graph embedding analysis

This study investigates the instability of node embeddings in graph neural networks caused by training randomness, with a focus on how embedding dimensionality affects both stability and downstream task performance. The authors systematically evaluate five representative methods—ASNE, DGI, GraphSAGE, node2vec, and VERSE—across multiple datasets and dimensionalities. They reveal, for the first time, a non-monotonic relationship between embedding dimension and stability: while some methods (e.g., node2vec and ASNE) become more stable as dimensionality increases, others show no such trend. Crucially, peak stability often does not coincide with optimal task performance. These findings underscore the need for a balanced trade-off among stability, predictive performance, and computational efficiency, offering both theoretical insights and practical guidance for selecting embedding dimensions.

本文通过传播随机特征，无需复杂模型设计和训练，利用随机游走和匿名游走诱导的隐式层次结构生成图嵌入，有效捕捉节点邻近性和结构角色。

To address manifold curvature distortion induced by multi-layer implicit structures in high-dimensional multiplex graph embedding, this work is the first to model node distributions from a Riemannian geometric perspective—revealing that nodes naturally reside on highly curved non-Euclidean manifolds, with distortion intensifying as dimensionality increases. We propose a synergistic framework integrating hierarchical dimensional embedding and a hyperbolic graph neural network (Hyperbolic GNN): the former progressively learns compact, expressive latent dimensions, while the latter explicitly encodes negative curvature in hyperbolic space; both components are jointly optimized for Gaussian curvature-aware embedding. Evaluated on real-world high-dimensional multiplex graphs, our method significantly reduces geometric distortion and consistently outperforms state-of-the-art approaches across downstream tasks—including link prediction and node classification.

Existing node embedding methods suffer from two key limitations: vector addition lacks network semantic interpretability, and relationships among multi-scale (coarse-grained) embeddings remain ill-defined. This paper proposes a multi-scale node embedding framework that unifies the resolution of both issues for the first time. Leveraging a hierarchical coarse-graining mechanism grounded in renormalization theory, and imposing vector-sum constraints alongside low-dimensional reconstruction optimization in the embedding space, our method ensures that the embedding of any coarse-grained block node is strictly equal to the statistical mean of its constituent node embeddings. This guarantees statistical consistency across resolutions. Evaluated on international trade and input-output networks, the framework achieves high-fidelity structural reconstruction—e.g., accurate triangle counting—and supports arbitrary-scale graph generation. It significantly enhances interpretability and practicality in multi-scale graph modeling and synthesis.

This study investigates the effectiveness of graph and text embeddings in reconstructing the hierarchical disciplinary structure of physics, as defined by the Physics and Astronomy Classification Scheme (PACS). Leveraging the APS citation network (graph structure) and full-text content (textual data), we systematically compare node2vec, residual2vec, Doc2Vec, and BERT embeddings. Hierarchical clustering and tree-matching evaluation quantify how well each embedding recovers the ground-truth PACS hierarchy. To our knowledge, this is the first quantitative, domain-specific comparison of graph versus text embeddings for modeling an authoritative scientific classification system. Results show that graph embeddings—particularly residual2vec—substantially outperform text embeddings and conventional methods: top-1 tree-matching accuracy improves by 12.7%, indicating that citation relationships better reflect disciplinary boundaries than lexical semantics. Moreover, neural embeddings consistently surpass non-neural baselines, and graph-based approaches demonstrate superior robustness across evaluation metrics.

该论文针对相似性评估和模型透明度问题，提出一种结合流形学习与基于排名的可解释图嵌入的新框架，生成上下文感知的、低维且高效的表示。

This work addresses the lack of a unified and reproducible evaluation framework in existing hyperbolic graph representation learning methods, which hinders systematic comparison and practical deployment. We propose an open-source, standardized framework that integrates multiple state-of-the-art hyperbolic graph embedding algorithms, offering consistent training pipelines, visualization tools, and evaluation interfaces for downstream tasks such as link prediction and node classification. The framework seamlessly interoperates with widely used network analysis libraries. Comprehensive experiments on real-world networks not only validate the predictive performance of various methods but also uncover their respective strengths and limitations, thereby providing empirical guidance for method selection. This significantly enhances reproducibility and practical efficiency in hyperbolic graph learning research.

This work addresses the challenge of efficient lossless compression for large-scale real-world graph data by proposing a novel algorithm that leverages geometric representations of graph structure through direct application of modern hyperbolic space embeddings. By capitalizing on the intrinsic hyperbolic geometry inherent in complex networks, the method achieves substantially improved compression efficiency while preserving lossless reconstruction. Experimental evaluation across diverse real-world graph datasets demonstrates that the proposed approach outperforms the current state-of-the-art methods by up to 42% in compression ratio, thereby validating the efficacy and superiority of hyperbolic embeddings for graph compression tasks.

This work proposes a universal graph foundation model designed to encode arbitrary graphs into vector representations that preserve both structural and semantic information, thereby supporting graph-level tasks and enabling cross-domain generalization. The approach integrates a multi-graph feature alignment mechanism with a density-maximized mean alignment algorithm to enhance consistency of node embeddings across datasets. Discriminative graph representations are learned through graph neural networks combined with contrastive learning, while a novel pooling-free, multi-layer reference distribution module efficiently aggregates node-level information into graph-level representations. Theoretical analysis provides an upper bound on the generalization error. Extensive experiments demonstrate that the model significantly outperforms strong baselines on few-shot graph classification and clustering tasks, validating its superior representational capacity and generalization ability.

Traditional vector retrieval relies on pairwise geometric similarity, which struggles to simultaneously achieve semantic alignment and consistency with the head-tail distribution of data. This work proposes a Graph Wiring framework combined with Spectral Indexing, modeling the embedding space as an energy network induced by the topology of feature column vectors. By integrating geometric similarity with spectral structural information and introducing τ-modulation for adaptive retrieval, the method leverages spectral graph theory, energy-based modeling, and epiplexity analysis. Implemented using the open-source arrowspace library, it significantly outperforms purely geometric retrieval across multiple benchmarks and industrial applications, effectively enhancing both semantic alignment and distributional consistency to meet the demands of modern RAG systems for flexible and efficient retrieval.