TL;DR
This work proposes a principled augmentation strategy based on degree-preserving edge rewiring, inspired by the configuration model, that generates alternative graph views that maintain node degrees while randomizing the graph topology.
Graph representation learning has largely focused on designing increasingly sophisticated models to transform graph topology into vector representations, or embeddings. However, the extent to which embedding quality depends on model learning, rather than on the underlying topological transformations, remains unclear. Here, we show that informative embeddings can be derived without complicated model design and gradient-based training. Propagating random features through implicit hierarchical structures induced by random walks and anonymous walks yields embeddings that capture node proximity and structural role, respectively. These two training-free embeddings preserve complementary aspects of graph organization and perform competitively with classic and recent methods across various node-, edge-, and graph-level tasks. They often require substantially less computation, resulting in a favorable quality-efficiency trade-off. Combining the two types of embeddings further improves inference quality of some tasks compared with using either embedding type alone. Our results suggest that informative graph embeddings can arise from carefully chosen topological transformations before any learning operation is applied.
Experiments show that incorporating NC-LID-based regularization consistently improves reconstruction performance over the baseline without structural regularization and the method using hub-aware regularization, which highlights NC-LID as a useful structural signal for enhancing distance-based graph autoencoders in dynamic settings.
This work introduces a novel method Schreier-Coset Graph Rewiring, a group-theoretic rewiring method that augments the input graph with a Schreier-Coset graph derived from a special linear group, creating a low-resistance bypass for long-range communication.
A Hypergraph-enhanced graph contrastive learning framework for Graph Out-Of-Distribution detection (termed HGOOD), which constructs two branches to hierarchically mine graph compact semantics in a comprehensive manner and introduces a cross-branch prototype contrast that aligns the captured graph patterns with their cross-branch clustering prototypes to enhance the semantic manifold of the in-distribution graph.
Similarity-guided Structural Matching Learning for Graph Dataset Condensation (SSGDC) is proposed, which efficiently reduces repository size while maintaining both task performance and structural information.
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