<p>Robust network representation learning requires Graph Neural Networks (GNNs) that remain reliable across diverse local connectivity patterns, where the standard homophily assumption can be too rigid in practice. Extensive attempts have been done to improve GNNs under different homophily level. However, they lack the ability to evolve with diverse node properties, limiting their adaptability across homophily and heterophily. In this paper, we develop an adaptive structural evolution framework (via node-wise architecture search) to automatically evolve high-performance GNNs capable of adapting to different local patterns across homophily / heterophily regimes. The key insight is to explore localized node patterns through diverse operations that evolve with node-specific demands. Firstly, we construct a search space for each node, in which the various operations are provided to meet the design requirements of nodes, regardless of homophily and heterophily, laying the foundation for models to evolve. Then, an architecture controller is developed to guide the operation selection based on the operations’ inputs and outputs, i.e., evolving operations in a self-taught manner. Extensive experiments are conducted on eleven datasets with different network sizes and homophily levels. Results show our method achieves the highest performance ranking compared with various baselines. Besides, the analyses of the searched architectures are consistent with networks’ homophily complexity metric, which demonstrate the effectiveness of evolving node-wise GNNs for exploring the diverse node properties.</p>