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Solution proposed: In this paper, we propose a novel method for predicting dependent edges in network models of nonequilibrium complex systems, based on overlapping module features. This approach addresses the many-to-many dependency prediction problem between nonequilibrium complex networks. By transforming node-based network models into edge-based models, we identify overlapping modular structures, enabling the prediction of many-to-many dependent edges. Experimental evaluation: This method is applied to dependency edge prediction in power and gas networks, curriculum and competency networks, and text and question networks. Results: The results indicate that the proposed dependency edge prediction method enhances the robustness of the network in power\u2013gas networks, accurately identifies supporting relationships in curriculum\u2013competency networks, and achieves better information gain in text\u2013question networks. Conclusion: These findings confirm that the overlapping module-based approach effectively predicts dependencies across various nonequilibrium complex systems in diverse fields.<\/jats:p>","DOI":"10.3390\/systems12100433","type":"journal-article","created":{"date-parts":[[2024,10,14]],"date-time":"2024-10-14T12:44:31Z","timestamp":1728909871000},"page":"433","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Predicting Dependent Edges in Nonequilibrium Complex Systems Based on Overlapping Module Characteristics"],"prefix":"10.3390","volume":"12","author":[{"given":"Qingyu","family":"Zou","sequence":"first","affiliation":[{"name":"College of Electrical and Information Engineering, Beihua University, Jilin 132000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Yan","sequence":"additional","affiliation":[{"name":"College of Electrical and Information Engineering, Beihua University, Jilin 132000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yue","family":"Gong","sequence":"additional","affiliation":[{"name":"College of Electrical and Information Engineering, Beihua University, Jilin 132000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingfei","family":"Hou","sequence":"additional","affiliation":[{"name":"College of Electrical and Information Engineering, Beihua University, Jilin 132000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-319-74412-4_1","article-title":"A Panorama of Future Interdependent Networks: From Intelligent Infrastructures to Smart Cities","volume":"Volume 145","author":"Amini","year":"2018","journal-title":"Sustainable Interdependent Networks: From Theory to Application"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/978-3-319-74412-4_3","article-title":"Toward a Smart City of Interdependent Critical Infrastructure Networks","volume":"Volume 145","author":"Amini","year":"2018","journal-title":"Sustainable Interdependent Networks: From Theory to Application"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1038\/nature08932","article-title":"Catastrophic cascade of failures in interdependent networks","volume":"464","author":"Buldyrev","year":"2010","journal-title":"Nature"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhang, C., Lei, Y., Shen, X., Li, Q., Yao, H., Cheng, D., Xie, Y., and Yu, W. 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