# Node Classification

In node classification on heterophilic graphs, the step before propagation has stayed fixed by degree normalisation, which acts spectrally as a valley whose zero is set by the normalisation rather than by the data, exactly where dense graphs' eigenvalues accumulate. SpecValley learns the valley's centre, sharpness and flank gains per graph, then feeds an ordinary ChebNet spectral filter. Across six heterophilic benchmarks it matches or exceeds the best published result on four, sits within the confidence interval of the best on Tolokers, and trails on Actor; crossing five aggregators with four filters attributes the gain to aggregation rather than to the downstream filter.

In node classification on heterophilic graphs, the step before propagation has stayed fixed by degree normalisation, which acts spectrally as a valley whose zero is set by the normalisation rather than by the data, exactly where dense graphs' eigenvalues accumulate. SpecValley learns the valley's centre, sharpness and flank gains per graph, then feeds an ordinary ChebNet spectral filter. Across six heterophilic benchmarks it matches or exceeds the best published result on four, sits within the confidence interval of the best on Tolokers, and trails on Actor; crossing five aggregators with four filters attributes the gain to aggregation rather than to the downstream filter.

Attention aggregation on heterogeneous graphs has long treated node types as static labels, and metapath aggregation can overlook the semantic contribution of intermediate nodes. TAHAN instead collects neighbors along metapath prefixes, merges them across metapaths and levels by node type, then fuses them with within-type attention followed by across-type attention. On DBLP and IMDB node classification its mean Macro-F1 and Micro-F1 exceed the listed baselines, with both IMDB gains significant after Holm correction; on ACM it falls below SeHGNN.

Attention aggregation on heterogeneous graphs has long treated node types as static labels, and metapath aggregation can overlook the semantic contribution of intermediate nodes. TAHAN instead collects neighbors along metapath prefixes, merges them across metapaths and levels by node type, then fuses them with within-type attention followed by across-type attention. On DBLP and IMDB node classification its mean Macro-F1 and Micro-F1 exceed the listed baselines, with both IMDB gains significant after Holm correction; on ACM it falls below SeHGNN.

When sensor failures spread along graph edges and value propagation loses its footing, PEMix conditions the distribution of missing node features on global structural representations, raising TADPOLE macro-F1 curve area from 0.7469 to 0.8243.

When sensor failures spread along graph edges and value propagation loses its footing, PEMix conditions the distribution of missing node features on global structural representations, raising TADPOLE macro-F1 curve area from 0.7469 to 0.8243.

EDiS separates one-time structural extraction from per-epoch graph composition: it decomposes the graph once into cacheable edge-disjoint subgraphs using feature-based scores and successive maximum-score covering forests, then recombines them into training graphs under edge-budget constraints without re-extracting structure; across 19 homophilic, heterophilic, and large-scale node-classification benchmarks at the same edge budget against 17 baselines, EDiS-Lite achieves the highest mean benchmark score and the lowest average rank and gap-to-best.

EDiS separates one-time structural extraction from per-epoch graph composition: it decomposes the graph once into cacheable edge-disjoint subgraphs using feature-based scores and successive maximum-score covering forests, then recombines them into training graphs under edge-budget constraints without re-extracting structure; across 19 homophilic, heterophilic, and large-scale node-classification benchmarks at the same edge budget against 17 baselines, EDiS-Lite achieves the highest mean benchmark score and the lowest average rank and gap-to-best.

The authors propose G2MLP, a training-time GNN-to-MLP distillation framework that uses Ollivier–Ricci curvature to allocate supervision between prediction-level and representation-level alignment, correcting spectral underfit on sparse graphs and spectral overfit on dense graphs; the graph-free MLP student achieves the best accuracy on all six node-classification benchmarks and transfers without architectural change to Graph Transformer teachers and link prediction.

The authors propose G2MLP, a training-time GNN-to-MLP distillation framework that uses Ollivier–Ricci curvature to allocate supervision between prediction-level and representation-level alignment, correcting spectral underfit on sparse graphs and spectral overfit on dense graphs; the graph-free MLP student achieves the best accuracy on all six node-classification benchmarks and transfers without architectural change to Graph Transformer teachers and link prediction.

The work introduces a first statistical framework for epistemic uncertainty in node classification, comprising an information-growth experimental protocol and a consistency criterion, and uses projective graph data-generating processes to ensure nested graphs are coherent observations of the same process; the analysis shows that graph evidential deep learning (EDL) methods retain non-vanishing epistemic uncertainty at the population optimum and regulate epistemic and aleatoric uncertainty externally through hyperparameters, thus failing consistency, whereas graph bootstrap ensembles (GB-Ens) capture both data and procedural uncertainty through graph resampling and randomized training and exhibit epistemic uncertainty contraction beyond standard deep ensembles under the same protocol.

The work introduces a first statistical framework for epistemic uncertainty in node classification, comprising an information-growth experimental protocol and a consistency criterion, and uses projective graph data-generating processes to ensure nested graphs are coherent observations of the same process; the analysis shows that graph evidential deep learning (EDL) methods retain non-vanishing epistemic uncertainty at the population optimum and regulate epistemic and aleatoric uncertainty externally through hyperparameters, thus failing consistency, whereas graph bootstrap ensembles (GB-Ens) capture both data and procedural uncertainty through graph resampling and randomized training and exhibit epistemic uncertainty contraction beyond standard deep ensembles under the same protocol.

The work introduces BHyGNN+, a self-supervised framework for heterophilic hypergraph representation learning that contrasts augmented views of a hypergraph against its dual (with node and hyperedge roles interchanged) using cosine similarity, learning representations without ground-truth labels and without negative samples, and achieving node-classification accuracy above supervised and self-supervised baselines on eleven benchmark datasets covering heterophilic and homophilic hypergraphs plus a synthetic heterophilic dataset.

The work introduces BHyGNN+, a self-supervised framework for heterophilic hypergraph representation learning that contrasts augmented views of a hypergraph against its dual (with node and hyperedge roles interchanged) using cosine similarity, learning representations without ground-truth labels and without negative samples, and achieving node-classification accuracy above supervised and self-supervised baselines on eleven benchmark datasets covering heterophilic and homophilic hypergraphs plus a synthetic heterophilic dataset.

This work fine-tunes baseline models on 27 widely used benchmark datasets, categorizes heterophilic datasets into malignant, benign, and ambiguous groups based on whether graph-aware models underperform their coupled graph-agnostic counterparts, re-evaluates 11 SOTA heterophily-specific models, and conducts the first quantitative evaluation of 11 homophily metrics on synthetic graphs from three generation methods, finding that most SOTA models do not significantly outperform the best baselines and that classic metrics remain competitive.

This work fine-tunes baseline models on 27 widely used benchmark datasets, categorizes heterophilic datasets into malignant, benign, and ambiguous groups based on whether graph-aware models underperform their coupled graph-agnostic counterparts, re-evaluates 11 SOTA heterophily-specific models, and conducts the first quantitative evaluation of 11 homophily metrics on synthetic graphs from three generation methods, finding that most SOTA models do not significantly outperform the best baselines and that classic metrics remain competitive.