{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T01:03:01Z","timestamp":1767142981420,"version":"build-2238731810"},"reference-count":64,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T00:00:00Z","timestamp":1744070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T00:00:00Z","timestamp":1744070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Data Sci. Eng."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In the rapidly advancing field of graph-based applications, accurate graph similarity computing (GSC) has become increasingly important. However, due to the complexity of graph structures, this task remains a challenge because of the intricate calculations involved. To solve the limitations of existing works, this paper introduces the Interpretable Graph Fusion Model (), a novel framework designed to enhance the accuracy and efficiency of graph similarity computation. Specifically, our model can fully utilize graph structure information and comprehensively assess graph similarity at both fine-grained and coarse-grained levels, ultimately achieving more accurate predictions. Experimented extensively across four real-world datasets,  demonstrates a significant improvement over existing SOTA methods to solve the GSC challenge. In numerous experimental tests, our model shows performance improvements in terms of MSE (Mean Squared Error), ranging from 4.66% to as much as 56.92% compared to the second-best method.<\/jats:p>","DOI":"10.1007\/s41019-024-00278-3","type":"journal-article","created":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T15:48:37Z","timestamp":1744127317000},"page":"396-410","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["IGFM: An Enhanced Graph Similarity Computation Method with Fine-Grained Analysis"],"prefix":"10.1007","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-4481-0724","authenticated-orcid":false,"given":"Min","family":"Pei","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2032-7727","authenticated-orcid":false,"given":"Jianke","family":"Yu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3908-6545","authenticated-orcid":false,"given":"Chen","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3158-9586","authenticated-orcid":false,"given":"Hanchen","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3554-3219","authenticated-orcid":false,"given":"Xiaoyang","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2674-1638","authenticated-orcid":false,"given":"Ying","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,4,8]]},"reference":[{"issue":"3","key":"278_CR1","doi-asserted-by":"publisher","first-page":"169","DOI":"10.14778\/2732232.2732236","volume":"7","author":"X Zhao","year":"2013","unstructured":"Zhao X, Xiao C, Lin X, Liu Q, Zhang W (2013) A partition-based approach to structure similarity search. Proc VLDB Endow 7(3):169\u2013180","journal-title":"Proc VLDB Endow"},{"key":"278_CR2","doi-asserted-by":"publisher","first-page":"3025","DOI":"10.1007\/s11280-020-00819-6","volume":"23","author":"T Zhang","year":"2020","unstructured":"Zhang T, Gao Y, Zheng B, Chen L, Wen S, Guo W (2020) Towards distributed node similarity search on graphs. World Wide Web 23:3025\u20133053","journal-title":"World Wide Web"},{"issue":"1","key":"278_CR3","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1109\/TITS.2020.3011799","volume":"23","author":"TS Jepsen","year":"2020","unstructured":"Jepsen TS, Jensen CS, Nielsen TD (2020) Relational fusion networks: graph convolutional networks for road networks. IEEE Trans Intell Transp Syst 23(1):418\u2013429","journal-title":"IEEE Trans Intell Transp Syst"},{"issue":"2","key":"278_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipm.2023.103571","volume":"61","author":"Y Zhang","year":"2024","unstructured":"Zhang Y, Cheung WK, Liu Q, Wang G, Yang L, Liu L (2024) Towards explaining graph neural networks via preserving prediction ranking and structural dependency. Inf Process Manag 61(2):103571","journal-title":"Inf Process Manag"},{"key":"278_CR5","doi-asserted-by":"crossref","unstructured":"Bai Y, Ding H, Gu K, Sun Y, Wang W (2020) Learning-based efficient graph similarity computation via multi-scale convolutional set matching. In: Proceedings of the AAAI conference on artificial intelligence, vol 34, pp 3219\u20133226","DOI":"10.1609\/aaai.v34i04.5720"},{"key":"278_CR6","doi-asserted-by":"crossref","unstructured":"Roy I, Velugoti VSBR, Chakrabarti S, De A (2022) Interpretable neural subgraph matching for graph retrieval. In: Proceedings of the AAAI conference on artificial intelligence, vol 36, pp 8115\u20138123","DOI":"10.1609\/aaai.v36i7.20784"},{"key":"278_CR7","doi-asserted-by":"crossref","unstructured":"Wang S, Hu L, Wang Y, He X, Sheng QZ, Orgun MA, Cao L, Ricci F, Philip SY (2021) Graph learning based recommender systems: a review. In: 30th international joint conference on artificial intelligence, IJCAI 2021, pp 4644\u20134652","DOI":"10.24963\/ijcai.2021\/630"},{"key":"278_CR8","doi-asserted-by":"crossref","unstructured":"Wang Y, Cong G, Song G, Xie K (2010) Community-based greedy algorithm for mining top-k influential nodes in mobile social networks. In: Proceedings of the 16th ACM SIGKDD international conference on knowledge discovery and data mining, pp 1039\u20131048","DOI":"10.1145\/1835804.1835935"},{"issue":"6","key":"278_CR9","doi-asserted-by":"publisher","first-page":"1050","DOI":"10.1109\/TKDE.2017.2785824","volume":"30","author":"G Liu","year":"2017","unstructured":"Liu G, Liu Y, Zheng K, Liu A, Li Z, Wang Y, Zhou X (2017) Mcs-gpm: multi-constrained simulation based graph pattern matching in contextual social graphs. IEEE Trans Knowl Data Eng 30(6):1050\u20131064","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"3","key":"278_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipm.2024.103683","volume":"61","author":"X Gong","year":"2024","unstructured":"Gong X, Wang H, Wang X, Chen C, Zhang W, Zhang Y (2024) Influence maximization on hypergraphs via multi-hop influence estimation. Inf Process Manag 61(3):103683","journal-title":"Inf Process Manag"},{"key":"278_CR11","unstructured":"Li Y, Gu C, Dullien T, Vinyals O, Kohli P (2019) Graph matching networks for learning the similarity of graph structured objects. In: International conference on machine learning. PMLR, pp 3835\u20133845"},{"key":"278_CR12","doi-asserted-by":"publisher","first-page":"688","DOI":"10.1007\/s10618-020-00733-5","volume":"35","author":"G Ma","year":"2021","unstructured":"Ma G, Ahmed NK, Willke TL, Yu PS (2021) Deep graph similarity learning: a survey. Data Min Knowl Disc 35:688\u2013725","journal-title":"Data Min Knowl Disc"},{"issue":"4","key":"278_CR13","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/0167-8655(83)90033-8","volume":"1","author":"H Bunke","year":"1983","unstructured":"Bunke H, Allermann G (1983) Inexact graph matching for structural pattern recognition. Pattern Recogn Lett 1(4):245\u2013253","journal-title":"Pattern Recogn Lett"},{"issue":"3\u20134","key":"278_CR14","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/S0167-8655(97)00179-7","volume":"19","author":"H Bunke","year":"1998","unstructured":"Bunke H, Shearer K (1998) A graph distance metric based on the maximal common subgraph. Pattern Recogn Lett 19(3\u20134):255\u2013259","journal-title":"Pattern Recogn Lett"},{"key":"278_CR15","doi-asserted-by":"crossref","unstructured":"Dijkman R, Dumas M, Garc\u00eda-Ba\u00f1uelos L (2009) Graph matching algorithms for business process model similarity search. In: Business process management: 7th international conference, BPM 2009, Ulm, Germany, September 8\u201310, 2009. Proceedings 7. Springer, pp 48\u201363","DOI":"10.1007\/978-3-642-03848-8_5"},{"issue":"1","key":"278_CR16","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1109\/TNNLS.2020.2978386","volume":"32","author":"Z Wu","year":"2020","unstructured":"Wu Z, Pan S, Chen F, Long G, Zhang C, Philip SY (2020) A comprehensive survey on graph neural networks. IEEE Trans Neural Netw Learn Syst 32(1):4\u201324","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"278_CR17","doi-asserted-by":"crossref","unstructured":"Neuhaus M, Riesen K, Bunke H (2006) Fast suboptimal algorithms for the computation of graph edit distance. In: Structural, syntactic, and statistical pattern recognition: joint IAPR international workshops, SSPR 2006 and SPR 2006, Hong Kong, China, August 17\u201319, 2006. Proceedings. Springer, pp 163\u2013172","DOI":"10.1007\/11815921_17"},{"key":"278_CR18","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.patrec.2018.05.002","volume":"134","author":"DB Blumenthal","year":"2020","unstructured":"Blumenthal DB, Gamper J (2020) On the exact computation of the graph edit distance. Pattern Recogn Lett 134:46\u201357","journal-title":"Pattern Recogn Lett"},{"issue":"1","key":"278_CR19","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1002\/nav.20053","volume":"52","author":"HW Kuhn","year":"2005","unstructured":"Kuhn HW (2005) The Hungarian method for the assignment problem. Naval Res Logist 52(1):7\u201321","journal-title":"Naval Res Logist"},{"key":"278_CR20","doi-asserted-by":"crossref","unstructured":"Fankhauser S, Riesen K, Bunke H (2011) Speeding up graph edit distance computation through fast bipartite matching. In: Graph-based representations in pattern recognition: 8th IAPR-TC-15 international workshop, GbRPR 2011, M\u00fcnster, Germany, May 18\u201320, 2011. Proceedings 8. Springer, pp 102\u2013111","DOI":"10.1007\/978-3-642-20844-7_11"},{"key":"278_CR21","doi-asserted-by":"crossref","unstructured":"Bai Y, Ding H, Bian S, Chen T, Sun Y, Wang W (2019) Simgnn: A neural network approach to fast graph similarity computation. In: Proceedings of the twelfth ACM international conference on web search and data mining, pp 384\u2013392","DOI":"10.1145\/3289600.3290967"},{"key":"278_CR22","first-page":"14110","volume":"34","author":"C Qin","year":"2021","unstructured":"Qin C, Zhao H, Wang L, Wang H, Zhang Y, Fu Y (2021) Slow learning and fast inference: efficient graph similarity computation via knowledge distillation. Adv Neural Inf Process Syst 34:14110\u201314121","journal-title":"Adv Neural Inf Process Syst"},{"key":"278_CR23","doi-asserted-by":"crossref","unstructured":"Zhang Z, Bu J, Ester M, Li Z, Yao C, Yu Z, Wang C (2021) H2mn: Graph similarity learning with hierarchical hypergraph matching networks. In: Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining, pp 2274\u20132284","DOI":"10.1145\/3447548.3467328"},{"key":"278_CR24","first-page":"22518","volume":"35","author":"R Ranjan","year":"2022","unstructured":"Ranjan R, Grover S, Medya S, Chakaravarthy V, Sabharwal Y, Ranu S (2022) Greed: a neural framework for learning graph distance functions. Adv Neural Inf Process Syst 35:22518\u201322530","journal-title":"Adv Neural Inf Process Syst"},{"key":"278_CR25","unstructured":"Ling X, Wu L, Wang S, Ma T, Xu F, Liu AX, Wu C, Ji S (2021) Multilevel graph matching networks for deep graph similarity learning. IEEE Trans Neural Netw Learn Syst"},{"issue":"8","key":"278_CR26","doi-asserted-by":"publisher","first-page":"1817","DOI":"10.14778\/3594512.3594514","volume":"16","author":"C Piao","year":"2023","unstructured":"Piao C, Xu T, Sun X, Rong Y, Zhao K, Cheng H (2023) Computing graph edit distance via neural graph matching. Proc VLDB Endow 16(8):1817\u20131829","journal-title":"Proc VLDB Endow"},{"key":"278_CR27","first-page":"30181","volume":"35","author":"W Zhuo","year":"2022","unstructured":"Zhuo W, Tan G (2022) Efficient graph similarity computation with alignment regularization. Adv Neural Inf Process Syst 35:30181\u201330193","journal-title":"Adv Neural Inf Process Syst"},{"issue":"3","key":"278_CR28","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/0378-8733(83)90028-X","volume":"5","author":"SB Seidman","year":"1983","unstructured":"Seidman SB (1983) Network structure and minimum degree. Soc Netw 5(3):269\u2013287","journal-title":"Soc Netw"},{"issue":"3.1","key":"278_CR29","first-page":"1","volume":"16","author":"J Cohen","year":"2008","unstructured":"Cohen J (2008) Trusses: cohesive subgraphs for social network analysis. Natl Sec Agency Tech Rep 16(3.1):1\u201329","journal-title":"Natl Sec Agency Tech Rep"},{"issue":"2","key":"278_CR30","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/BF02289146","volume":"14","author":"RD Luce","year":"1949","unstructured":"Luce RD, Perry AD (1949) A method of matrix analysis of group structure. Psychometrika 14(2):95\u2013116","journal-title":"Psychometrika"},{"key":"278_CR31","unstructured":"Socher R, Chen D, Manning CD, Ng A (2013) Reasoning with neural tensor networks for knowledge base completion. Adv Neural Inf Process Syst 26"},{"key":"278_CR32","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-0769-0_30","volume-title":"Euclidean distance matrices and applications","author":"N Krislock","year":"2012","unstructured":"Krislock N, Wolkowicz H (2012) Euclidean distance matrices and applications. Springer, Berlin"},{"key":"278_CR33","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1109\/TSMC.1983.6313167","volume":"3","author":"A Sanfeliu","year":"1983","unstructured":"Sanfeliu A, Fu K-S (1983) A distance measure between attributed relational graphs for pattern recognition. IEEE Trans Syst Man Cybern 3:353\u2013362","journal-title":"IEEE Trans Syst Man Cybern"},{"issue":"8","key":"278_CR34","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1016\/S0167-8655(97)00060-3","volume":"18","author":"H Bunke","year":"1997","unstructured":"Bunke H (1997) On a relation between graph edit distance and maximum common subgraph. Pattern Recogn Lett 18(8):689\u2013694","journal-title":"Pattern Recogn Lett"},{"issue":"1","key":"278_CR35","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1145\/321556.321562","volume":"17","author":"DG Corneil","year":"1970","unstructured":"Corneil DG, Gotlieb CC (1970) An efficient algorithm for graph isomorphism. J ACM 17(1):51\u201364","journal-title":"J ACM"},{"issue":"6\u20137","key":"278_CR36","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1016\/S0167-8655(01)00017-4","volume":"22","author":"M-L Fern\u00e1ndez","year":"2001","unstructured":"Fern\u00e1ndez M-L (2001) Valiente G: a graph distance metric combining maximum common subgraph and minimum common supergraph. Pattern Recogn Lett 22(6\u20137):753\u2013758","journal-title":"Pattern Recogn Lett"},{"key":"278_CR37","doi-asserted-by":"crossref","unstructured":"Chen L, Gao Y, Li X, Jensen CS, Chen G (2015) Efficient metric indexing for similarity search. In: 2015 IEEE 31st international conference on data engineering. IEEE, pp 591\u2013602","DOI":"10.1109\/ICDE.2015.7113317"},{"issue":"7","key":"278_CR38","doi-asserted-by":"publisher","first-page":"950","DOI":"10.1016\/j.imavis.2008.04.004","volume":"27","author":"K Riesen","year":"2009","unstructured":"Riesen K, Bunke H (2009) Approximate graph edit distance computation by means of bipartite graph matching. Image Vis Comput 27(7):950\u2013959","journal-title":"Image Vis Comput"},{"issue":"3","key":"278_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipm.2023.103639","volume":"61","author":"Y Duan","year":"2024","unstructured":"Duan Y, Liu J, Chen S, Chen L, Wu J (2024) G-prompt: graphon-based prompt tuning for graph classification. Inf Process Manag 61(3):103639","journal-title":"Inf Process Manag"},{"issue":"4","key":"278_CR40","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipm.2024.103752","volume":"61","author":"B Shang","year":"2024","unstructured":"Shang B, Zhao Y, Liu J (2024) Knowledge graph representation learning with relation-guided aggregation and interaction. Inf Process Manag 61(4):103752","journal-title":"Inf Process Manag"},{"issue":"3","key":"278_CR41","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipm.2024.103676","volume":"61","author":"Z Liu","year":"2024","unstructured":"Liu Z, Meng L, Sheng QZ, Chu D, Yu J, Song X (2024) Poi recommendation for random groups based on cooperative graph neural networks. Inf Process Manag 61(3):103676","journal-title":"Inf Process Manag"},{"key":"278_CR42","doi-asserted-by":"crossref","unstructured":"Bai J, Zhao P (2021) Tagsim: type-aware graph similarity learning and computation. Proc VLDB Endow 15(2)","DOI":"10.14778\/3489496.3489513"},{"key":"278_CR43","doi-asserted-by":"crossref","unstructured":"Jin D, Wang L, Zheng Y, Li X, Jiang F, Lin W, Pan S (2022) Cgmn: a contrastive graph matching network for self-supervised graph similarity learning. arXiv preprint arXiv:2205.15083","DOI":"10.24963\/ijcai.2022\/292"},{"key":"278_CR44","doi-asserted-by":"crossref","unstructured":"Wang R, Zhang T, Yu T, Yan J, Yang X (2021) Combinatorial learning of graph edit distance via dynamic embedding. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp 5241\u20135250","DOI":"10.1109\/CVPR46437.2021.00520"},{"issue":"4","key":"278_CR45","doi-asserted-by":"publisher","first-page":"1349","DOI":"10.1016\/j.patcog.2014.11.002","volume":"48","author":"K Riesen","year":"2015","unstructured":"Riesen K, Bunke H (2015) Improving bipartite graph edit distance approximation using various search strategies. Pattern Recognit 48(4):1349\u20131363","journal-title":"Pattern Recognit"},{"issue":"6","key":"278_CR46","doi-asserted-by":"publisher","first-page":"649","DOI":"10.14778\/3055330.3055332","volume":"10","author":"F Zhang","year":"2017","unstructured":"Zhang F, Zhang W, Zhang Y, Qin L, Lin X (2017) Olak: an efficient algorithm to prevent unraveling in social networks. Proc VLDB Endow 10(6):649\u2013660","journal-title":"Proc VLDB Endow"},{"key":"278_CR47","doi-asserted-by":"crossref","unstructured":"Zhang F, Zhang Y, Qin L, Zhang W, Lin X (2018) Efficiently reinforcing social networks over user engagement and tie strength. In: 2018 IEEE 34th international conference on data engineering (ICDE). IEEE, pp 557\u2013568","DOI":"10.1109\/ICDE.2018.00057"},{"key":"278_CR48","doi-asserted-by":"crossref","unstructured":"Linghu Q, Zhang F, Lin X, Zhang W, Zhang Y (2020) Global reinforcement of social networks: The anchored coreness problem. In: Proceedings of the 2020 ACM SIGMOD international conference on management of data, pp 2211\u20132226","DOI":"10.1145\/3318464.3389744"},{"issue":"2","key":"278_CR49","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1016\/S0304-3975(98)00091-7","volume":"210","author":"H Matsuda","year":"1999","unstructured":"Matsuda H, Ishihara T, Hashimoto A (1999) Classifying molecular sequences using a linkage graph with their pairwise similarities. Theor Comput Sci 210(2):305\u2013325","journal-title":"Theor Comput Sci"},{"issue":"10","key":"278_CR50","doi-asserted-by":"publisher","first-page":"5051","DOI":"10.1109\/TKDE.2020.3047224","volume":"34","author":"R Sun","year":"2020","unstructured":"Sun R, Chen C, Wang X, Zhang Y, Wang X (2020) Stable community detection in signed social networks. IEEE Trans Knowl Data Eng 34(10):5051\u20135055","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"278_CR51","doi-asserted-by":"crossref","unstructured":"Sun R, Zhu Q, Chen C, Wang X, Zhang Y, Wang X (2020) Discovering cliques in signed networks based on balance theory. In: Database systems for advanced applications: 25th international conference, DASFAA 2020, Jeju, South Korea, September 24\u201327, 2020, Proceedings, Part II 25. Springer, pp 666\u2013674","DOI":"10.1007\/978-3-030-59416-9_43"},{"key":"278_CR52","doi-asserted-by":"crossref","unstructured":"Yu J, Wang H, Wang X, Li Z, Qin L, Zhang W, Liao J, Zhang Y (2023) Group-based fraud detection network on e-commerce platforms. In: Proceedings of the 29th ACM SIGKDD conference on knowledge discovery and data mining, pp 5463\u20135475","DOI":"10.1145\/3580305.3599836"},{"issue":"19","key":"278_CR53","doi-asserted-by":"publisher","first-page":"9051","DOI":"10.3390\/app11199051","volume":"11","author":"X Liu","year":"2021","unstructured":"Liu X, Wang X (2021) Cohesive subgraph identification in weighted bipartite graphs. Appl Sci 11(19):9051","journal-title":"Appl Sci"},{"key":"278_CR54","unstructured":"Xu K, Hu W, Leskovec J, Jegelka S (2018) How powerful are graph neural networks? In: International conference on learning representations"},{"key":"278_CR55","unstructured":"Mena G, Belanger D, Linderman S, Snoek J (2018) Learning latent permutations with gumbel-sinkhorn networks. In: International conference on learning representations, vol 2018"},{"issue":"29\u201347","key":"278_CR56","first-page":"5","volume":"20","author":"D Bruff","year":"2005","unstructured":"Bruff D (2005) The assignment problem and the Hungarian method. Notes Math 20(29\u201347):5","journal-title":"Notes Math"},{"key":"278_CR57","unstructured":"Jang E, Gu S, Poole B (2016) Categorical reparameterization with gumbel-softmax. In: International conference on learning representations"},{"key":"278_CR58","doi-asserted-by":"crossref","unstructured":"Wang X, Ding X, Tung AK, Ying S, Jin H (2012) An efficient graph indexing method. In: 2012 IEEE 28th international conference on data engineering. IEEE, pp 210\u2013221","DOI":"10.1109\/ICDE.2012.28"},{"key":"278_CR59","doi-asserted-by":"crossref","unstructured":"Liang Y, Zhao P (2017) Similarity search in graph databases: a multi-layered indexing approach. In: 2017 IEEE 33rd international conference on data engineering (ICDE). IEEE, pp 783\u2013794","DOI":"10.1109\/ICDE.2017.129"},{"key":"278_CR60","doi-asserted-by":"crossref","unstructured":"Yanardag P, Vishwanathan S (2015) Deep graph kernels. In: Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, pp 1365\u20131374","DOI":"10.1145\/2783258.2783417"},{"key":"278_CR61","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1007\/s10115-007-0103-5","volume":"14","author":"N Wale","year":"2008","unstructured":"Wale N, Watson IA, Karypis G (2008) Comparison of descriptor spaces for chemical compound retrieval and classification. Knowl Inf Syst 14:347\u2013375","journal-title":"Knowl Inf Syst"},{"key":"278_CR62","doi-asserted-by":"crossref","unstructured":"Riesen K, Emmenegger S, Bunke H (2013) A novel software toolkit for graph edit distance computation. In: Graph-based representations in pattern recognition: 9th IAPR-TC-15 international workshop, GbRPR 2013, Vienna, Austria, May 15\u201317, 2013. Proceedings 9. Springer, pp 142\u2013151","DOI":"10.1007\/978-3-642-38221-5_15"},{"key":"278_CR63","unstructured":"Kingma D, Ba J (2015) Adam: A method for stochastic optimization. In: International conference on learning representations (ICLR)"},{"issue":"1","key":"278_CR64","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/s00778-019-00587-4","volume":"29","author":"FD Malliaros","year":"2020","unstructured":"Malliaros FD, Giatsidis C, Papadopoulos AN, Vazirgiannis M (2020) The core decomposition of networks: theory, algorithms and applications. VLDB J 29(1):61\u201392","journal-title":"VLDB J"}],"updated-by":[{"DOI":"10.1007\/s41019-025-00298-7","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T00:00:00Z","timestamp":1749081600000}}],"container-title":["Data Science and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41019-024-00278-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s41019-024-00278-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41019-024-00278-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,18]],"date-time":"2025-09-18T07:55:33Z","timestamp":1758182133000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s41019-024-00278-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,8]]},"references-count":64,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["278"],"URL":"https:\/\/doi.org\/10.1007\/s41019-024-00278-3","relation":{},"ISSN":["2364-1185","2364-1541"],"issn-type":[{"value":"2364-1185","type":"print"},{"value":"2364-1541","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,8]]},"assertion":[{"value":"29 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 November 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 December 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 April 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 June 2025","order":5,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":6,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1007\/s41019-025-00298-7","URL":"https:\/\/doi.org\/10.1007\/s41019-025-00298-7","order":8,"name":"change_details","label":"Change Details","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.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interests"}}]}}