link prediction

Existing link prediction (LP) evaluation lacks systematic control over critical factors—including network type, geodesic distance distribution, class imbalance, and metric sensitivity—limiting the generalizability of empirical conclusions. Method: We propose the first hypothesis-driven, multidimensional controllable evaluation framework, employing controlled-variable experiments, multi-network benchmarking, and rigorous statistical testing to systematically identify and quantify six previously overlooked sources of evaluation bias. Contribution/Results: We reveal the substantial impact of geodesic distance distribution and class imbalance on the performance of mainstream LP methods; demonstrate the inadequacy of conventional metrics (e.g., AUC) in early-retrieval scenarios; and introduce a hierarchical evaluation paradigm alongside application-oriented best-practice guidelines. This work establishes a methodological foundation for fair, reproducible comparison and reliable deployment of LP methods.

Current evaluation of mathematical research relies heavily on manual peer review, lacking interpretable, quantitative methodologies. Method: We construct a three-layer citation graph—linking theorems to papers and papers to mathematical domains—and propose the first dynamic influence assessment framework for mathematical knowledge graphs, integrating PageRank-style algorithms with graph neural networks. Our approach enables fine-grained, time-aware scoring of theorems, papers, and subfields, while explicitly modeling evolutionary pathways of cross-domain influence. Contribution/Results: Experiments produce annual influence ranking maps covering major branches of mathematics, enabling quantification of cross-domain impact and traceable, attribution-aware analysis. This work introduces the first data-driven, structurally grounded, and interpretable quantitative tool for scholarly evaluation in mathematics.

This work systematically investigates the theoretical foundations and computational feasibility of graph similarity measures. Addressing mainstream graph distance definitions—including graph edit distance, spectral distance, and subgraph matching—the paper establishes, for the first time, a unified mathematical characterization of their essential properties and applicability boundaries, thereby clarifying intrinsic connections among spectral, combinatorial, and learning-based approaches. Leveraging rigorous tools from graph edit distance theory, Laplacian spectral analysis, subgraph isomorphism testing, and computational complexity theory, the study precisely delineates the computability boundaries of these distances, identifies the fundamental sources of their NP-hardness, and characterizes conditions under which efficient approximation is feasible. The results provide a principled theoretical framework for selecting appropriate graph similarity algorithms and prescribe scalable approximate computation strategies for large-scale graphs—bridging deep theoretical insight with practical algorithmic guidance.

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.

To address the lack of systematic evaluation criteria for backbone extraction in weighted complex networks, this paper introduces the first standardized evaluation framework specifically designed for weighted networks, alongside the open-source Python toolkit *netbone*. The framework uniformly integrates mainstream algorithms—including SDisparity, Global-Threshold, and Noise-Reduction—enabling plug-and-play method integration. It defines a comprehensive set of 12 multidimensional metrics covering structural fidelity, information retention, and other key properties, thereby supporting reproducible and comparable empirical analysis. Experimental validation on the US air transportation network demonstrates that *netbone* significantly improves both the efficiency and interpretability of backbone method selection. Since its release, *netbone* has become the de facto standard in the field, widely adopted for algorithm validation and benchmarking studies.

This study addresses the fragmentation and difficulty of systematically integrating domain knowledge in Physical Internet (PI) research by introducing GraphRAG technology into PI literature reviews for the first time. Leveraging GPT-4o mini and Neo4j, a domain-specific knowledge graph is constructed to enable the structured interconnection of complex bibliographic information and graph retrieval-augmented generation. This approach systematically delineates the evolutionary trajectory of PI literature while precisely identifying emerging research trends and critical gaps. Consequently, it significantly enhances the accessibility of domain knowledge and deepens the understanding of current research dynamics, thereby providing a robust foundation for future innovation.

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.

This study addresses a central challenge in modeling the evolution of complex networks: selecting the optimal network generative model from a set of candidates. It presents the first systematic review and classification of existing model selection methods, organizing them into four categories based on their underlying principles. The work provides a comprehensive analysis of each approach’s theoretical foundations, technical implementation, and available software tools. By offering a panoramic overview of the current landscape, this research not only clarifies key methodological distinctions but also identifies promising directions for future work. Ultimately, it lays the groundwork for developing a unified and efficient framework for network model selection, serving as an essential reference for researchers in the field.

This study addresses the limitations of traditional handcrafted approaches to link prediction in complex networks, which often suffer from suboptimal performance and poor generalization. To overcome these challenges, the authors propose a novel code evolution framework that integrates large language models with a genetic algorithm to automatically search for and optimize the program structure of link prediction algorithms. The method innovatively explores adaptive combinations of node and link features. Extensive experiments on 580 real-world networks demonstrate that the proposed approach achieves an average AUC of 0.915, substantially outperforming existing hand-designed methods (AUC = 0.783). Furthermore, it exhibits high computational efficiency and scales effectively to networks with millions of links.

This work addresses the underexplored impact of the implicit two-stage sampling mechanism—used in partitioning training, validation, and test sets—on link prediction performance. The authors propose a β-sampling strategy, wherein the probability of a link being sampled is proportional to the β-th power of the product of its endpoint node degrees, enabling systematic investigation of how second-stage sampling affects predictive accuracy. Large-scale experiments across 45 real-world networks demonstrate that prediction performance improves significantly when missing links are more likely to connect high-degree nodes. The findings reveal that the optimal sampling strategy is neither uniform random nor degree-preserving, underscoring the critical role of structural characteristics inherent in missing links for effective link prediction.