  Due to the performance degradation of graph neural networks (GNNs) under
distribution shifts, the work on out-of-distribution (OOD) generalization on
graphs has received widespread attention. A novel perspective involves
distinguishing potential confounding biases from different environments through
environmental identification, enabling the model to escape
environmentally-sensitive correlations and maintain stable performance under
distribution shifts. However, in graph data, confounding factors not only
affect the generation process of node features but also influence the complex
interaction between nodes. We observe that neglecting either aspect of them
will lead to a decrease in performance. In this paper, we propose IENE, an OOD
generalization method on graphs based on node-level environmental
identification and extrapolation techniques. It strengthens the model's ability
to extract invariance from two granularities simultaneously, leading to
improved generalization. Specifically, to identify invariance in features, we
utilize the disentangled information bottleneck framework to achieve mutual
promotion between node-level environmental estimation and invariant feature
learning. Furthermore, we extrapolate topological environments through graph
augmentation techniques to identify structural invariance. We implement the
conceptual method with specific algorithms and provide theoretical analysis and
proofs for our approach. Extensive experimental evaluations on two synthetic
and four real-world OOD datasets validate the superiority of IENE, which
outperforms existing techniques and provides a flexible framework for enhancing
the generalization of GNNs.
