{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T17:10:35Z","timestamp":1780506635053,"version":"3.54.1"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,27]],"date-time":"2022-09-27T00:00:00Z","timestamp":1664236800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundamental Research Funds for the Central Universities, Southwest Minzu University","award":["ZYN2022006"],"award-info":[{"award-number":["ZYN2022006"]}]},{"name":"Fundamental Research Funds for the Central Universities, Southwest Minzu University","award":["2022JDGD0011"],"award-info":[{"award-number":["2022JDGD0011"]}]},{"name":"Fundamental Research Funds for the Central Universities, Southwest Minzu University","award":["23GJHZ0149"],"award-info":[{"award-number":["23GJHZ0149"]}]},{"name":"Fundamental Research Funds for the Central Universities, Southwest Minzu University","award":["QN2021186001L"],"award-info":[{"award-number":["QN2021186001L"]}]},{"name":"Fundamental Research Funds for the Central Universities, Southwest Minzu University","award":["G2021186002L"],"award-info":[{"award-number":["G2021186002L"]}]},{"name":"Fundamental Research Funds for the Central Universities, Southwest Minzu University","award":["G2022186003L"],"award-info":[{"award-number":["G2022186003L"]}]},{"name":"Sichuan Science and Technology Program","award":["ZYN2022006"],"award-info":[{"award-number":["ZYN2022006"]}]},{"name":"Sichuan Science and Technology Program","award":["2022JDGD0011"],"award-info":[{"award-number":["2022JDGD0011"]}]},{"name":"Sichuan Science and Technology Program","award":["23GJHZ0149"],"award-info":[{"award-number":["23GJHZ0149"]}]},{"name":"Sichuan Science and Technology Program","award":["QN2021186001L"],"award-info":[{"award-number":["QN2021186001L"]}]},{"name":"Sichuan Science and Technology Program","award":["G2021186002L"],"award-info":[{"award-number":["G2021186002L"]}]},{"name":"Sichuan Science and Technology Program","award":["G2022186003L"],"award-info":[{"award-number":["G2022186003L"]}]},{"name":"Research Fund for International Young Scientists of Ministry of Science and Technology of China","award":["ZYN2022006"],"award-info":[{"award-number":["ZYN2022006"]}]},{"name":"Research Fund for International Young Scientists of Ministry of Science and Technology of China","award":["2022JDGD0011"],"award-info":[{"award-number":["2022JDGD0011"]}]},{"name":"Research Fund for International Young Scientists of Ministry of Science and Technology of China","award":["23GJHZ0149"],"award-info":[{"award-number":["23GJHZ0149"]}]},{"name":"Research Fund for International Young Scientists of Ministry of Science and Technology of China","award":["QN2021186001L"],"award-info":[{"award-number":["QN2021186001L"]}]},{"name":"Research Fund for International Young Scientists of Ministry of Science and Technology of China","award":["G2021186002L"],"award-info":[{"award-number":["G2021186002L"]}]},{"name":"Research Fund for International Young Scientists of Ministry of Science and Technology of China","award":["G2022186003L"],"award-info":[{"award-number":["G2022186003L"]}]},{"name":"Foreign Talents Program of Ministry of Science and Technology of China","award":["ZYN2022006"],"award-info":[{"award-number":["ZYN2022006"]}]},{"name":"Foreign Talents Program of Ministry of Science and Technology of China","award":["2022JDGD0011"],"award-info":[{"award-number":["2022JDGD0011"]}]},{"name":"Foreign Talents Program of Ministry of Science and Technology of China","award":["23GJHZ0149"],"award-info":[{"award-number":["23GJHZ0149"]}]},{"name":"Foreign Talents Program of Ministry of Science and Technology of China","award":["QN2021186001L"],"award-info":[{"award-number":["QN2021186001L"]}]},{"name":"Foreign Talents Program of Ministry of Science and Technology of China","award":["G2021186002L"],"award-info":[{"award-number":["G2021186002L"]}]},{"name":"Foreign Talents Program of Ministry of Science and Technology of China","award":["G2022186003L"],"award-info":[{"award-number":["G2022186003L"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The goal of software defect prediction is to make predictions by mining the historical data using models. Current software defect prediction models mainly focus on the code features of software modules. However, they ignore the connection between software modules. This paper proposed a software defect prediction framework based on graph neural network from a complex network perspective. Firstly, we consider the software as a graph, where nodes represent the classes, and edges represent the dependencies between the classes. Then, we divide the graph into multiple subgraphs using the community detection algorithm. Thirdly, the representation vectors of the nodes are learned through the improved graph neural network model. Lastly, we use the representation vector of node to classify the software defects. The proposed model is tested on the PROMISE dataset, using two graph convolution methods, based on the spectral domain and spatial domain in the graph neural network. The investigation indicated that both convolution methods showed an improvement in various metrics, such as accuracy, F-measure, and MCC (Matthews correlation coefficient) by 86.6%, 85.8%, and 73.5%, and 87.5%, 85.9%, and 75.5%, respectively. The average improvement of various metrics was noted as 9.0%, 10.5%, and 17.5%, and 6.3%, 7.0%, and 12.1%, respectively, compared with the benchmark models.<\/jats:p>","DOI":"10.3390\/e24101373","type":"journal-article","created":{"date-parts":[[2022,9,27]],"date-time":"2022-09-27T23:12:12Z","timestamp":1664320332000},"page":"1373","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Research of Software Defect Prediction Model Based on Complex Network and Graph Neural Network"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8189-8208","authenticated-orcid":false,"given":"Mengtian","family":"Cui","sequence":"first","affiliation":[{"name":"Key Laboratory of Computer System, State Ethnic Affairs Commission, Southwest Minzu University, Chengdu 610041, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8301-0794","authenticated-orcid":false,"given":"Songlin","family":"Long","sequence":"additional","affiliation":[{"name":"Key Laboratory of Computer System, State Ethnic Affairs Commission, Southwest Minzu University, Chengdu 610041, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1114-5806","authenticated-orcid":false,"given":"Yue","family":"Jiang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Computer System, State Ethnic Affairs Commission, Southwest Minzu University, Chengdu 610041, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xu","family":"Na","sequence":"additional","affiliation":[{"name":"Swiss Center for Data and Network Sciences, University of Fribourg, 1700 Fribourg, Switzerland"},{"name":"Faculty of Business, Economics and Informatics, University of Zurich, R\u00e4mistrasse 71, 8006 Zurich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1109\/MC.2022.3145680","article-title":"Software Development Metrics with a Purpose","volume":"55","author":"Robles","year":"2022","journal-title":"Computer"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Liu, Y., Sun, F., Yang, J., and Zhou, D. (2020, January 3\u20136). Software Defect Prediction Model Based on Improved BP Neural Network. Proceedings of the 2019 6th International Conference on Dependable Systems and Their Applications (DSA), Harbin, China.","DOI":"10.1109\/DSA.2019.00095"},{"key":"ref_3","first-page":"721","article-title":"A Novel Feature Selection Method Based on Maximum Likelihood Logistic Regression for Imbalanced Learning in Software Defect Prediction","volume":"17","author":"Bashir","year":"2020","journal-title":"Int. Arab J. Inf. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1007\/s13198-021-01326-1","article-title":"Effective software defect prediction using support vector machines (SVMs)","volume":"13","author":"Goyal","year":"2022","journal-title":"Int. J. Syst. Assur. Eng. Manag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"e739","DOI":"10.7717\/peerj-cs.739","article-title":"Software defect prediction using hybrid model (CBIL) of convolutional neural network (CNN) and bidirectional long short-term memory (Bi-LSTM)","volume":"7","author":"Farid","year":"2021","journal-title":"PeerJ Comput. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1049\/iet-sen.2019.0149","article-title":"Software defect prediction via LSTM","volume":"14","author":"Deng","year":"2020","journal-title":"IET Softw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2968","DOI":"10.1016\/j.physa.2011.03.036","article-title":"Community structure of complex software systems: Analysis and applications","volume":"390","author":"Bajec","year":"2011","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zhou, Y., Zhu, Y., and Chen, L. (2020, January 24\u201327). Software Defect-Proneness Prediction with Package Cohesion and Coupling Metrics Based on Complex Network Theory. Proceeding of the International Symposium on Dependable Software Engineering: Theories, Tools, and Applications, Guangzhou, China.","DOI":"10.1007\/978-3-030-62822-2_12"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1007\/s10664-021-09965-5","article-title":"Evaluating network embedding techniques\u2019 performances in software bug prediction","volume":"26","author":"Qu","year":"2021","journal-title":"Empir. Softw. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"96501","DOI":"10.1109\/ACCESS.2021.3095335","article-title":"A Review on Community Detection in Large Complex Networks from Conventional to Deep Learning Methods: A Call for the Use of Parallel Meta-Heuristic Algorithms","volume":"9","author":"Tan","year":"2021","journal-title":"IEEE Access"},{"key":"ref_11","first-page":"128","article-title":"Solutio problematis ad geometriam situs pertinentis","volume":"8","author":"Euler","year":"1741","journal-title":"Comment. Acad. Sci. Petropolitanae"},{"key":"ref_12","unstructured":"Wheeldon, R., and Counsell, S. (2003, January 26\u201327). Power law distributions in class relationships. Proceedings of the Third IEEE International Workshop on Source Code Analysis and Manipulation, Amsterdam, The Netherlands."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"026113","DOI":"10.1103\/PhysRevE.69.026113","article-title":"Finding and evaluating community structure in networks","volume":"69","author":"Newman","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"P10008","DOI":"10.1088\/1742-5468\/2008\/10\/P10008","article-title":"Fast unfolding of communities in large networks","volume":"2008","author":"Blondel","year":"2008","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_15","unstructured":"Gori, M., Monfardini, G., and Scarselli, F. (August, January 31). A new model for learning in graph domains. Proceedings of the 2005 IEEE International Joint Conference on Neural Networks, Montreal, QC, Canada."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1109\/TNN.2008.2005605","article-title":"The Graph Neural Network Model","volume":"20","author":"Scarselli","year":"2008","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"60588","DOI":"10.1109\/ACCESS.2021.3071274","article-title":"Graph Neural Network: A Comprehensive Review on Non-Euclidean Space","volume":"9","author":"Asif","year":"2021","journal-title":"IEEE Access"},{"key":"ref_18","unstructured":"Estrach, J.B., Zaremba, W., Szlam, A., and LeCun, Y. (2014, January 14\u201316). Spectral networks and deep locally connected networks on graphs. Proceedings of the 2nd International Conference on Learning Representations, ICLR, Banff, AB, Canada."},{"key":"ref_19","unstructured":"Defferrard, M., Bresson, X., and Vandergheynst, P. (2016). Convolutional neural networks on graphs with fast localized spectral filtering. arXiv."},{"key":"ref_20","unstructured":"Kipf, T.N., and Welling, M. (2017, January 24\u201326). Semi-Supervised Classification with Graph Convolutional Networks. Proceedings of the 5th International Conference on Learning Representations, ICLR 2017, Toulon, France. Available online: https:\/\/openreview.net\/forum?id=SJU4ayYgl."},{"key":"ref_21","unstructured":"Hamilton, W., Ying, Z., and Leskovec, J. (2017). Inductive representation learning on large graphs. arXiv."},{"key":"ref_22","unstructured":"Velickovic, P., Cucurull, G., Casanova, A., Romero, A., Li\u00f2, P., and Bengio, Y. (May, January 30). Graph Attention Networks. Proceedings of the 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada. Available online: https:\/\/openreview.net\/forum?id=rJXMpikCZ."},{"key":"ref_23","unstructured":"Xu, K., Hu, W., Leskovec, J., and Jegelka, S. (2019, January 6\u20139). How Powerful are Graph Neural Networks?. Proceedings of the 7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA. Available online: https:\/\/openreview.net\/forum?id=ryGs6iA5Km."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1109\/TR.2022.3149658","article-title":"Software Bug Number Prediction Based on Complex Network Theory and Panel Data Model","volume":"71","author":"Yang","year":"2022","journal-title":"IEEE Trans. Reliab."},{"key":"ref_25","unstructured":"Van Rossum, G., and Drake, F.L. (2009). Python 3 Reference Manual, CreateSpace."},{"key":"ref_26","unstructured":"Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., and Antiga, L. (2019). PyTorch: An Imperative Style, High-Performance Deep Learning Library. Advances in Neural Information Processing Systems 32, Curran Associates, Inc.. Available online: http:\/\/papers.neurips.cc\/paper\/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Jureczko, M., and Madeyski, L. (2010, January 12\u201313). Towards identifying software project clusters with regard to defect prediction. Proceedings of the 6th International Conference on Predictive Models in Software Engineering, Timisoara, Romania.","DOI":"10.1145\/1868328.1868342"},{"key":"ref_28","unstructured":"Mani, I., and Zhang, I. (2003, January 21\u201324). kNN approach to unbalanced data distributions: A case study involving information extraction. Proceedings of the Workshop on Learning from Imbalanced Datasets, ICML, Washington, DC, USA."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"6147","DOI":"10.1007\/s11227-021-04113-8","article-title":"Software-defect prediction within and across projects based on improved self-organizing data mining","volume":"78","author":"Zhang","year":"2022","journal-title":"J. Supercomput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2023","DOI":"10.1007\/s10462-021-10044-w","article-title":"Handling Class-Imbalance with KNN (Neighbourhood) Under-Sampling for Software Defect Prediction","volume":"55","author":"Goyal","year":"2022","journal-title":"Artif. Intell. Rev."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/10\/1373\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:40:37Z","timestamp":1760143237000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/10\/1373"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,27]]},"references-count":30,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["e24101373"],"URL":"https:\/\/doi.org\/10.3390\/e24101373","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,27]]}}}