The Post-GCN Decade Revisited: Curvature-Stratified Evaluation of Relational Learning

Graph neural networks are widely used for transductive node classification, with accuracy typically measured on randomly drawn train/validation/test splits. Reported accuracy has been shown to shift substantially across different random splits of the same dataset, making published comparisons between architectures unreliable. The classical remedy in non-graph settings is stratified $k$-fold cross-validation, which ensures each test fold reflects the full class distribution of the dataset. We argue that class stratification alone is insufficient for graphs: nodes are not isolated but connected, and folds that differ in their distribution of local neighbourhood homophily expose the model to systematically different relational conditions that directly affect message-passing behaviour. The resulting cross-fold variation reflects the homophily composition of each split, inflating reported variance beyond what model behaviour alone would produce. To address this, we propose \hp{}, a topology-aware stratification procedure that treats node homophily as the primary stratification axis, aligning folds with respect to local relational consistency alongside the class marginal that standard stratification already controls. Stratifying on homophily alone does not guarantee class balance, so \hp{} incorporates class label as a secondary axis, preserving class representativeness as a natural consequence of the procedure. We evaluate \hp{} on a broad benchmark suite comprising 15 node-classification datasets spanning the full homophily spectrum and 7 GNN architectures. \hp{} achieves a mean stability rank of 1.49 compared to 2.31 for random $k$-fold, achieving the lowest mean stability rank on 13 of 15 datasets while preserving class balance close to class-stratified splits and substantially better than random. We argue that homophily-aware split construction merits broader adoption for GNN evaluation.

Evaluating Knowledge Graph Completion (KGC) models remains challenging because standard assessment relies on isolated rank-based metrics such as MRR, Hits$@$k, and Mean Rank, which often produce conflicting model orderings across datasets. A model that leads on MRR may trail on Hits@1, and strong performance on one dataset may not generalize to another. This fragmentation hinders comparison, enables selective reporting, and obscures real progress. We reframe KGC evaluation as a Multi-Criteria Decision-Making (MCDM) problem and present a meta-analysis of seven aggregators across five tests: consistency, cross-dataset stability, metric independence, robustness under noise, and generalizability. Each test is averaged over leave-one-model-out (LOMO) and leave-one-group-out (LOGO) removals so that reliability reflects aggregator behavior across diverse model subsets. Across tail $(h,r,?)$ and relation $(h,?,t)$ prediction, Pareto-optimal analysis identifies Z-score as the most balanced aggregator, which ranks DualE highest for tail prediction and FMS (Flow-Modulated Scoring) highest for relation prediction. A test-sensitivity analysis using the same removals shows that consistency and stability are largely removal-invariant, while generalizability and independence are the most sensitive. The framework resolves evaluation inconsistencies and offers evidence-based guidance for aggregator selection and model benchmarking in KGC.

Over the past decade, Graph Neural Networks (GNNs) have achieved great success on machine learning tasks with relational data. However, recent studies have found that heterophily can cause significant performance degradation of GNNs, especially on node-level tasks. Numerous heterophilic benchmark datasets have been put forward to validate the efficacy of heterophily-specific GNNs, and various homophily metrics have been designed to help recognize these challenging datasets. Nevertheless, there still exist multiple pitfalls that severely hinder the proper evaluation of new models and metrics: 1) lack of hyperparameter tuning; 2) insufficient evaluation on the truly challenging heterophilic datasets; 3) missing quantitative evaluation for homophily metrics on synthetic graphs. To overcome these challenges, we first train and fine-tune baseline models on $27$ most widely used benchmark datasets, and categorize them into three distinct groups: malignant, benign and ambiguous heterophilic datasets. We identify malignant and ambiguous heterophily as the truly challenging subsets of tasks, and to our best knowledge, we are the first to propose such taxonomy. Then, we re-evaluate $11$ state-of-the-arts (SOTA) GNNs, covering six popular methods, with fine-tuned hyperparameters on different groups of heterophilic datasets. Based on the model performance, we comprehensively reassess the effectiveness of different methods on heterophily. At last, we evaluate $11$ popular homophily metrics on synthetic graphs with three different graph generation approaches. To overcome the unreliability of observation-based comparison and evaluation, we conduct the first quantitative evaluation and provide detailed analysis.