{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T01:47:13Z","timestamp":1782265633984,"version":"3.54.5"},"reference-count":33,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T00:00:00Z","timestamp":1781568000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Community detection in attributed networks becomes considerably more challenging when the number of communities is unknown in advance. Most existing deep community detection methods assume a fixed community count, whereas reinforcement learning (RL)-based alternatives often suffer from overestimated action values and unstable target updates. To address these limitations, we propose GCR-Net (Graph Community Recognition Network), an RL-guided framework that combines representation learning with adaptive community-count selection. The method adapts decoupled value estimation and gradual anchor-network updates from established deep RL techniques to a formal MDP over candidate community counts. Experiments on citation, social, biomedical, and proteininteraction benchmarks, together with synthetic graphs with more than ten communities, show that GCR-Net delivers competitive NMI and ARI scores with lower variance and more stable optimization than conventional RL baselines. Statistical tests indicate that the clearest gains concern training stability rather than large accuracy margins.<\/jats:p>","DOI":"10.3390\/a19060484","type":"journal-article","created":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T03:27:21Z","timestamp":1781666841000},"page":"484","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["GCR-Net: Stable Reinforcement Learning for Community Detection with Unknown Community Count in Attributed Networks"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-8845-2740","authenticated-orcid":false,"given":"Wencai","family":"He","sequence":"first","affiliation":[{"name":"College of Cyber Security, Tarim University, Alar 843300, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-9107-3357","authenticated-orcid":false,"given":"Zhijie","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-7580-7557","authenticated-orcid":false,"given":"Yuanbin","family":"He","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Tarim University, Alar 843300, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-6857-9288","authenticated-orcid":false,"given":"Ziyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Tarim University, Alar 843300, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-0560-1158","authenticated-orcid":false,"given":"Mingshen","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Tarim University, Alar 843300, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-6945-6376","authenticated-orcid":false,"given":"He","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Tarim University, Alar 843300, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,16]]},"reference":[{"key":"ref_1","first-page":"67","article-title":"Node anomaly detection via multiscale time-frequency fusion and hidden Markov generations in complex networks","volume":"Volume 16536","author":"Hong","year":"2026","journal-title":"Database Systems for Advanced Applications\u2014DASFAA 2026"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1080\/15427951.2004.10129093","article-title":"Graph clustering and minimum cut trees","volume":"1","author":"Flake","year":"2004","journal-title":"Internet Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"718","DOI":"10.14778\/1687627.1687709","article-title":"Graph clustering based on structural\/attribute similarities","volume":"2","author":"Zhou","year":"2009","journal-title":"Proc. VLDB Endow."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1921632.1921638","article-title":"Clustering large attributed graphs: A balance between structural and attribute similarities","volume":"5","author":"Cheng","year":"2011","journal-title":"ACM Trans. Knowl. Discov. Data (TKDD)"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1007\/s10898-014-0247-2","article-title":"SymNMF: Nonnegative low-rank approximation of a similarity matrix for graph clustering","volume":"62","author":"Kuang","year":"2015","journal-title":"J. Glob. Optim."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wang, C., Pan, S., Long, G., Zhu, X., and Jiang, J. (2017). MGAE: Marginalized graph autoencoder for graph clustering. Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, Association for Computing Machinery.","DOI":"10.1145\/3132847.3132967"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Pan, S., Hu, R., Long, G., Jiang, J., Yao, L., and Zhang, C. (2018). Adversarially regularized graph autoencoder for graph embedding. Proceedings of the 27th International Joint Conference on Artificial Intelligence, AAAI Press.","DOI":"10.24963\/ijcai.2018\/362"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wang, C., Pan, S., Hu, R., Long, G., Jiang, J., and Zhang, C. (2019). Attributed graph clustering: A deep attentional embedding approach. Proceedings of the 28th International Joint Conference on Artificial Intelligence, AAAI Press.","DOI":"10.24963\/ijcai.2019\/509"},{"key":"ref_9","unstructured":"Hassani, K., and Khasahmadi, A.H. (2020). Contrastive multi-view representation learning on graphs. Proceedings of the 37th International Conference on Machine Learning, Curran Associates, Inc."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhu, Y., Xu, Y., Yu, F., Liu, Q., Wu, S., and Wang, L. (2021). Graph contrastive learning with adaptive augmentation. Proceedings of the Web Conference 2021, Association for Computing Machinery.","DOI":"10.1145\/3442381.3449802"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhao, H., Yang, X., Wang, Z., Yang, E., and Deng, C. (2021). Graph debiased contrastive learning with joint representation clustering. Proceedings of the 30th International Joint Conference on Artificial Intelligence, AAAI Press.","DOI":"10.24963\/ijcai.2021\/473"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Li, X., Li, B., Mabu, S., and Hirasawa, K. (2012). A continuous estimation of distribution algorithm by evolving graph structures using reinforcement learning. 2012 IEEE Congress on Evolutionary Computation, IEEE.","DOI":"10.1109\/CEC.2012.6256481"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Duan, Y., Wang, Z., Lu, J., Lin, X., and Zhou, J. (2018). GraphBit: Bitwise interaction mining via deep reinforcement learning. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, IEEE.","DOI":"10.1109\/CVPR.2018.00863"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Liu, Y., Liang, K., Xia, J., Yang, X., Zhou, S., Liu, M., Liu, X., and Li, S.Z. (2023). Reinforcement graph clustering with unknown cluster number. Proceedings of the 31st ACM International Conference on Multimedia, Association for Computing Machinery.","DOI":"10.1145\/3581783.3612155"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1109\/TCSVT.2021.3055625","article-title":"Low-rank tensor graph learning for multi-view subspace clustering","volume":"32","author":"Chen","year":"2021","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7603","DOI":"10.1609\/aaai.v36i7.20726","article-title":"Deep graph clustering via dual correlation reduction","volume":"Volume 36","author":"Liu","year":"2022","journal-title":"Proceedings of the AAAI Conference on Artificial Intelligence"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"9037","DOI":"10.1109\/TKDE.2022.3220948","article-title":"Rethinking graph auto-encoder models for attributed graph clustering","volume":"35","author":"Mrabah","year":"2023","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_18","first-page":"51","article-title":"PVGCL: Graph contrastive learning with purified view modeling for spurious link detection","volume":"Volume 16536","author":"Xue","year":"2026","journal-title":"Database Systems for Advanced Applications\u2014DASFAA 2026"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhao, P. (2015). gSparsify: Graph motif based sparsification for graph clustering. Proceedings of the 24th ACM International Conference on Information and Knowledge Management, Association for Computing Machinery.","DOI":"10.1145\/2806416.2806543"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Yin, H., Benson, A.R., Leskovec, J., and Gleich, D.F. (2017). Local higher-order graph clustering. Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Association for Computing Machinery.","DOI":"10.1145\/3097983.3098069"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1109\/TMM.2010.2041101","article-title":"Video annotation through search and graph reinforcement mining","volume":"12","author":"Moxley","year":"2010","journal-title":"IEEE Trans. Multimed."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1919","DOI":"10.1109\/TPAMI.2022.3161600","article-title":"Learning deep binary descriptors via bitwise interaction mining","volume":"45","author":"Wang","year":"2023","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Jia, Y., Tan, Z., and Zhang, J. (2019). DKDR: An approach of knowledge graph and deep reinforcement learning for disease diagnosis. 2019 IEEE Intl Conf on Parallel & Distributed Processing with Applications, Big Data & Cloud Computing, Sustainable Computing & Communications, Social Computing & Networking (ISPA\/BDCloud\/SocialCom\/SustainCom), IEEE.","DOI":"10.1109\/ISPA-BDCloud-SustainCom-SocialCom48970.2019.00187"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"85348","DOI":"10.1109\/ACCESS.2020.2991257","article-title":"Reinforcement learning over knowledge graphs for explainable dialogue intent mining","volume":"8","author":"Yang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Qiao, W., Feng, Y., Li, T., Zhang, Z., Xu, Z., Ma, Z., Shen, Y., Ma, J., and Liu, Y. (2025). SLOT: Provenance-driven APT detection through graph reinforcement learning. Proceedings of the 2025 ACM SIGSAC Conference on Computer and Communications Security, Association for Computing Machinery.","DOI":"10.1145\/3719027.3744788"},{"key":"ref_26","first-page":"2613","article-title":"Double Q-learning","volume":"Volume 23","author":"Hasselt","year":"2010","journal-title":"Advances in Neural Information Processing Systems"},{"key":"ref_27","first-page":"2094","article-title":"Deep reinforcement learning with double Q-learning","volume":"Volume 30","author":"Hasselt","year":"2016","journal-title":"Proceedings of the AAAI Conference on Artificial Intelligence"},{"key":"ref_28","unstructured":"Lillicrap, T.P., Hunt, J.J., Pritzel, A., Heess, N., Erez, T., Tassa, Y., Silver, D., and Wierstra, D. (2016, January 2\u20134). Continuous control with deep reinforcement learning. Proceedings of the International Conference on Learning Representations (ICLR), San Juan, Puerto Rico."},{"key":"ref_29","first-page":"40","article-title":"Revisiting semi-supervised learning with graph embeddings","volume":"Volume 48","author":"Yang","year":"2016","journal-title":"Proceedings of the 33rd International Conference on Machine Learning"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Cui, G., Zhou, J., Yang, C., and Liu, Z. (2020). Adaptive graph encoder for attributed graph embedding. Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Association for Computing Machinery.","DOI":"10.1145\/3394486.3403140"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"9978","DOI":"10.1609\/aaai.v35i11.17198","article-title":"Deep fusion clustering network","volume":"Volume 35","author":"Tu","year":"2021","journal-title":"Proceedings of the AAAI Conference on Artificial Intelligence"},{"key":"ref_32","unstructured":"Xia, J., Wu, L., Wang, G., Chen, J., and Li, S.Z. (2022). ProGCL: Rethinking hard negative mining in graph contrastive learning. Proceedings of the 39th International Conference on Machine Learning, Curran Associates, Inc."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Liu, Y., Zheng, Y., Zhang, D., Chen, H., Peng, H., and Pan, S. (2022). Towards unsupervised deep graph structure learning. Proceedings of the ACM Web Conference 2022, Association for Computing Machinery.","DOI":"10.1145\/3485447.3512186"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/6\/484\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T01:15:58Z","timestamp":1782263758000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/6\/484"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,16]]},"references-count":33,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["a19060484"],"URL":"https:\/\/doi.org\/10.3390\/a19060484","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,16]]}}}