{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,28]],"date-time":"2025-08-28T12:02:36Z","timestamp":1756382556585,"version":"3.37.3"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,11,8]],"date-time":"2024-11-08T00:00:00Z","timestamp":1731024000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,11,8]],"date-time":"2024-11-08T00:00:00Z","timestamp":1731024000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"published-print":{"date-parts":[[2025,1]]},"DOI":"10.1007\/s11227-024-06613-9","type":"journal-article","created":{"date-parts":[[2024,11,8]],"date-time":"2024-11-08T02:59:59Z","timestamp":1731034799000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Triangle-induced and degree-wise sampling over large graphs in social networks"],"prefix":"10.1007","volume":"81","author":[{"given":"Elaheh","family":"Gavagsaz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8314-9051","authenticated-orcid":false,"given":"Alireza","family":"Souri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,11,8]]},"reference":[{"key":"6613_CR1","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.knosys.2018.03.022","volume":"151","author":"P Goyal","year":"2018","unstructured":"Goyal P, Ferrara E (2018) Graph embedding techniques, applications, and performance: a survey. Knowl-Based Syst 151:78\u201394","journal-title":"Knowl-Based Syst"},{"key":"6613_CR2","unstructured":"Bo D, Wang X, Liu Y, Fang Y, Li Y, Shi C (2023) A survey on spectral graph neural networks. https:\/\/arxiv.org\/abs\/2302.05631"},{"key":"6613_CR3","unstructured":"Gao X, Yu J, Jiang W, Chen T, Zhang W, Yin H (2024) Graph condensation: a survey. https:\/\/arxiv.org\/abs\/2401.11720"},{"issue":"5","key":"6613_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3535101","volume":"55","author":"S Wu","year":"2022","unstructured":"Wu S, Sun F, Zhang W, Xie X, Cui B (2022) Graph neural networks in recommender systems: a survey. ACM Comput Surv 55(5):1\u201337","journal-title":"ACM Comput Surv"},{"issue":"10","key":"6613_CR5","doi-asserted-by":"publisher","first-page":"1535","DOI":"10.1038\/nprot.2009.177","volume":"4","author":"A Theocharidis","year":"2009","unstructured":"Theocharidis A, Van Dongen S, Enright AJ, Freeman TC (2009) Network visualization and analysis of gene expression data using BioLayout Express 3D. Nat Protoc 4(10):1535\u20131550","journal-title":"Nat Protoc"},{"issue":"1482","key":"6613_CR6","doi-asserted-by":"publisher","first-page":"2261","DOI":"10.1098\/rspb.2001.1800","volume":"268","author":"RFI Cancho","year":"2001","unstructured":"Cancho RFI, Sol\u00e9 RV (2001) The small world of human language. Proc R Soc Lond Ser B Biol Sci 268(1482):2261\u20132265","journal-title":"Proc R Soc Lond Ser B Biol Sci"},{"issue":"9","key":"6613_CR7","doi-asserted-by":"publisher","first-page":"4309","DOI":"10.1016\/j.eswa.2014.01.002","volume":"41","author":"D Rhouma","year":"2014","unstructured":"Rhouma D, Romdhane LB (2014) An efficient algorithm for community mining with overlap in social networks. Expert Syst Appl 41(9):4309\u20134321","journal-title":"Expert Syst Appl"},{"key":"6613_CR8","unstructured":"Guo Z et al. (2022) Graph-based molecular representation learning. https:\/\/arxiv.org\/abs\/2207.04869"},{"key":"6613_CR9","doi-asserted-by":"publisher","first-page":"8846","DOI":"10.1109\/TITS.2023.3257759","volume":"24","author":"S Rahmani","year":"2023","unstructured":"Rahmani S, Baghbani A, Bouguila N, Patterson Z (2023) Graph neural networks for intelligent transportation systems: a survey. IEEE Trans Intell Transp Syst 24:8846\u20138885","journal-title":"IEEE Trans Intell Transp Syst"},{"key":"6613_CR10","first-page":"335","volume":"24","author":"J Yu","year":"2023","unstructured":"Yu J, Yin H, Xia X, Chen T, Li J, Huang Z (2023) Self-supervised learning for recommender systems: a survey. IEEE Trans Knowl Data Eng 24:335\u2013355","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"4","key":"6613_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3545798","volume":"41","author":"R Zheng","year":"2023","unstructured":"Zheng R, Qu L, Cui B, Shi Y, Yin H (2023) Automl for deep recommender systems: a survey. ACM Trans Inf Syst 41(4):1\u201338","journal-title":"ACM Trans Inf Syst"},{"key":"6613_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2024.01.003","volume":"1056","author":"W Wang","year":"2024","unstructured":"Wang W et al (2024) Epidemic spreading on higher-order networks. Phys Rep 1056:1\u201370","journal-title":"Phys Rep"},{"key":"6613_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.bdr.2016.07.002","volume":"6","author":"S Aridhi","year":"2016","unstructured":"Aridhi S, Nguifo EM (2016) Big graph mining: frameworks and techniques. Big Data Res 6:1\u201310","journal-title":"Big Data Res"},{"issue":"1\u20132","key":"6613_CR14","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1016\/j.tcs.2007.09.013","volume":"389","author":"VE Alekseev","year":"2007","unstructured":"Alekseev VE, Boliac R, Korobitsyn DV, Lozin VV (2007) NP-hard graph problems and boundary classes of graphs. Theoret Comput Sci 389(1\u20132):219\u2013236","journal-title":"Theoret Comput Sci"},{"key":"6613_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s42254-023-00676-y","volume":"6","author":"O Artime","year":"2024","unstructured":"Artime O et al (2024) Robustness and resilience of complex networks. Nat Rev Phys 6:1\u201318","journal-title":"Nat Rev Phys"},{"key":"6613_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2023.03.005","volume":"1017","author":"P Ji","year":"2023","unstructured":"Ji P et al (2023) Signal propagation in complex networks. Phys Rep 1017:1\u201396","journal-title":"Phys Rep"},{"key":"6613_CR17","first-page":"559","volume":"10","author":"WID Mining","year":"2006","unstructured":"Mining WID (2006) Data mining: concepts and techniques. Morgan Kaufmann 10:559\u2013569","journal-title":"Morgan Kaufmann"},{"key":"6613_CR18","doi-asserted-by":"crossref","unstructured":"Kherif F, Latypova A (2020) Principal component analysis. In: Machine learning. Elsevier, pp 209\u2013225","DOI":"10.1016\/B978-0-12-815739-8.00012-2"},{"key":"6613_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2021.108334","volume":"122","author":"L Guo","year":"2022","unstructured":"Guo L, Dai Q (2022) Graph clustering via variational graph embedding. Pattern Recogn 122:108334","journal-title":"Pattern Recogn"},{"key":"6613_CR20","doi-asserted-by":"crossref","unstructured":"Leskovec J, Faloutsos C (2006) Sampling from large graphs. In: Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 631\u2013636","DOI":"10.1145\/1150402.1150479"},{"key":"6613_CR21","doi-asserted-by":"crossref","unstructured":"Zhu J, Li H, Chen M, Dai Z, Zhu M (2018) Enhancing stratified graph sampling algorithms based on approximate degree distribution. In: Computer science on-line conference. Springer, pp 197\u2013207","DOI":"10.1007\/978-3-319-91189-2_20"},{"key":"6613_CR22","unstructured":"Hu P, Lau WC (2013) A survey and taxonomy of graph sampling. https:\/\/arxiv.org\/abs\/1308.5865"},{"key":"6613_CR23","doi-asserted-by":"crossref","unstructured":"Ruan Y, Fuhry D, Liang J, Wang Y, Parthasarathy S (2015) Community discovery: simple and scalable approaches. In: User community discovery. Springer, pp 23\u201354","DOI":"10.1007\/978-3-319-23835-7_2"},{"key":"6613_CR24","doi-asserted-by":"crossref","unstructured":"Voudigari E, Salamanos N, Papageorgiou T, Yannakoudakis EJ (2016) Rank degree: an efficient algorithm for graph sampling. In: 2016 IEEE\/ACM international conference on advances in social networks analysis and mining (ASONAM). IEEE, pp 120\u2013129","DOI":"10.1109\/ASONAM.2016.7752223"},{"key":"6613_CR25","doi-asserted-by":"crossref","unstructured":"Li R-H, Yu JX, Qin L, Mao R, Jin T (2015) On random walk based graph sampling. In: 2015 IEEE 31st international conference on data engineering. IEEE, pp 927\u2013938","DOI":"10.1109\/ICDE.2015.7113345"},{"issue":"4","key":"6613_CR26","doi-asserted-by":"publisher","first-page":"905","DOI":"10.1007\/s10618-020-00683-y","volume":"34","author":"MI Yousuf","year":"2020","unstructured":"Yousuf MI, Kim S (2020) Guided sampling for large graphs. Data Min Knowl Disc 34(4):905\u2013948","journal-title":"Data Min Knowl Disc"},{"key":"6613_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2021.115773","volume":"186","author":"M Jaouadi","year":"2021","unstructured":"Jaouadi M, Romdhane LB (2021) A distributed model for sampling large scale social networks. Expert Syst Appl 186:115773","journal-title":"Expert Syst Appl"},{"key":"6613_CR28","doi-asserted-by":"crossref","unstructured":"Gjoka M, Kurant M, Butts CT, Markopoulou A (2010) Walking in facebook: a case study of unbiased sampling of OSNs. In: 2010 Proceedings IEEE Infocom. IEEE, pp 1\u20139","DOI":"10.1109\/INFCOM.2010.5462078"},{"key":"6613_CR29","doi-asserted-by":"publisher","first-page":"77106","DOI":"10.1109\/ACCESS.2020.2989504","volume":"8","author":"G Cai","year":"2020","unstructured":"Cai G, Lu G, Guo J, Ling C, Li R (2020) Fast representative sampling in large-scale online social networks. IEEE Access 8:77106\u201377119","journal-title":"IEEE Access"},{"issue":"4","key":"6613_CR30","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1137\/070710111","volume":"51","author":"A Clauset","year":"2009","unstructured":"Clauset A, Shalizi CR, Newman ME (2009) Power-law distributions in empirical data. SIAM Rev 51(4):661\u2013703","journal-title":"SIAM Rev"},{"issue":"1","key":"6613_CR31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41467-019-09038-8","volume":"10","author":"P Holme","year":"2019","unstructured":"Holme P (2019) Rare and everywhere: Perspectives on scale-free networks. Nat Commun 10(1):1\u20133","journal-title":"Nat Commun"},{"issue":"2","key":"6613_CR32","doi-asserted-by":"publisher","first-page":"1709","DOI":"10.1109\/TVCG.2020.3030440","volume":"27","author":"Z Zhou","year":"2020","unstructured":"Zhou Z et al (2020) Context-aware sampling of large networks via graph representation learning. IEEE Trans Visual Comput Graphics 27(2):1709\u20131719","journal-title":"IEEE Trans Visual Comput Graphics"},{"key":"6613_CR33","doi-asserted-by":"publisher","first-page":"2508","DOI":"10.1016\/j.procs.2022.09.309","volume":"207","author":"M Jaouadi","year":"2022","unstructured":"Jaouadi M, Romdhane LB (2022) Distributed sampling of social networks: a new approach based on node\u2019s importance. Procedia Comput Sci 207:2508\u20132517","journal-title":"Procedia Comput Sci"},{"key":"6613_CR34","unstructured":"Ahmed N, Neville J, Kompella RR (2011) Network sampling via edge-based node selection with graph induction. https:\/\/docs.lib.purdue.edu\/cstech\/1747"},{"issue":"10","key":"6613_CR35","doi-asserted-by":"publisher","first-page":"3731","DOI":"10.1007\/s10489-019-01479-4","volume":"49","author":"D Batjargal","year":"2019","unstructured":"Batjargal D, Khan KU, Lee Y-K (2019) EM-FGS: graph sparsification via faster semi-metric edges pruning. Appl Intell 49(10):3731\u20133748","journal-title":"Appl Intell"},{"issue":"88","key":"6613_CR36","first-page":"1","volume":"22","author":"CM Le","year":"2021","unstructured":"Le CM (2021) Edge sampling using local network information. J Mach Learn Res 22(88):1\u201329","journal-title":"J Mach Learn Res"},{"issue":"3","key":"6613_CR37","first-page":"1","volume":"14","author":"F Ghaljaie","year":"2017","unstructured":"Ghaljaie F, Naderifar M, Goli H (2017) Snowball sampling: a purposeful method of sampling in qualitative research. Strides Dev Med Educ 14(3):1\u20136","journal-title":"Strides Dev Med Educ"},{"key":"6613_CR38","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2020.105891","volume":"198","author":"L Zhang","year":"2020","unstructured":"Zhang L, Jiang H, Wang F, Feng D (2020) DRaWS: a dual random-walk based sampling method to efficiently estimate distributions of degree and clique size over social networks. Knowl-Based Syst 198:105891","journal-title":"Knowl-Based Syst"},{"key":"6613_CR39","doi-asserted-by":"crossref","unstructured":"Yao X, Shao Y, Cui B, Chen L (2021) Uninet: scalable network representation learning with metropolis-hastings sampling. In: 2021 IEEE 37th international conference on data engineering (ICDE). IEEE, pp 516\u2013527","DOI":"10.1109\/ICDE51399.2021.00051"},{"issue":"1","key":"6613_CR40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s13278-017-0441-6","volume":"7","author":"N Salamanos","year":"2017","unstructured":"Salamanos N, Voudigari E, Yannakoudakis EJ (2017) Deterministic graph exploration for efficient graph sampling. Soc Netw Anal Min 7(1):1\u201314","journal-title":"Soc Netw Anal Min"},{"issue":"1","key":"6613_CR41","doi-asserted-by":"publisher","DOI":"10.1007\/s11432-021-3370-4","volume":"66","author":"J Zhang","year":"2023","unstructured":"Zhang J, Chen H, Yu D, Pei Y, Deng Y (2023) Cluster-preserving sampling algorithm for large-scale graphs. SCIENCE CHINA Inf Sci 66(1):112103","journal-title":"SCIENCE CHINA Inf Sci"},{"issue":"10","key":"6613_CR42","doi-asserted-by":"publisher","first-page":"3557","DOI":"10.1007\/s10489-018-1162-x","volume":"48","author":"D Rhouma","year":"2018","unstructured":"Rhouma D, Romdhane LB (2018) An efficient multilevel scheme for coarsening large scale social networks. Appl Intell 48(10):3557\u20133576","journal-title":"Appl Intell"},{"key":"6613_CR43","volume-title":"Cybersecurity and applied mathematics","author":"L Metcalf","year":"2016","unstructured":"Metcalf L, Casey W (2016) Cybersecurity and applied mathematics. Syngress"},{"issue":"1","key":"6613_CR44","first-page":"1","volume":"14","author":"S Arifuzzaman","year":"2019","unstructured":"Arifuzzaman S, Khan M, Marathe M (2019) Fast parallel algorithms for counting and listing triangles in big graphs. ACM Trans Knowl Discov Data (TKDD) 14(1):1\u201334","journal-title":"ACM Trans Knowl Discov Data (TKDD)"},{"issue":"4\u20135","key":"6613_CR45","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/j.physrep.2005.10.009","volume":"424","author":"S Boccaletti","year":"2006","unstructured":"Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D-U (2006) Complex networks: structure and dynamics. Phys Rep 424(4\u20135):175\u2013308","journal-title":"Phys Rep"},{"key":"6613_CR46","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198805090.001.0001","volume-title":"Networks","author":"M Newman","year":"2018","unstructured":"Newman M (2018) Networks. Oxford University Press"},{"key":"6613_CR47","doi-asserted-by":"publisher","DOI":"10.1016\/j.jocs.2022.101819","volume":"63","author":"M Curado","year":"2022","unstructured":"Curado M, Rodriguez R, Terroso-Saenz F, Tortosa L, Vicent JF (2022) A centrality model for directed graphs based on the two-way-random path and associated indices for characterizing the nodes. J Comput Sci 63:101819","journal-title":"J Comput Sci"},{"issue":"11","key":"6613_CR48","doi-asserted-by":"publisher","first-page":"2088","DOI":"10.1109\/TKDE.2019.2947035","volume":"32","author":"P De Meo","year":"2019","unstructured":"De Meo P, Levene M, Messina F, Provetti A (2019) A general centrality framework-based on node navigability. IEEE Trans Knowl Data Eng 32(11):2088\u20132100","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"2","key":"6613_CR49","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1109\/JSTSP.2022.3153168","volume":"16","author":"P-D Yu","year":"2022","unstructured":"Yu P-D, Tan CW, Fu H-L (2022) Epidemic source detection in contact tracing networks: epidemic centrality in graphs and message-passing algorithms. IEEE J Sel Top Signal Process 16(2):234\u2013249","journal-title":"IEEE J Sel Top Signal Process"},{"key":"6613_CR50","unstructured":"Leskovec J, Krevl A (2014) SNAP Datasets. Available: http:\/\/snap.stanford.edu\/data"},{"issue":"1","key":"6613_CR51","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1145\/1217299.1217301","volume":"1","author":"J Leskovec","year":"2007","unstructured":"Leskovec J, Kleinberg J, Faloutsos C (2007) Graph evolution: densification and shrinking diameters. ACM Trans Knowl Discovery Data (TKDD) 1(1):2","journal-title":"ACM Trans Knowl Discovery Data (TKDD)"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-024-06613-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-024-06613-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-024-06613-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,8]],"date-time":"2024-11-08T03:21:15Z","timestamp":1731036075000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-024-06613-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,8]]},"references-count":51,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["6613"],"URL":"https:\/\/doi.org\/10.1007\/s11227-024-06613-9","relation":{},"ISSN":["0920-8542","1573-0484"],"issn-type":[{"type":"print","value":"0920-8542"},{"type":"electronic","value":"1573-0484"}],"subject":[],"published":{"date-parts":[[2024,11,8]]},"assertion":[{"value":"13 October 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 November 2024","order":2,"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 no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"145"}}