{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:42:30Z","timestamp":1760146950179,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T00:00:00Z","timestamp":1735603200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Hubei Key Laboratory of Intelligent Geo-Information Processing","award":["KLIGIP-2022B11","KLIGIP-2021B01"],"award-info":[{"award-number":["KLIGIP-2022B11","KLIGIP-2021B01"]}]},{"name":"Deep-time Digital Earth (DDE) Big Science Program","award":["KLIGIP-2022B11","KLIGIP-2021B01"],"award-info":[{"award-number":["KLIGIP-2022B11","KLIGIP-2021B01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Knowledge graphs, as an important research direction in artificial intelligence, have been widely applied in many fields and tasks. The relations in knowledge graphs have explicit semantics and play a crucial role in knowledge completion and reasoning. Correctly measuring the inferential value of relations and identifying important relations in a knowledge graph can effectively improve the effectiveness of knowledge graphs in reasoning tasks. However, the existing methods primarily consider the connectivity and structural characteristics of relations, but neglect the semantics and the mutual influence of relations in reasoning tasks. This leads to truly valuable relations being difficult to fully utilize in long-chain reasoning. To address this problem, this work, inspired by information entropy and uncertainty-measurement methods in knowledge bases, proposes a method called Relation Importance Measurement based on Information Entropy (RIMIE) to measure the inferential value of relations in knowledge graphs. RIMIE considers the semantics of relations and the role of relations in reasoning. Specifically, based on the values of relations in logical chains, RIMIE partitions the logical sample set into multiple equivalence classes, and generates a knowledge structure for each relation. Correspondingly, to effectively measure the inferential values of relations in knowledge graphs, the concept of relation entropy is proposed, and it is calculated according to the knowledge structures. Finally, to objectively assess the effectiveness of RIMIE, a group of experiments are conducted, which compare the influences of the relations selected according to RIMIE and other patterns on the triple classifications by knowledge graph representation learning. The experimental results confirm what is claimed above.<\/jats:p>","DOI":"10.3390\/a18010006","type":"journal-article","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T14:21:12Z","timestamp":1735654872000},"page":"6","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Measuring the Inferential Values of Relations in Knowledge Graphs"],"prefix":"10.3390","volume":"18","author":[{"given":"Xu","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Computer Science, China University of Geosciences, Wuhan 430078, China"}]},{"given":"Xiaojun","family":"Kang","sequence":"additional","affiliation":[{"name":"School of Computer Science, China University of Geosciences, Wuhan 430078, China"},{"name":"Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan 430078, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0367-9528","authenticated-orcid":false,"given":"Hong","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Computer Science, China University of Geosciences, Wuhan 430078, China"},{"name":"Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan 430078, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1409-9473","authenticated-orcid":false,"given":"Lijun","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Computer Science, China University of Geosciences, Wuhan 430078, China"},{"name":"Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan 430078, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1109\/TNNLS.2021.3070843","article-title":"A survey on knowledge graphs: Representation, acquisition, and applications","volume":"33","author":"Ji","year":"2021","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Xiao, F., Wen, J., and Pedrycz, W. (2022). Generalized divergence-based decision making method with an application to pattern classification. IEEE Trans. Knowl. Data Eng.","DOI":"10.1109\/TKDE.2022.3177896"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2021\/8403738","article-title":"Identification of influential nodes via effective distance-based centrality mechanism in complex networks","volume":"2021","author":"Ullah","year":"2021","journal-title":"Complexity"},{"key":"ref_4","first-page":"1","article-title":"Knowledge graph embedding for link prediction: A comparative analysis","volume":"15","author":"Rossi","year":"2021","journal-title":"ACM Trans. Knowl. Discov. Data (TKDD)"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1777","DOI":"10.1016\/j.physa.2011.09.017","article-title":"Identifying influential nodes in complex networks","volume":"391","author":"Chen","year":"2012","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3284","DOI":"10.1109\/TFUZZ.2021.3112226","article-title":"LFIC: Identifying influential nodes in complex networks by local fuzzy information centrality","volume":"30","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"112136","DOI":"10.1016\/j.chaos.2022.112136","article-title":"Node influence ranking in complex networks: A local structure entropy approach","volume":"160","author":"Lei","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"125498","DOI":"10.1016\/j.physa.2020.125498","article-title":"Social interaction layers in complex networks for the dynamical epidemic modeling of COVID-19 in Brazil","volume":"564","author":"Scabini","year":"2021","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1748","DOI":"10.1109\/COMST.2023.3273282","article-title":"Cyber threat intelligence mining for proactive cybersecurity defense: A survey and new perspectives","volume":"25","author":"Sun","year":"2023","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1038\/s43587-022-00252-6","article-title":"A complex systems approach to aging biology","volume":"2","author":"Cohen","year":"2022","journal-title":"Nat. Aging"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1617","DOI":"10.1016\/j.ins.2022.06.075","article-title":"Influence maximization in social networks using graph embedding and graph neural network","volume":"607","author":"Kumar","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.ins.2020.12.091","article-title":"Positive opinion maximization in signed social networks","volume":"558","author":"He","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Yu, E.Y., Chen, D.B., and Zhao, J.Y. (2018). Identifying critical edges in complex networks. Sci. Rep., 8.","DOI":"10.1038\/s41598-018-32631-8"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"107528","DOI":"10.1016\/j.knosys.2021.107528","article-title":"Improving graph neural network via complex-network-based anchor structure","volume":"233","author":"Dong","year":"2021","journal-title":"Knowl.-Based Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"105580","DOI":"10.1016\/j.knosys.2020.105580","article-title":"Finding influential nodes in social networks based on neighborhood correlation coefficient","volume":"194","author":"Zareie","year":"2020","journal-title":"Knowl.-Based Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"118902","DOI":"10.1088\/1674-1056\/aceee8","article-title":"SLGC: Identifying influential nodes in complex networks from the perspectives of self-centrality, local centrality, and global centrality","volume":"32","author":"Ai","year":"2023","journal-title":"Chin. Phys. B"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zhang, J., and Luo, Y. (2017, January 26\u201327). Degree centrality, betweenness centrality, and closeness centrality in social network. Proceedings of the 2017 2nd International Conference on Modelling, Simulation and Applied Mathematics (MSAM2017), Bangkok, Thailand.","DOI":"10.2991\/msam-17.2017.68"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"108130","DOI":"10.1016\/j.patcog.2021.108130","article-title":"Community-based k-shell decomposition for identifying influential spreaders","volume":"120","author":"Sun","year":"2021","journal-title":"Pattern Recognit."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"088901","DOI":"10.1088\/1674-1056\/abea86","article-title":"LCH: A local clustering H-index centrality measure for identifying and ranking influential nodes in complex networks","volume":"30","author":"Xu","year":"2021","journal-title":"Chin. Phys. B"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/s10844-023-00822-z","article-title":"Leveraging neighborhood and path information for influential spreaders recognition in complex networks","volume":"62","author":"Ullah","year":"2024","journal-title":"J. Intell. Inf. Syst."},{"key":"ref_21","first-page":"30","article-title":"Closeness centrality of friendship and lollipop graphs","volume":"4","author":"Barman","year":"2023","journal-title":"Innov. Multidiscip. Res. Present Future Time"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1140\/epjb\/e2004-00111-4","article-title":"Betweenness centrality in large complex networks","volume":"38","author":"Barthelemy","year":"2004","journal-title":"Eur. Phys. J. B"},{"key":"ref_23","unstructured":"Deng, R., Li, M., and Zhang, Q. (2024). Structural analysis and the sum of nodes\u2019 betweenness centrality in complex networks. arXiv."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"113753","DOI":"10.1016\/j.chaos.2023.113753","article-title":"The two-steps eigenvector centrality in complex networks","volume":"173","author":"Xu","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"211281","DOI":"10.1109\/ACCESS.2020.3038791","article-title":"A re-ranking algorithm for identifying influential nodes in complex networks","volume":"8","author":"Yu","year":"2020","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Li, Z., Ren, T., Ma, X., Liu, S., Zhang, Y., and Zhou, T. (2019). Identifying influential spreaders by gravity model. Sci. Rep., 9.","DOI":"10.1038\/s41598-019-44930-9"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"110456","DOI":"10.1016\/j.chaos.2020.110456","article-title":"A generalized gravity model for influential spreaders identification in complex networks","volume":"143","author":"Li","year":"2021","journal-title":"Chaos Solitons Fractals"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3290","DOI":"10.1109\/TIT.2016.2555904","article-title":"Structural information and dynamical complexity of networks","volume":"62","author":"Li","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Park, N., Kan, A., Dong, X.L., Zhao, T., and Faloutsos, C. (2019, January 4\u20138). Estimating node importance in knowledge graphs using graph neural networks. Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Anchorage, AK, USA.","DOI":"10.1145\/3292500.3330855"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Park, N., Kan, A., Dong, X.L., Zhao, T., and Faloutsos, C. (2020, January 6\u201310). Multiimport: Inferring node importance in a knowledge graph from multiple input signals. Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Virtual.","DOI":"10.1145\/3394486.3403093"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Fensel, D., \u015eim\u015fek, U., Angele, K., Huaman, E., K\u00e4rle, E., Panasiuk, O., Toma, I., Umbrich, J., Wahler, A., and Fensel, D. (2020). Introduction: What is a knowledge graph?. Knowledge Graphs: Methodology, Tools and Selected Use Cases, Springer.","DOI":"10.1007\/978-3-030-37439-6"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"102179","DOI":"10.1016\/j.jocs.2023.102179","article-title":"Ranking influential nodes in complex network using edge weight degree based shell decomposition","volume":"74","author":"Maji","year":"2023","journal-title":"J. Comput. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.trit.2016.11.001","article-title":"A survey on rough set theory and its applications","volume":"1","author":"Zhang","year":"2016","journal-title":"CAAI Trans. Intell. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"116187","DOI":"10.1016\/j.eswa.2021.116187","article-title":"Tri-level attribute reduction in rough set theory","volume":"190","author":"Zhang","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.ins.2020.05.010","article-title":"Attribute group for attribute reduction","volume":"535","author":"Chen","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1007\/s13042-020-01243-y","article-title":"Entropy based optimal scale combination selection for generalized multi-scale information tables","volume":"12","author":"Bao","year":"2021","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1007\/s10115-019-01363-0","article-title":"Measures of uncertainty for knowledge bases","volume":"62","author":"Li","year":"2020","journal-title":"Knowl. Inf. Syst."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Fang, T., Chen, Z., Song, Y., and Bosselut, A. (2024). Complex reasoning over logical queries on commonsense knowledge graphs. arXiv.","DOI":"10.18653\/v1\/2024.acl-long.613"},{"key":"ref_39","unstructured":"Han, X., Cao, S., Xin, L., Lin, Y., Liu, Z., Sun, M., and Li, J. (November, January 31). OpenKE: An Open Toolkit for Knowledge Embedding. Proceedings of the EMNLP, Brussels, Belgium."},{"key":"ref_40","first-page":"2787","article-title":"Translating embeddings for modeling multi-relational data","volume":"26","author":"Bordes","year":"2013","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_41","unstructured":"Trouillon, T., Welbl, J., Riedel, S., Gaussier, \u00c9., and Bouchard, G. (2016, January 19\u201324). Complex embeddings for simple link prediction. Proceedings of the International Conference on Machine Learning (PMLR), New York, NY, USA."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Li, R., Chen, X., Li, C., Shen, Y., Zhao, J., Wang, Y., Han, W., Sun, H., Deng, W., and Zhang, Q. (2023). To copy rather than memorize: A vertical learning paradigm for knowledge graph completion. arXiv.","DOI":"10.18653\/v1\/2023.acl-long.349"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/1\/6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:57:48Z","timestamp":1760115468000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/1\/6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,31]]},"references-count":42,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["a18010006"],"URL":"https:\/\/doi.org\/10.3390\/a18010006","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2024,12,31]]}}}