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Article

A Two-View Hierarchical Contrastive Learning-Driven Method for Community Detection

1
School of Computer, Qinghai Normal University, Xining 810008, China
2
State Key Laboratory of Tibetan Intelligence, Xining 810008, China
3
Key Laboratory of Tibetan Information Processing, Ministry of Education, Xining 810008, China
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(12), 2121; https://doi.org/10.3390/math14122121 (registering DOI)
Submission received: 11 May 2026 / Revised: 10 June 2026 / Accepted: 11 June 2026 / Published: 14 June 2026
(This article belongs to the Section E1: Mathematics and Computer Science)

Abstract

Effectively integrating graph topology and node attributes, while assigning nodes with both semantic similarity and structural closeness to the same community, remains a key challenge in attributed graph community detection. To address this challenge, this study proposes TVHCL-CD, a two-view hierarchical contrastive learning-driven method for community detection. The proposed method constructs an attribute view and a modularity view from the node attribute matrix and the modularity matrix, respectively, to model attribute semantics and high-order community structure priors. Structure-aware two-view representations are then learned in parallel through dual-view graph attention encoders incorporating multi-order neighborhood priors. Furthermore, a structure-enhanced Graph Transformer fusion module is designed to achieve node-level adaptive fusion of the two-view representations by introducing a learnable adjacency bias into global self-attention and a view-aware gating mechanism into the feed-forward network. To align the optimization objective with community semantics, a hierarchical contrastive learning strategy is further developed. Specifically, view-level consistency contrastive learning constructs modularity-guided augmented views to improve representation robustness, while community-level semantic contrastive learning incorporates partial ground-truth labels to enhance intra-community compactness and inter-community separation. Finally, clustering is performed on the fused representations to obtain community partitions. Experimental results on eight real-world attributed graphs and the generated tree-like attributed graph Tree-2500 indicate that TVHCL-CD achieves competitive performance under the semi-supervised transductive setting, while ablation results support the contributions of its main components.
Keywords: attributed graph community detection; two-view representation learning; modularity-based prior; structure-enhanced Graph Transformer; hierarchical contrastive learning attributed graph community detection; two-view representation learning; modularity-based prior; structure-enhanced Graph Transformer; hierarchical contrastive learning

Share and Cite

MDPI and ACS Style

Liu, S.; Xiao, Y.; Huang, T.; Zhang, Y.; Wang, Y. A Two-View Hierarchical Contrastive Learning-Driven Method for Community Detection. Mathematics 2026, 14, 2121. https://doi.org/10.3390/math14122121

AMA Style

Liu S, Xiao Y, Huang T, Zhang Y, Wang Y. A Two-View Hierarchical Contrastive Learning-Driven Method for Community Detection. Mathematics. 2026; 14(12):2121. https://doi.org/10.3390/math14122121

Chicago/Turabian Style

Liu, Shun, Yuzhi Xiao, Tao Huang, Yuanli Zhang, and Yifei Wang. 2026. "A Two-View Hierarchical Contrastive Learning-Driven Method for Community Detection" Mathematics 14, no. 12: 2121. https://doi.org/10.3390/math14122121

APA Style

Liu, S., Xiao, Y., Huang, T., Zhang, Y., & Wang, Y. (2026). A Two-View Hierarchical Contrastive Learning-Driven Method for Community Detection. Mathematics, 14(12), 2121. https://doi.org/10.3390/math14122121

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