route network encoding

该研究提出一种在Mapper诱导的结构化表示上进行学习的框架，解决传统方法可能忽略数据多尺度结构的问题。

This paper addresses efficiency and performance bottlenecks in learning from combinatorial data—such as web pages, social networks, and molecular structures—by proposing the first unified framework for connectivity-aware modeling, integrating topological data analysis (TDA) with graph representation learning. Methodologically, it systematically employs persistent homology to capture higher-order topological features, synergizes hypergraph modeling with graph neural networks (GNNs), and incorporates combinatorial optimization to ensure algorithmic scalability. Compared to conventional approaches, the framework achieves an average 12.7% improvement in prediction accuracy across molecular property prediction, community detection, and web page ranking tasks, while reducing time complexity to near-linear. This advancement significantly enhances structural connectivity modeling capability and cross-domain generalizability.

Graph neural networks (GNNs) struggle to model featureless graphs—such as social and biological networks—while existing attribute encoders exhibit poor adaptability to scale-free topologies and heterogeneous numerical graph metrics. Method: We propose PropEnc, a universal property encoder that introduces a novel differentiable encoding paradigm based on histogram binning and inverted indexing. It generates low-dimensional, dense, order-preserving embeddings for arbitrary continuous or discrete graph metrics (e.g., degree, centrality), eliminating high-dimensional sparse representations and achieving over 90% dimensionality reduction. PropEnc initializes node representations via graph metric-driven encoding and refines them through end-to-end learnable mappings. Contribution/Results: Evaluated on multiple featureless social network graph classification benchmarks, PropEnc consistently outperforms baselines by 3–8% in accuracy, demonstrating superior efficiency, generalizability, and robustness across diverse scale-free and heterogeneous graph structures.

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.

Network data often violate metric space axioms—due to incomplete and asymmetric relationships—making conventional metric embeddings inadequate. Method: We propose the first axiomatized framework for projecting networks into *q*-metric spaces, introducing two interpretable axioms that formally characterize valid projections; we rigorously prove existence and uniqueness of such mappings. Furthermore, we design a metric-tree-based approximate nearest-neighbor search paradigm that preserves theoretical uniqueness while substantially accelerating similarity retrieval over network structures. Contribution/Results: Experiments demonstrate that our method delivers high-quality approximate solutions to combinatorial optimization tasks. It establishes a novel geometric modeling paradigm for non-metric network data, enabling both theoretically grounded representation and efficient large-scale computation.

This work addresses the high computational complexity of cut-set computation in multi-path ensemble attribute evaluation by proposing an efficient algorithm and developing a vectorized computing framework based on matrix operations, which reformulates path attribute calculations as parallelizable array operations. For the first time, this approach provides a practical implementation of the formal model for path set attributes, integrating an optimized cut-set algorithm with array-oriented programming languages to substantially improve computational efficiency. Empirical evaluations across network simulations of varying complexity demonstrate that the method yields predictable and acceptable execution times, thereby establishing a practical foundation for large-scale multi-path analysis.

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。

This study addresses how to preserve relational structure rather than individual element information under constrained representations. To this end, it constructs a unified relational compression framework that integrates graph summarization and spectral sparsification within a common interface. Furthermore, the work introduces a finite-codeword collision model, establishing precise correspondences among relational geometry, Rényi-2 occupancy, and spherical geometry. Adopting a “source–description–reconstruction” paradigm, the proposed approach synthesizes techniques from graph theory, spectral analysis, and relational distillation. Through evaluations on both graph and image tasks, the study demonstrates complementary pathways for diverse relational requirements, achieves a unified assessment of constrained representations, and provides a novel theoretical foundation for relational information compression.

This work addresses the core challenge in network automation: automatically generating deployable network topologies from natural language requirements while satisfying structural and resilience constraints. We propose a large language model (LLM)-based, constraint-driven framework that translates natural language into compliant topologies through hierarchical intent parsing and systematic validation. To facilitate evaluation, we introduce the first benchmark for this task, releasing a public dataset encompassing four real-world scenarios and characterizing common generation error patterns. Extensive experiments across multiple proprietary and open-source LLMs demonstrate the framework’s effectiveness, with performance quantified using metrics including topological correctness, node/edge F1 scores, and server-content connectivity. Our results provide actionable guidance for model selection in AI-driven network design.

This work addresses the challenge of efficiently compressing edge weights in weighted graph adjacency matrices by proposing a line-graph-based graph signal modeling approach. Specifically, edge weights are treated as graph signals defined on the line graph and are compressed through transform coding using graph filter banks, followed by quantization and entropy coding. The method innovatively introduces an edge smoothness metric that can be computed without explicitly constructing the line graph, enabling effective prediction of compression performance. Experimental results demonstrate that the proposed framework consistently outperforms existing matrix preprocessing techniques on both synthetic and real-world datasets, thereby validating its efficacy and practicality for lossy graph weight compression.