A Method for Calculating Node Similarity in Hypernetworks Based on Higher-order Distance Distribution
YANG Yusheng, GUO Lei, FAN Jingyan, HU Feng
a. College of Computer; b. The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Qinghai Normal University, Xining 810008, China
Abstract：To address the limitations of traditional hypernetwork node similarity methods in capturing higher-order topological structures, a method for calculating node similarity in hypernetworks based on Higher-order Distance Distribution (HDDNS) is proposed. The method generates higher-order distance distributions for nodes and employs Jensen-Shannon divergence to quantify inter-node similarity. To evaluate its effectiveness, this study conducted systematic experiments on three synthetic hypernetworks and five real-world hypernetworks, comparative analysis with five existing methods demonstrates that HDDNS exhibits superior performance in two key evaluation dimensions: mutual similarity metrics and propagation influence, the results indicate that HDDNS enables more precise and efficient computation of inter-node similarity.
杨煜升, 郭磊, 樊静妍, 胡枫. 基于高阶距离分布的超网络节点相似性计算方法[J]. 复杂系统与复杂性科学, 2026, 23(3): 1-10.
YANG Yusheng, GUO Lei, FAN Jingyan, HU Feng. A Method for Calculating Node Similarity in Hypernetworks Based on Higher-order Distance Distribution[J]. Complex Systems and Complexity Science, 2026, 23(3): 1-10.
[1] ANASTASIEI B, DOSPINESCU N, DOSPINESCU O. Word-of-mouth engagement in online social networks: influence of networkcentrality and density[J]. Electronics, 2023, 12(13): 2857. [2] MA A, WANG X, LI J, et al. Single-cell biological network inference using a heterogeneous graph transformer[J]. Nature Communications, 2023, 14(1): 964. [3] DUAN J, LI D, HUANG H J. Reliability of the traffic network against cascading failures with individuals acting independently or collectively[J]. Transportation Research Part C: Emerging Technologies, 2023, 147: 104017. [4] HASAN M K, HABIB A K M A, ISLAM S, et al. Smart grid communication networks for electric vehicles empowering distributed energy generation: Constraints, challenges, and recommendations[J]. Energies, 2023, 16(3): 1140. [5] 周涛, 柏文洁, 汪秉宏, 等. 复杂网络研究概述[J]. 物理, 2005(1): 31-36. ZHOU T, BAI W J, WANG B H, et al. A brief review of complex networks[J]. Physics, 2005(1): 31-36. [6] ARENAS A, DÍAZ-GUILERA A, KURTHS J, et al. Synchronization in complex networks[J]. Physics reports, 2008, 469(3): 93-153. [7] 顾亦然, 朱梓嫣. 基于LeaderRank和节点相似度的复杂网络重要节点排序算法[J]. 电子科技大学学报, 2017, 46(2): 441-448. GU Y R, ZHU Z Y. Node ranking in complex networks based on LeaderRank and modes similarity[J]. Journal of University of Electronic Science and Technology of China, 2017, 46(2): 441-448. [8] ROGHANI H, BOUYER A. A fast local balanced label diffusion algorithm for community detection in social networks[J]. IEEE Transactions on Knowledge and Data Engineering, 2022, 35(6): 5472-5484. [9] SAXENA A, FLETCHER G, PECHENIZKIY M. NodeSim: node similarity based network embedding for diverse link prediction[J]. EPJ Data Science, 2022, 11(1): 24. [10] JACCARD P. Étude comparative de la distribution florale dans une portion des Alpes et des Jura[J]. Bull Soc Vaudoise Sci Nat, 1901, 37: 547-579. [11] SALTON G. Automatic text analysis: automatic document indexing and classification methods are examined and their effectiveness is assessed[J]. Science, 1970, 168(3929): 335-343. [12] KATZ L. A new status index derived from sociometric analysis[J]. Psychometrika, 1953, 18(1): 39-43. [13] LÜ L, JIN C H, ZHOU T. Similarity index based on local paths for link prediction of complex networks[J]. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 2009, 80(4): 046122. [14] LIU W, LÜ L. Link prediction based on local random walk[J]. Europhysics Letters, 2010, 89(5): 58007. [15] 穆俊芳, 梁吉业, 郑文萍, 等. 面向复杂网络的节点相似性度量[J]. 计算机科学与探索, 2020, 14(5): 749-759. MU J F, LIANG J Y, ZHEN W P, et al. Node similarity measure for complex networks[J]. Journal of Frontiers of Computer Science and Technology, 2020, 14(5): 749-759. [16] BERGE C. Graphs and Hypergraphs[M]. Amsterdam: North-Holland Publishing Company, 1973. [17] ESTRADA E, RODRíGUEZ-VELáZQUEZ J A. Subgraph centrality and clustering in complex hyper-networks[J]. Physica A: Statistical Mechanics and Its Applications, 2006, 364: 581-94. [18] 潘旭伟, 曾雪梅, 李涛. 基于超网络的社会化标签相似性研究[J]. 运筹与管理, 2023, 32(9): 215-221. PAN X W, ZENG X M, LI T. Hypernetwork-based tags similarity measure for social tagging systems[J]. Operations Research and Management Science, 2023, 32(9): 215-221. [19] SURANA A, CHEN C, RAJAPAKSE I. Hypergraph similarity measures[J]. IEEE Transactions on Network Science and Engineering, 2022, 10(2): 658-674. [20] AKSOY S G, JOSLYN C, MARRERO C O, et al. Hypernetwork science via high-order hypergraph walks[J]. EPJ Data Science, 2020, 9(1): 16. [21] ZHANG Q, LI M, DENG Y. Measure the structure similarity of nodes in complex networks based on relative entropy[J]. Physica A: Statistical Mechanics and Its Applications, 2018, 491: 749-763. [22] 王小刚, 闫光辉, 周宁. 多阶邻接分布熵下的复杂网络节点相似性分析方法[J]. 控制理论与应用, 2021, 38(6): 739-747. WANG X G, YAN G H, ZHOU N. Analysis method of nodes similarity with multi-layer adjacency entropy[J]. Control Theory & Applications, 2021, 38(6): 739-747. [23] HU F, GUO J L, LI F X, et al. Hypernetwork models based on random hypergraphs[J]. International Journal of Modern Physics C, 2019, 30(8): 1950052. [24] BARABÁSI A L, ALBERT R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439): 509-512. [25] WATTS D J, STROGATZ S H. Collective dynamics of ‘small-world' networks[J]. Nature, 1998, 393(6684): 440-442. [26] BENSON A R, ABEBE R, SCHAUB M T, et al. Simplicial closure and higher-order link prediction[J]. Proceedings of the National Academy of Sciences, 2018, 115(48): E11221-E11230. [27] GOH K I, CUSICK M E, VALLE D, et al. The human disease network[J]. Proceedings of the National Academy of Sciences, 2007, 104(21): 8685-8690. [28] OZELLA L, PAOLOTTI D, LICHAND G, et al. Using wearable proximity sensors to characterize social contact patterns in a village of rural Malawi[J]. EPJ Data Science, 2021, 10(1): 46. [29] 吴英晗, 田阔, 李明达, 等. 利用节点传播熵识别超网络重要节点[J]. 计算机工程与应用, 2023, 59(19): 66-74. WU Y H, TIAN K, LI M D, et al. Important node recognition in hypernetwork based on node propagation entropy[J]. Computer Engineering and Applications, 2023, 59(19): 66-74.
