Graph domain adaptation (GDA) aims to transfer knowledge from a labeled source graph to an unlabeled target graph under distribution shifts. However, existing methods are largely feature-centric and overlook structural discrepancies, which become particularly detrimental under significant topology shifts. Such discrepancies alter both geometric relationships and spectral properties, leading to unreliable transfer of graph neural networks (GNNs). To address this limitation, we propose Dual-Aligned Structural Basis Distillation (DSBD) for GDA, a novel framework that explicitly models and adapts cross-domain structural variation. DSBD constructs a differentiable structural basis by synthesizing continuous probabilistic prototype graphs, enabling gradient-based optimization over graph topology. The basis is learned under source-domain supervision to preserve semantic discriminability, while being explicitly aligned to the target domain through a dual-alignment objective. Specifically, geometric consistency is enforced via permutation-invariant topological moment matching, and spectral consistency is achieved through Dirichlet energy calibration, jointly capturing structural characteristics across domains. Furthermore, we introduce a decoupled inference paradigm that mitigates source-specific structural bias by training a new GNN on the distilled structural basis. Extensive experiments on graph and image benchmarks demonstrate that DSBD consistently outperforms state-of-the-art methods.

翻译：图域自适应旨在通过分布迁移将知识从有标签源图迁移到无标签目标图中。然而，现有方法大多以特征为中心而忽略结构差异，在拓扑结构显著变化时这种缺陷尤为突出。此类差异会同时改变几何关系与谱特性，导致图神经网络迁移的不可靠性。为解决该限制，我们提出面向图域自适应的双对齐结构基蒸馏框架，该框架显式建模并适配跨域结构变异。通过合成连续概率原型图构建可微结构基，DSBD实现了基于梯度的图拓扑优化。该结构基在源域监督下学习以保持语义可判别性，同时通过双对齐目标与目标域显式对齐：具体地，通过置换不变拓扑矩匹配实现几何一致性，通过狄利克雷能量校准实现谱一致性，从而联合捕获跨域结构特征。此外，我们引入解耦推理范式，通过在蒸馏结构基上训练新图神经网络来消除源特异性结构偏差。在图和图像基准数据集上的大量实验表明，DSBD始终优于现有最优方法。