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A survey on the recent random walk-based methods for embedding graphs

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Abstract

Machine learning, deep learning and NLP methods on graphs are vastly present in different fields and have important roles in various domains from self-driving cars to friend recommendations on social media platforms. However, to apply these methods on graphs, the data usually need to be in an acceptable size and format. In fact, graphs normally have high dimensions, and therefore we need to transform them to a low-dimensional vector space. Embedding is a low-dimensional space into which one can translate high-dimensional vectors in a way that intrinsic features of the input data are preserved. In this review, we first explain the importance of graphs and the embedding methods applied to them. Next, we will review some of the random walk-based embedding methods as well as their strengths and weaknesses that have been developed recently. Later, we will address research directions for future research.

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References

  1. Gavagsaz E, Souri A (2025) Triangle-induced and degree-wise sampling over large graphs in social networks. J Supercomput 81(1):1–29

    Article  MATH  Google Scholar 

  2. Mohsin SF, Jami SI, Wasi S, Siddiqui MS (2024) An automated information extraction system from the knowledge graph based annual financial reports. PeerJ Comput Sci 10:2004

    Article  Google Scholar 

  3. Rajvanshi A, Sikka K, Lin X, Lee B, Chiu H-P, Velasquez A (2024) Saynav: grounding large language models for dynamic planning to navigation in new environments. In: Proceedings of the International Conference on Automated Planning and Scheduling, vol 34, pp 464–474

  4. Steiner T, Verborgh R, Troncy R, Gabarro J, Walle R (2012) Adding realtime coverage to the google knowledge graph. In: 11th International Semantic Web Conference (ISWC 2012), vol 914. Citeseer, pp 65–68

  5. Mao X, Sun H, Zhu X, Li J (2022) Financial fraud detection using the related-party transaction knowledge graph. Proc Comput Sci 199:733–740

    Article  MATH  Google Scholar 

  6. Soleymani S, Gravel N, Huang L-C, Yeung W, Bozorgi E, Bendzunas NG, Kochut KJ, Kannan N (2023) Dark kinase annotation, mining, and visualization using the protein kinase ontology. PeerJ 11:16087

    Article  Google Scholar 

  7. Krinkin K, Kulikov I, Vodyaho A, Zhukova N (2020) Architecture of a telecommunications network monitoring system based on a knowledge graph. In: 2020 26th Conference of Open Innovations Association (FRUCT). IEEE, pp 231–239

  8. Buchgeher G, Gabauer D, Martinez-Gil J, Ehrlinger L (2021) Knowledge graphs in manufacturing and production: a systematic literature review. IEEE Access 9:55537–55554

    Article  MATH  Google Scholar 

  9. Tezerjani MD, Carrillo D, Qu D, Dhakal S, Mirzaeinia A, Yang Q (2024) Real-time motion planning for autonomous vehicles in dynamic environments. arXiv preprint arXiv:2406.02916

  10. Ahmed U, Srivastava G, Djenouri Y, Lin JC-W (2022) Knowledge graph based trajectory outlier detection in sustainable smart cities. Sustain Cities Soc 78:103580

    Article  MATH  Google Scholar 

  11. Liu Y, Ding J, Fu Y, Li Y (2023) Urbankg: an urban knowledge graph system. ACM Trans Intell Syst Technol 14(4):1–25

    Article  MATH  Google Scholar 

  12. Luo B, Wilson RC, Hancock ER (2003) Spectral embedding of graphs. Pattern Recogn 36(10):2213–2230

    Article  MATH  Google Scholar 

  13. Cai H, Zheng VW, Chang KC-C (2018) A comprehensive survey of graph embedding: problems, techniques, and applications. IEEE Trans Knowl Data Eng 30(9):1616–1637

    Article  MATH  Google Scholar 

  14. Koren Y, Bell R, Volinsky C (2009) Matrix factorization techniques for recommender systems. Computer 42(8):30–37. https://doi.org/10.1109/MC.2009.263

    Article  MATH  Google Scholar 

  15. Ruthotto L, Haber E (2021) An introduction to deep generative modeling. CoRR arXiv:2103.05180

  16. Manchanda S, Gupta S, Ranu S, Bedathur SJ (2024) Generative modeling of labeled graphs under data scarcity. In: Learning on Graphs Conference. PMLR, pp 32:1–32:18

  17. Xian X, Wu T, Ma X, Qiao S, Shao Y, Wang C, Yuan L, Wu Y (2022) Generative graph neural networks for link prediction. https://arxiv.org/abs/2301.00169

  18. Hou Z, Liu X, Cen Y, Dong Y, Yang H, Wang C, Tang J (2022) GraphMAE: self-supervised masked graph autoencoders. arXiv:2205.10803

  19. Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by back-propagating errors. Nature 323:533–536

    Article  MATH  Google Scholar 

  20. Shervashidze N, Schweitzer P, Leeuwen EJ, Mehlhorn K, Borgwardt KM (2011) Weisfeiler–Lehman graph kernels. J Mach Learn Res 12(77):2539–2561

    MathSciNet  MATH  Google Scholar 

  21. Nikolentzos G, Siglidis G, Vazirgiannis M (2021) Graph kernels: a survey. J Artif Intell Res 72:943–1027

    Article  MathSciNet  MATH  Google Scholar 

  22. Perez RC, Da Veiga S, Garnier J, Staber B (2024) Gaussian process regression with sliced wasserstein Weisfeiler–Lehman graph kernels. In: International Conference on Artificial Intelligence and Statistics. PMLR, pp 1297–1305

  23. Song Y, Luo H, Pi S, Gui C, Sun B (2020) Graph kernel based clustering algorithm in MANETs. IEEE Access 8:107650–107660. https://doi.org/10.1109/ACCESS.2020.3001137

    Article  Google Scholar 

  24. Perozzi B, Al-Rfou R, Skiena S (2014) Deepwalk: online learning of social representations. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp 701–710

  25. Sipser M (1996) Introduction to the theory of computation. ACM SIGACT News 27(1):27–29

    Article  MATH  Google Scholar 

  26. Li J-C, Zhao D-L, Ge B-F, Yang K-W, Chen Y-W (2018) A link prediction method for heterogeneous networks based on BP neural network. Phys A 495:1–17

    Article  MATH  Google Scholar 

  27. Tang J, Qu M, Wang M, Zhang M, Yan J, Mei Q (2015) Line: large-scale information network embedding. In: Proceedings of the 24th International Conference on World Wide Web, pp 1067–1077

  28. Wang X, Bo D, Shi C, Fan S, Ye Y, Philip SY (2022) A survey on heterogeneous graph embedding: methods, techniques, applications and sources. IEEE Trans Big Data 9(2):415–436

    Article  MATH  Google Scholar 

  29. Tang L, Liu H (2009) Relational learning via latent social dimensions. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp 817–826

  30. Tang L, Liu H (2011) Leveraging social media networks for classification. Data Min Knowl Discov 23:447–478

    Article  MathSciNet  MATH  Google Scholar 

  31. Church KW (2017) Word2vec. Nat Lang Eng 23(1):155–162

    Article  Google Scholar 

  32. Tenenbaum JB, Silva VD, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319–2323

    Article  MATH  Google Scholar 

  33. Lin Y-Y, Liu T-L, Chen H-T (2005) Semantic manifold learning for image retrieval. In: Proceedings of the 13th Annual ACM International Conference on Multimedia, pp 249–258

  34. He X, Niyogi P (2003) Locality preserving projections. In: Advances in Neural Information Processing Systems, vol 16

  35. Gong C, Tao D, Yang J, Fu K (2014) Signed Laplacian embedding for supervised dimension reduction. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 28

  36. Sun L, Ji S, Ye J (2008) Hypergraph spectral learning for multi-label classification. In: Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp 668–676

  37. Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500):2323–2326

    Article  MATH  Google Scholar 

  38. Cao S, Lu W, Xu Q (2015) Grarep: learning graph representations with global structural information. In: Proceedings of the 24th ACM International on Conference on Information and Knowledge Management, pp 891–900

  39. Nie F, Zhu W, Li X (2017) Unsupervised large graph embedding. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 31

  40. Pang T, Nie F, Han J (2017) Flexible orthogonal neighborhood preserving embedding. In: IJCAI, vol 361, pp 2592–2598

  41. Shaw B, Jebara T (2009) Structure preserving embedding. In: Proceedings of the 26th Annual International Conference on Machine Learning, pp 937–944

  42. Lim D, Maron H, Law MT, Lorraine J, Lucas J (2023) Graph metanetworks for processing diverse neural architectures. arXiv preprint arXiv:2312.04501

  43. Li M, Liu JY, Sigal L, Liao R (2022) Graphpnas: learning distribution of good neural architectures via deep graph generative models. arXiv preprint arXiv:2211.15155

  44. Yun S, Jeong M, Kim R, Kang J, Kim HJ (2019) Graph transformer networks. In: Advances in Neural Information Processing Systems, vol 32

  45. Veličković P, Cucurull G, Casanova A, Romero A, Lio P, Bengio Y (2017) Graph attention networks. arXiv preprint arXiv:1710.10903

  46. Hamilton W, Ying Z, Leskovec J (2017) Inductive representation learning on large graphs. In: Advances in Neural Information Processing Systems, vol 30

  47. Zhang C, Song D, Huang C, Swami A, Chawla NV (2019) Heterogeneous graph neural network. In: Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp 793–803

  48. Xu K, Hu W, Leskovec J, Jegelka S (2018) How powerful are graph neural networks? arXiv preprint arXiv:1810.00826

  49. Wang D, Cui P, Zhu W (2016) Structural deep network embedding. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp 1225–1234

  50. Taniguchi S, Iwasawa Y, Kumagai W, Matsuo Y (2022) Langevin autoencoders for learning deep latent variable models. Adv Neural Inf Process Syst 35:13277–13289

    MATH  Google Scholar 

  51. Chang S (2022) Deep clustering with fusion autoencoder. arXiv preprint arXiv:2201.04727

  52. Katuwal R, Suganthan PN (2019) Stacked autoencoder based deep random vector functional link neural network for classification. Appl Soft Comput 85:105854

    Article  MATH  Google Scholar 

  53. Kipf TN, Welling M (2016) Variational graph auto-encoders. arXiv preprint arXiv:1611.07308

  54. Man T, Shen H, Liu S, Jin X, Cheng X (2016) Predict anchor links across social networks via an embedding approach. In: IJCAI, vol 16, pp 1823–1829

  55. Zhou C, Liu Y, Liu X, Liu Z, Gao J (2017) Scalable graph embedding for asymmetric proximity. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 31

  56. Xiong C, Power R, Callan J (2017) Explicit semantic ranking for academic search via knowledge graph embedding. In: Proceedings of the 26th International Conference on World Wide Web, pp 1271–1279

  57. Feng J, Huang M, Yang Y, Zhu X (2016) Gake: graph aware knowledge embedding. In: Proceedings of COLING 2016, the 26th International Conference on Computational Linguistics: Technical Papers, pp 641–651

  58. Ren X, He W, Qu M, Voss CR, Ji H, Han J (2016) Label noise reduction in entity typing by heterogeneous partial-label embedding. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp 1825–1834

  59. Cheng M, Xu H (2024) A Quasi-Wasserstein loss for learning graph neural networks. In: Proceedings of the ACM on Web Conference 2024, pp 815–826

  60. Gui H, Liu J, Tao F, Jiang M, Norick B, Han J (2016) Large-scale embedding learning in heterogeneous event data. In: 2016 IEEE 16th International Conference on Data Mining (ICDM). IEEE, pp 907–912

  61. Liu L, Cheung WK, Li X, Liao L (2016) Aligning users across social networks using network embedding. In: IJCAI, vol 16, pp 1774–1780

  62. Zhang C, Zhang K, Yuan Q, Peng H, Zheng Y, Hanratty T, Wang S, Han J (2017) Regions, periods, activities: uncovering urban dynamics via cross-modal representation learning. In: Proceedings of the 26th International Conference on World Wide Web, pp 361–370

  63. Bordes A, Usunier N, Garcia-Duran A, Weston J, Yakhnenko O (2013) Translating embeddings for modeling multi-relational data. In: Advances in Neural Information Processing Systems, vol 26

  64. Wang Z, Zhang J, Feng J, Chen Z (2014) Knowledge graph embedding by translating on hyperplanes. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 28

  65. Lin Y, Liu Z, Sun M, Liu Y, Zhu X (2015) Learning entity and relation embeddings for knowledge graph completion. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 29

  66. Ji G, He S, Xu L, Liu K, Zhao J (2015) Knowledge graph embedding via dynamic mapping matrix. In: Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing, vol 1. Long Papers, pp 687–696

  67. Socher R, Chen D, Manning CD, Ng A (2013) Reasoning with neural tensor networks for knowledge base completion. In: Advances in Neural Information Processing Systems, vol 26

  68. Yang B, Yih W-t, He X, Gao J, Deng L (2014) Embedding entities and relations for learning and inference in knowledge bases. arXiv preprint arXiv:1412.6575

  69. Trouillon T, Welbl J, Riedel S, Gaussier É, Bouchard G (2016) Complex embeddings for simple link prediction. In: International Conference on Machine Learning. PMLR, pp 2071–2080

  70. Sun Z, Deng Z-H, Nie J-Y, Tang J (2019) Rotate: knowledge graph embedding by relational rotation in complex space. arXiv preprint arXiv:1902.10197

  71. Pržulj N (2007) Biological network comparison using graphlet degree distribution. Bioinformatics 23(2):177–183

    Article  Google Scholar 

  72. Tong H, Faloutsos C (2006) Center-piece subgraphs: problem definition and fast solutions. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp 404–413

  73. Narayanan A, Chandramohan M, Venkatesan R, Chen L, Liu Y, Jaiswal S (2017) graph2vec: learning distributed representations of graphs. arXiv preprint arXiv:1707.05005

  74. Cao S, Lu W, Xu Q (2016) Deep neural networks for learning graph representations. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 30

  75. Shervashidze N, Vishwanathan S, Petri T, Mehlhorn K, Borgwardt K (2009) Efficient graphlet kernels for large graph comparison. In: Artificial Intelligence and Statistics. PMLR, pp 488–495

  76. Ying Z, You J, Morris C, Ren X, Hamilton W, Leskovec J (2018) Hierarchical graph representation learning with differentiable pooling. In: Advances in Neural Information Processing Systems, vol 31

  77. Alsentzer E, Finlayson S, Li M, Zitnik M (2020) Subgraph neural networks. Adv Neural Inf Process Syst 33:8017–8029

    MATH  Google Scholar 

  78. Shervashidze N, Schweitzer P, Van Leeuwen EJ, Mehlhorn K, Borgwardt KM (2011) Weisfeiler–Lehman graph kernels. J Mach Learn Res 12(9):2539

    MathSciNet  MATH  Google Scholar 

  79. Wang H, Wang J, Wang J, Zhao M, Zhang W, Zhang F, Xie X, Guo M (2018) Graphgan: graph representation learning with generative adversarial nets. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 32

  80. Qiu J, Dong Y, Ma H, Li J, Wang K, Tang J (2018) Network embedding as matrix factorization: unifying deepwalk, line, pte, and node2vec. In: Proceedings of the Eleventh ACM International Conference on Web Search and Data Mining, pp 459–467

  81. You J, Ying R, Ren X, Hamilton W, Leskovec J (2018) Graphrnn: generating realistic graphs with deep auto-regressive models. In: International Conference on Machine Learning. PMLR, pp 5708–5717

  82. She L, Chai J (2017) Interactive learning of grounded verb semantics towards human-robot communication. In: Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics, vol 1. Long Papers, pp 1634–1644

  83. Jin W, Ma Y, Liu X, Tang X, Wang S, Tang J (2020) Graph structure learning for robust graph neural networks. In: Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp 66–74

  84. Cherian A, Sullivan A (2019) Sem-gan: semantically-consistent image-to-image translation. In: 2019 IEEE Winter Conference on Applications of Computer Vision (WACV). IEEE, pp 1797–1806

  85. Fraccaro M, Sønderby SK, Paquet U, Winther O (2016) Sequential neural models with stochastic layers. In: Advances in Neural Information Processing Systems, vol 29

  86. Brin S, Page L (1998) The anatomy of a large-scale hypertextual web search engine. Comput Netw ISDN Syst 30(1–7):107–117

    Article  MATH  Google Scholar 

  87. Grover A, Leskovec J (2016) node2vec: scalable feature learning for networks. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp 855–864

  88. Fortunato S (2010) Community detection in graphs. Phys Rep 486(3–5):75–174

    Article  MathSciNet  MATH  Google Scholar 

  89. Yang J, Leskovec J (2014) Overlapping communities explain core-periphery organization of networks. Proc IEEE 102(12):1892–1902

    Article  MATH  Google Scholar 

  90. Henderson K, Gallagher B, Eliassi-Rad T, Tong H, Basu S, Akoglu L, Koutra D, Faloutsos C, Li L (2012) Rolx: structural role extraction & mining in large graphs. In: Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp 1231–1239

  91. Tang J, Qu M, Mei Q (2015) Pte: predictive text embedding through large-scale heterogeneous text networks. In: Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp 1165–1174

  92. Le Q, Mikolov T (2014) Distributed representations of sentences and documents. In: International Conference on Machine Learning. PMLR, pp 1188–1196

  93. Dong Y, Chawla NV, Swami A (2017) metapath2vec: scalable representation learning for heterogeneous networks. In: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp 135–144

  94. Sun Y, Han J, Yan X, Yu PS, Wu T (2011) Pathsim: meta path-based top-k similarity search in heterogeneous information networks. Proc VLDB Endow 4(11):992–1003

    Article  MATH  Google Scholar 

  95. Keshavarzi A, Kannan N, Kochut K (2021) Regpattern2vec: link prediction in knowledge graphs. In: 2021 IEEE International IOT, Electronics and Mechatronics Conference (IEMTRONICS). IEEE, pp 1–7

  96. Rabin MO, Scott D (1959) Finite automata and their decision problems. IBM J Res Dev 3(2):114–125. https://doi.org/10.1147/rd.32.0114

    Article  MathSciNet  MATH  Google Scholar 

  97. Friedl JE (2006) Mastering regular expressions. O’Reilly Media Inc., Sebastopol

    MATH  Google Scholar 

  98. Lee D, Yannakakis M (1996) Principles and methods of testing finite state machines-a survey. Proc IEEE 84(8):1090–1123

    Article  MATH  Google Scholar 

  99. Bozorgi E, Soleimani S, Alqaiidi SK, Arabnia HR, Kochut K (2024) Subgraph2vec: a random walk-based algorithm for embedding knowledge graphs. arXiv preprint arXiv:2405.02240

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E.B Corresponding author; wrote the main manuscript and created the tables and figures, reviewed the paper. S.A wrote two of the methods and conclusion, reviewed the paper. A.S wrote two of the methods and conclusion, reviewed the paper. H.A reviewed the paper. K.K reviewed the paper.

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Correspondence to Elika Bozorgi.

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Bozorgi, E., Alqaaidi, S.K., Shams, A. et al. A survey on the recent random walk-based methods for embedding graphs. J Supercomput 81, 619 (2025). https://doi.org/10.1007/s11227-025-07019-x

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