Graph neural networks (GNNs) have become increasingly popular in modeling graph-structured data due to their ability to learn node representations by aggregating local structure information. However, it is widely acknowledged that the test graph structure may differ from the training graph structure, resulting in a structure shift. In this paper, we experimentally find that the performance of GNNs drops significantly when the structure shift happens, suggesting that the learned models may be biased towards specific structure patterns. To address this challenge, we propose the Cluster Information Transfer (\textbf{CIT}) mechanism, which can learn invariant representations for GNNs, thereby improving their generalization ability to various and unknown test graphs with structure shift. The CIT mechanism achieves this by combining different cluster information with the nodes while preserving their cluster-independent information. By generating nodes across different clusters, the mechanism significantly enhances the diversity of the nodes and helps GNNs learn the invariant representations. We provide a theoretical analysis of the CIT mechanism, showing that the impact of changing clusters during structure shift can be mitigated after transfer. Additionally, the proposed mechanism is a plug-in that can be easily used to improve existing GNNs. We comprehensively evaluate our proposed method on three typical structure shift scenarios, demonstrating its effectiveness in enhancing GNNs' performance.

Unsupervised Graph Domain Adaptation (UGDA) involves the transfer of knowledge from a label-rich source graph to an unlabeled target graph under domain discrepancies. Despite the proliferation of methods designed for this emerging task, the lack of standard experimental settings and fair performance comparisons makes it challenging to understand which and when models perform well across different scenarios.

In all, structure shift is unique to graph data due to the non-IID nature caused by node interconnections. In this section, we provide additional details about the datasets used in our benchmark. The labels categorize airports by activity levels, measured in terms of flights or passenger numbers. Each dataset's nodes symbolize papers, while edges reflect their citation relationships. Specifically, "ACMv9" (A) includes papers from ACM spanning 2000 to 2010, "Citationv1" (C) consists of DBLP collected between 2004 and 2008.

In this paper, we experimentally find that the performance of GNNs drops significantly when the structure shift happens, suggesting that the learned models may be biased towards specific structure patterns.

Graph-based learning has achieved remarkable success in domains ranging from recommendation to fraud detection and particle physics by effectively capturing underlying interaction patterns. However, it often struggles to generalize when distribution shifts occur, particularly those involving changes in network connectivity or interaction patterns. Existing approaches designed to mitigate such shifts typically require retraining with full access to source data, rendering them infeasible under strict computational or privacy constraints. To address this limitation, we propose a test-time structural alignment (TSA) algorithm for Graph Test-Time Adaptation (GTTA), a novel method that aligns graph structures during inference without revisiting the source domain. Built upon a theoretically grounded treatment of graph data distribution shifts, TSA integrates three key strategies: an uncertainty-aware neighborhood weighting that accommodates structure shifts, an adaptive balancing of self-node and neighborhood-aggregated representations driven by node representations' signal-to-noise ratio, and a decision boundary refinement that corrects remaining label and feature shifts. Extensive experiments on synthetic and real-world datasets demonstrate that TSA can consistently outperform both non-graph TTA methods and state-of-the-art GTTA baselines.

Graph neural networks (GNNs) have become increasingly popular in modeling graph-structured data due to their ability to learn node representations by aggregating local structure information. However, it is widely acknowledged that the test graph structure may differ from the training graph structure, resulting in a structure shift. In this paper, we experimentally find that the performance of GNNs drops significantly when the structure shift happens, suggesting that the learned models may be biased towards specific structure patterns. To address this challenge, we propose the Cluster Information Transfer (\textbf{CIT}) mechanism, which can learn invariant representations for GNNs, thereby improving their generalization ability to various and unknown test graphs with structure shift. The CIT mechanism achieves this by combining different cluster information with the nodes while preserving their cluster-independent information.

Powerful as they are, graph neural networks (GNNs) are known to be vulnerable to distribution shifts. Recently, test-time adaptation (TTA) has attracted attention due to its ability to adapt a pre-trained model to a target domain without re-accessing the source domain. However, existing TTA algorithms are primarily designed for attribute shifts in vision tasks, where samples are independent. These methods perform poorly on graph data that experience structure shifts, where node connectivity differs between source and target graphs. We attribute this performance gap to the distinct impact of node attribute shifts versus graph structure shifts: the latter significantly degrades the quality of node representations and blurs the boundaries between different node categories. To address structure shifts in graphs, we propose AdaRC, an innovative framework designed for effective and efficient adaptation to structure shifts by adjusting the hop-aggregation parameters in GNNs. To enhance the representation quality, we design a prediction-informed clustering loss to encourage the formation of distinct clusters for different node categories. Additionally, AdaRC seamlessly integrates with existing TTA algorithms, allowing it to handle attribute shifts effectively while improving overall performance under combined structure and attribute shifts. We validate the effectiveness of AdaRC on both synthetic and real-world datasets, demonstrating its robustness across various combinations of structure and attribute shifts.