{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T11:04:46Z","timestamp":1779793486707,"version":"3.53.1"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.12271362"],"award-info":[{"award-number":["No.12271362"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Intell"],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1007\/s10489-026-07261-7","type":"journal-article","created":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T07:50:13Z","timestamp":1778485813000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["SADGE: a status-aware graph embedding method for link prediction in directed graphs"],"prefix":"10.1007","volume":"56","author":[{"given":"Wenhua","family":"Yu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaofei","family":"Qin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luchao","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changxiang","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenlin","family":"Yu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,11]]},"reference":[{"issue":"7","key":"7261_CR1","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1002\/asi.20591","volume":"58","author":"D Liben-Nowell","year":"2007","unstructured":"Liben-Nowell D, Kleinberg J (2007) The link-prediction problem for social networks. J Am Soc Inform Sci Technol 58(7):1019\u20131031. https:\/\/doi.org\/10.1002\/asi.20591","journal-title":"J Am Soc Inform Sci Technol"},{"key":"7261_CR2","unstructured":"Bordes, A., Usunier, N., Garcia-Dur\u00e1n, A., Weston, J., Yakhnenko, O.: Translating embeddings for modeling multi-relational data. In: Advances in Neural Information Processing Systems, vol. 26, pp. 2787\u20132795 (2013)"},{"issue":"4","key":"7261_CR3","doi-asserted-by":"publisher","first-page":"1241","DOI":"10.1093\/bioinformatics\/btz718","volume":"36","author":"X Yue","year":"2020","unstructured":"Yue X, Wang Z, Huang J, Parthasarathy S, Moosavi P (2020) Graph embedding on biomedical networks: methods, applications and evaluations. Bioinformatics 36(4):1241\u20131251. https:\/\/doi.org\/10.1093\/bioinformatics\/btz718","journal-title":"Bioinformatics"},{"key":"7261_CR4","doi-asserted-by":"publisher","unstructured":"Cavallaro, L., Calderoni, F., Catanese, S., Meo, P.D., Ficara, A., Fiumara, G.: Robust link prediction in criminal networks: a case study of the sicilian mafia. Expert Systems with Applications. 161, 113666 (2020) https:\/\/doi.org\/10.1016\/j.eswa.2020.113666","DOI":"10.1016\/j.eswa.2020.113666"},{"key":"7261_CR5","doi-asserted-by":"publisher","unstructured":"Singh, N., Singh, H.: A comprehensive review of similarity based link prediction methods for complex networks including computational biology. J Adv Zool. 44(S6), 1281\u20131294 (2023) https:\/\/doi.org\/10.17762\/jaz.v44iS6.2433","DOI":"10.17762\/jaz.v44iS6.2433"},{"issue":"1","key":"7261_CR6","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1007\/s41019-024-00267-6","volume":"10","author":"Z Zhou","year":"2025","unstructured":"Zhou Z, Wan G, Du B (2025) Common neighbor completion with information entropy for link prediction in social networks. Data Sci Eng 10(1):40\u201353. https:\/\/doi.org\/10.1007\/s41019-024-00267-6","journal-title":"Data Sci Eng"},{"issue":"1","key":"7261_CR7","doi-asserted-by":"publisher","first-page":"6586622","DOI":"10.1049\/2024\/6586622","volume":"2024","author":"X Li","year":"2024","unstructured":"Li X, Tang H, Wang H, Miao G, Cheng M (2024) An improved jaccard coefficient-based clustering approach with application to diagnosis and rul estimation. IET Signal Process 2024(1):6586622. https:\/\/doi.org\/10.1049\/2024\/6586622","journal-title":"IET Signal Process"},{"key":"7261_CR8","doi-asserted-by":"publisher","unstructured":"Ravichandran, M., Srinivasan, S., Mathivanan, S.K., Rajadurai, H., Malar, B.A., Mallik, S., Qin, H.: Adamic\u2013adar similarity indexed wald boost data classification for diabetic disease diagnosis with big data. Syst Soft Comput. 6, 200175 (2024) https:\/\/doi.org\/10.1016\/j.sasc.2024.200175","DOI":"10.1016\/j.sasc.2024.200175"},{"key":"7261_CR9","doi-asserted-by":"publisher","unstructured":"Vidza, M.-S., Budka, M., Chai, W.K., Thrush, M., Alves, M.T.: Expanding the katz index for link prediction: A case study on a live fish movement network. arXiv. (2024) https:\/\/doi.org\/10.48550\/arXiv.2404.12871","DOI":"10.48550\/arXiv.2404.12871"},{"key":"7261_CR10","doi-asserted-by":"publisher","unstructured":"Jeh, G., Widom, J.: Simrank: A measure of structural-context similarity. In: Proceedings of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 538\u2013543 (2002). https:\/\/doi.org\/10.1145\/775047.775126","DOI":"10.1145\/775047.775126"},{"key":"7261_CR11","doi-asserted-by":"publisher","unstructured":"Tong, H., Faloutsos, C., Pan, J.-Y.: Fast random walk with restart and its applications. In: Proceedings of the 6th IEEE International Conference on Data Mining (ICDM), pp. 613\u2013622 (2006). https:\/\/doi.org\/10.1109\/ICDM.2006.70","DOI":"10.1109\/ICDM.2006.70"},{"key":"7261_CR12","doi-asserted-by":"publisher","unstructured":"Kapoor, P., Kaushal, S., Kumar, H., Kanwar, K.: A survey on feature extraction and learning techniques for link prediction in homogeneous and heterogeneous complex networks. Artif Intell Rev. 57, 348 (2024) https:\/\/doi.org\/10.1007\/s10462-024-10998-7","DOI":"10.1007\/s10462-024-10998-7"},{"key":"7261_CR13","doi-asserted-by":"publisher","unstructured":"Sun, G., Tian, H., Liu, Y., Wang, S., Jia, L., Zhang, Y.: Link prediction algorithm based on connected coupling degree of nodes and preference degree of topology connectivity between predicted nodes. Alexandria Eng J. 129, 649\u2013657 (2025) https:\/\/doi.org\/10.1016\/j.aej.2025.06.045","DOI":"10.1016\/j.aej.2025.06.045"},{"key":"7261_CR14","doi-asserted-by":"publisher","unstructured":"Grover, A., Leskovec, J.: node2vec: Scalable feature learning for networks. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 855\u2013864 (2016). https:\/\/doi.org\/10.1145\/2939672.2939754","DOI":"10.1145\/2939672.2939754"},{"key":"7261_CR15","doi-asserted-by":"publisher","unstructured":"Perozzi, A., Al-Rfou, R., Skiena, S.: Deepwalk: Online learning of social representations. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 701\u2013710 (2014). https:\/\/doi.org\/10.1145\/2623330.2623732","DOI":"10.1145\/2623330.2623732"},{"issue":"21","key":"7261_CR16","doi-asserted-by":"publisher","first-page":"25816","DOI":"10.1007\/s10489-023-04887-9","volume":"53","author":"X Lin","year":"2023","unstructured":"Lin X, Chen X, Zheng Z (2023) Deep manifold matrix factorization autoencoder using global connectivity for link prediction. Appl Intell 53(21):25816\u201325835. https:\/\/doi.org\/10.1007\/s10489-023-04887-9","journal-title":"Appl Intell"},{"key":"7261_CR17","doi-asserted-by":"publisher","unstructured":"Ou, M., Cui, P., Pei, J., Zhang, Z., Zhu, W.: Asymmetric transitivity preserving graph embedding. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1105\u20131114 (2016). https:\/\/doi.org\/10.1145\/2939672.2939751","DOI":"10.1145\/2939672.2939751"},{"key":"7261_CR18","doi-asserted-by":"publisher","unstructured":"Zhou, C., Liu, Y., Liu, X., Liu, Z., Gao, J.: Scalable graph embedding for asymmetric proximity. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 31, pp. 2942\u20132948 (2017). https:\/\/doi.org\/10.1609\/aaai.v31i1.10878","DOI":"10.1609\/aaai.v31i1.10878"},{"key":"7261_CR19","doi-asserted-by":"publisher","unstructured":"Wang, D., Cui, P., Zhu, W.: Structural deep network embedding. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1225\u20131234 (2016). https:\/\/doi.org\/10.1145\/2939672.2939753","DOI":"10.1145\/2939672.2939753"},{"key":"7261_CR20","unstructured":"Tong, Z., Liang, Y., Sun, C., Li, X., Rosenblum, D.S., Lim, A.: Digraph inception convolutional networks. In: Advances in Neural Information Processing Systems, vol. 33, pp. 17907\u201317918 (2020)"},{"key":"7261_CR21","unstructured":"Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. In: Proceedings of the International Conference on Learning Representations (ICLR) (2017)"},{"key":"7261_CR22","unstructured":"Veli\u010dkovi\u0107, P., Cucurull, G., Casanova, A., Romero, A., Li\u00f2, P., Bengio, Y.: Graph attention networks. In: Proceedings of the International Conference on Learning Representations (ICLR) (2018)"},{"key":"7261_CR23","doi-asserted-by":"publisher","unstructured":"Yao, Y., He, Y., Huang, Z., Xu, Z., Yang, F., Tang, J., Gao, K.: Deep non-negative matrix factorization with edge generator for link prediction in complex networks. Applied Intelligence. 1, 592\u2013613 (2024) https:\/\/doi.org\/10.1007\/s10489-023-05211-1","DOI":"10.1007\/s10489-023-05211-1"},{"key":"7261_CR24","doi-asserted-by":"publisher","unstructured":"Zhang, H., Kou, G., Peng, Y., al.: Role-aware random walk for network embedding. Information Sciences. 652, 119765 (2024) https:\/\/doi.org\/10.1016\/j.ins.2023.119765","DOI":"10.1016\/j.ins.2023.119765"},{"issue":"3","key":"7261_CR25","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1093\/bib\/bbac151","volume":"23","author":"Y-Y Feng","year":"2022","unstructured":"Feng Y-Y, Yu H, Feng Y-H, Shi J-Y (2022) Directed graph attention networks for predicting asymmetric drug-drug interactions. Brief Bioinform 23(3):151. https:\/\/doi.org\/10.1093\/bib\/bbac151","journal-title":"Brief Bioinform"},{"key":"7261_CR26","doi-asserted-by":"publisher","unstructured":"Zhu, S., Li, J., Peng, H., Wang, S., He, L.: Adversarial directed graph embedding. In: Proceedings of the Thirty-Fifth AAAI Conference on Artificial Intelligence, vol. 35, pp. 4741\u20134748 (2021). https:\/\/doi.org\/10.1609\/AAAI.V35I5.16605","DOI":"10.1609\/AAAI.V35I5.16605"},{"key":"7261_CR27","doi-asserted-by":"publisher","unstructured":"Si, J., Xie, C., Zhou, J., Yu, S., Chen, L., Xuan, Q., Miao, C.: Inductive subgraph embedding for link prediction. Mobile Networks and Applications. 30, 312\u2013323 (2025) https:\/\/doi.org\/10.1007\/s11036-024-02339-3","DOI":"10.1007\/s11036-024-02339-3"},{"key":"7261_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-025-06394-5","author":"Y Yao","year":"2025","unstructured":"Yao Y, Guo P, Mao Z, Ti Z, He Y, Nian F, Zhang R, Ma N (2025) Multi-scale contrastive learning via aggregated subgraph for link prediction. Appl Intell. https:\/\/doi.org\/10.1007\/s10489-025-06394-5","journal-title":"Appl Intell"},{"key":"7261_CR29","doi-asserted-by":"publisher","unstructured":"Wang, S., Wang, B., Shen, Z., Deng, B., Kang, Z.: Multi-domain graph foundation models: Robust knowledge transfer via topology alignment. arXiv preprint arXiv:2502.02017. (2025) https:\/\/doi.org\/10.48550\/arXiv.2502.02017","DOI":"10.48550\/arXiv.2502.02017"},{"issue":"6","key":"7261_CR30","doi-asserted-by":"publisher","first-page":"10283","DOI":"10.1109\/TNNLS.2025.3540063","volume":"36","author":"Z Shen","year":"2025","unstructured":"Shen Z, Kang Z (2025) When heterophily meets heterogeneous graphs: Latent graphs guided unsupervised representation learning. IEEE Transactions on Neural Networks and Learning Systems 36(6):10283\u201310296. https:\/\/doi.org\/10.1109\/TNNLS.2025.3540063","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"7261_CR31","doi-asserted-by":"publisher","unstructured":"Li, B., Pan, E., Kang, Z.: Pc-conv: Unifying homophily and heterophily with two-fold filtering. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 38, pp. 13437\u201313445 (2024). https:\/\/doi.org\/10.1609\/aaai.v38i12.29246","DOI":"10.1609\/aaai.v38i12.29246"},{"key":"7261_CR32","doi-asserted-by":"publisher","unstructured":"Leskovec, J., Huttenlocher, D., Kleinberg, J.: Signed networks in social media. In: Proceedings of the 28th SIGCHI Conference on Human Factors in Computing Systems, pp. 1361\u20131370 (2010). https:\/\/doi.org\/10.1145\/1753326.1753532","DOI":"10.1145\/1753326.1753532"},{"key":"7261_CR33","doi-asserted-by":"publisher","unstructured":"Huang, J., Shen, H., Hou, L., Cheng, X.: Signed graph attention networks. In: International Conference on Artificial Neural Networks, pp. 566\u2013577 (2019). https:\/\/doi.org\/10.1007\/978-3-030-30493-5_53","DOI":"10.1007\/978-3-030-30493-5_53"},{"issue":"4","key":"7261_CR34","doi-asserted-by":"publisher","first-page":"4580","DOI":"10.1109\/TNNLS.2022.3151046","volume":"35","author":"W Lin","year":"2024","unstructured":"Lin W, Li B (2024) Status-aware signed heterogeneous network embedding with graph neural networks. IEEE Transactions on Neural Networks and Learning Systems 35(4):4580\u20134592. https:\/\/doi.org\/10.1109\/TNNLS.2022.3151046","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"7261_CR35","unstructured":"Zhang, M., Chen, Y.: Link prediction based on graph neural networks. In: Advances in Neural Information Processing Systems, vol. 31, pp. 5171\u20135181 (2018)"},{"issue":"2","key":"7261_CR36","doi-asserted-by":"publisher","first-page":"2024","DOI":"10.1111\/tgis.70042","volume":"29","author":"Q Qiu","year":"2025","unstructured":"Qiu Q, Lu S, Ma K, Zhu Y, Huang Z, Xie Z, Tao L, Wang S (2025) Negative sample generation for geographic knowledge graph embedding via joint entity semantic similarity and clustering. Trans GIS 29(2):2024\u20132040. https:\/\/doi.org\/10.1111\/tgis.70042","journal-title":"Trans GIS"},{"key":"7261_CR37","doi-asserted-by":"crossref","unstructured":"Ahrabian, K., Feizi, A., Salehi, Y., Hamilton, W.L., Bose, A.J.: Structure aware negative sampling in knowledge graphs. In: Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing, pp. 6093\u20136101 (2020)","DOI":"10.18653\/v1\/2020.emnlp-main.492"},{"key":"7261_CR38","doi-asserted-by":"publisher","unstructured":"Cai, L., Wang, W.Y.: Kbgan: Adversarial learning for knowledge graph embeddings. In: Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers), pp. 1470\u20131480. Association for Computational Linguistics, New Orleans, Louisiana (2018). https:\/\/doi.org\/10.18653\/v1\/N18-1133","DOI":"10.18653\/v1\/N18-1133"},{"key":"7261_CR39","doi-asserted-by":"publisher","unstructured":"Wang, H., Wang, J., Wang, J., Zhao, M., Zhang, W., Zhang, F., Xie, X., Guo, M.: Graphgan: Graph representation learning with generative adversarial nets. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32, pp. 2508\u20132515 (2018). https:\/\/doi.org\/10.1609\/aaai.v32i1.11872","DOI":"10.1609\/aaai.v32i1.11872"},{"key":"7261_CR40","doi-asserted-by":"publisher","unstructured":"\u0160ubelj, L., Bajec, M.: Model of complex networks based on citation dynamics. In: Proceedings of the 22nd International Conference on World Wide Web Companion, pp. 527\u2013530 (2013). https:\/\/doi.org\/10.1145\/2487788.2487987","DOI":"10.1145\/2487788.2487987"},{"key":"7261_CR41","doi-asserted-by":"publisher","unstructured":"Giles, C.L., Bollacker, K.D., Lawrence, S.: Citeseer: An automatic citation indexing system. In: Proceedings of the Third ACM Conference on Digital Libraries, pp. 89\u201398 (1998). https:\/\/doi.org\/10.1145\/276675.276685","DOI":"10.1145\/276675.276685"},{"key":"7261_CR42","doi-asserted-by":"publisher","unstructured":"Leskovec, J., Huttenlocher, D., Kleinberg, J.: Predicting positive and negative links in online social networks. In: Proceedings of the 19th International Conference on World Wide Web, pp. 641\u2013650 (2010). https:\/\/doi.org\/10.1145\/1772690.1772756","DOI":"10.1145\/1772690.1772756"},{"key":"7261_CR43","doi-asserted-by":"publisher","unstructured":"\u0160ubelj, L., Bajec, M.: Software systems through complex networks science: Review, analysis and applications. In: Proceedings of the First International Workshop on Software Mining, pp. 9\u201316 (2012). https:\/\/doi.org\/10.1145\/2384416.2384418","DOI":"10.1145\/2384416.2384418"},{"issue":"6","key":"7261_CR44","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1088\/1367-2630\/9\/6\/186","volume":"9","author":"G Palla","year":"2007","unstructured":"Palla G, Farkas IJ, Pollner P, Der\u00e9nyi I, Vicsek T (2007) Directed network modules. New J Phys 9(6):186. https:\/\/doi.org\/10.1088\/1367-2630\/9\/6\/186","journal-title":"New J Phys"},{"key":"7261_CR45","doi-asserted-by":"publisher","unstructured":"Khosla, M., Leonhardt, J., Nejdl, W., Anand, A.: Node representation learning for directed graphs. In: Joint European Conference on Machine Learning and Knowledge Discovery in Databases (ECML PKDD 2019). Lecture Notes in Computer Science, vol. 11906, pp. 395\u2013411 (2019). https:\/\/doi.org\/10.1007\/978-3-030-46150-8_24","DOI":"10.1007\/978-3-030-46150-8_24"},{"key":"7261_CR46","doi-asserted-by":"publisher","unstructured":"Sun, J., Bandyopadhyay, B., Bashizade, A., Liang, J., Sadayappan, P., Parthasarathy, S.: Atp: Directed graph embedding with asymmetric transitivity preservation. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33, pp. 265\u2013272 (2019). https:\/\/doi.org\/10.1609\/aaai.v33i01.3301265","DOI":"10.1609\/aaai.v33i01.3301265"}],"container-title":["Applied Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-026-07261-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10489-026-07261-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-026-07261-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T10:43:56Z","timestamp":1779792236000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10489-026-07261-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":46,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2026,5]]}},"alternative-id":["7261"],"URL":"https:\/\/doi.org\/10.1007\/s10489-026-07261-7","relation":{},"ISSN":["0924-669X","1573-7497"],"issn-type":[{"value":"0924-669X","type":"print"},{"value":"1573-7497","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5]]},"assertion":[{"value":"17 October 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 April 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 May 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no competing interests or conflicts of interest related to the content of this manuscript. Financial or personal relationships have not influenced the work presented in this document.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"252"}}