enhances the exchange of information between the target node and surrounding nodes, achieving a smooth vector representation. Subsequently, we adopt the optimal structure obtained through evolutionary search to perform label smoothing, further boosting the robustness of the framework. We conduct experiments on nine real-world networks with different homophily ratios, where outstanding performance demonstrates that the ability of EGNN can match or surpass SOTA baselines.