Diversity Curves for Graph Representation Learning

Unsupervised graph clustering is a fundamental technique for uncovering underlying semantic patterns in large-scale networks. Although Graph Contrastive Learning has demonstrated promising performance, existing methods often suffer from the "structural isolation" issue during mini-batch training, making it challenging to capture cohesive community structures that characterize the global topological distribution. To address these challenges, we propose SCISE, a Scalable unsupervised graph Clustering framework that preserves structural Integrity by synergizing community-aware sampling with constrained Structural Entropy. Specifically, we first introduce the Structural Entropy Community Constraint operator (SECC), which optimizes structural information within a constrained solution space to mitigate community fragmentation and enhance partition cohesion. Second, to prevent global information loss during batch training, we design a Community-Aware Sampling Expansion (CSampE) mechanism that incorporates the community context of target nodes into sampling batches, effectively breaking structural barriers and preserving topological integrity. Finally, we devise a Structural Contrastive Learning (StructCL) module that refines edge weights based on intra-batch structural similarity, guiding the encoder to learn representations in a higher-order structural space. Extensive experiments on six mainstream benchmark datasets demonstrate that SCISE significantly outperforms state-of-the-art algorithms, with ablation studies and robustness analyses further validating its effectiveness and reliability for real-world large-scale graphs.

Graph self-supervised learning typically relies on large-scale unlabeled datasets, heavily inflating computational costs. However, empirical evidence suggests that these datasets contain substantial redundancy-our analysis reveals that uniformly subsampling 50% of graphs retains over 96% of downstream performance. To exploit this redundancy, we introduce GraphSculptor for pre-training coreset construction. Unlike methods dependent on additional training-time signals or limited solely to topological statistics, GraphSculptor provides a label-free solution that constructs coresets via two complementary perspectives: intrinsic structure and contextual semantics. Concretely, structural diversity is quantified using intrinsic graph statistics, yielding a structural feature vector for each graph, while semantic diversity is captured by utilizing a pre-trained language model to encode descriptions generated via graph-to-text. GraphSculptor integrates these signals into a unified metric space and performs cluster-aware selection to preserve joint structural-semantic diversity. We further derive a theoretical bound on the loss gap between coreset and full-data pre-training, offering theoretical motivation for our selection formulation. Extensive experiments demonstrate that GraphSculptor effectively sculpts the dataset: a 10% coreset achieves 99.6% of full-data performance while reducing pre-training time by nearly 90%, offering a scalable solution for data-efficient graph pre-training.

Representation learning is central to graph machine learning, powering tasks such as link prediction and node classification. However, most graph embeddings are hard to interpret, offering limited insight into how learned features relate to graph structure. Many networks naturally admit a role-mixture view, where nodes are best described as mixtures over latent archetypal factors. Motivated by this structure, we propose a compositional graph embedding framework grounded in Aitchison geometry, the canonical geometry for comparing mixtures. Nodes are represented as simplex-valued compositions and embedded via isometric log-ratio (ILR) coordinates, which preserve Aitchison distances while enabling unconstrained optimization in Euclidean space. This yields intrinsically interpretable embeddings whose geometry reflects relative trade-offs among archetypes and supports coherent behavior under component restriction; we consider both fixed and learnable ILR bases. Across node classification and link prediction, our method achieves competitive performance with strong baselines while providing explainability by construction rather than post-hoc. Finally, subcompositional coherence enables principled component restriction: removing and renormalizing subsets preserves a well-defined geometry, which we exploit via subcompositional dimensionality removal to probe how archetype groups influence representations and predictions.