Learning the Graph and the Embedding Together: Classifier-Independent Rewiring for Heterophilic Node Classification

Graph neural networks lose much of their advantage on heterophilic graphs, where connected nodes often carry different labels. Graph rewiring is a popular remedy, but rewiring methods are usually evaluated with a single classifier, which makes it hard to tell whether the gains come from the new topology or from that particular pairing. We propose an affinity-guided rewiring method that estimates the graph and the node representation together. It alternates, in the spirit of expectation maximisation, between training a lightweight graph neural network on the current graph and re-weighting candidate edges under a modularity objective with a pseudo-label homophily term. Candidate edges come from a compact pool scored by a contrastively learned node similarity and a neighbourhood-distribution affinity. The method returns two classifier-independent outputs: a rewired graph and a node embedding learned on it. Across six heterophilic benchmarks and five downstream classifiers, it improves accuracy over the original graph with normalised features in 23 of 30 classifier-dataset combinations, with a mean gain of 5.8 points, and reduces the accuracy spread between classifiers about fourfold. A controlled ablation shows that the two outputs are each useful and play complementary roles: the embedding contributes most of the accuracy gain, while the rewired graph makes different classifiers agree. A fully unsupervised variant, which uses no labels during rewiring, retains most of the improvement. The rewired graphs are also more homophilic and improve label propagation and community detection.