Graph Neural Networks (GNNs) have been gaining more attention due to their excellent performance in modeling various graph-structured data. However, most of the current GNNs only consider fixed-neighbor discrete message-passing, disregarding the importance of the local structure of different nodes and the implicit information between nodes for smoothing features. Previous approaches either focus on adaptive selection for aggregation structures or treat discrete graph convolution as a continuous diffusion process, but none of them comprehensively considered the above issues, significantly limiting the model's performance. To this end, we present a novel approach called Flexible Diffusion Convolution (Flexi-DC), which exploits the neighborhood information of nodes to set a particular continuous diffusion for each node to smooth features. Specifically, Flexi-DC first extracts the local structure knowledge based on the degrees of nodes in the graph data and then injects it into the diffusion convolution module to smooth features. Additionally, we utilize the extracted knowledge to smooth labels. Flexi-DC is an efficient framework that can significantly improve the performance of most GNN architectures. Experimental results demonstrate that Flexi-DC outperforms their vanilla implementations by an average accuracy of 13.24% (GCN), 16.37% (JKNet), and 11.98% (ARMA) on nine graph datasets with different homophily ratios.

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 apersonalizedneighborhood structure utilizingbehavior-levelcrossover 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.