无需预设聚类数，基于双曲空间的结构信息学习实现高效去偏图聚类。

Graph clustering is a longstanding topic in machine learning. Recently, deep methods have achieved results but still require predefined cluster numbers K and struggle with imbalanced graphs. We study deep graph clustering without K considering realistic imbalance through structural information theory. In the literature, structural information is rarely used in deep clustering, and its classic discrete definition neglects node attributes while exhibiting prohibitive complexity. In this paper, we establish a differentiable structural information framework, generalizing the discrete formalism to the continuous realm. We design a hyperbolic model (LSEnet) to learn the neural partitioning tree in the Lorentz model. Theoretically, we demonstrate its capability in clustering without K and identifying minority clusters. Second, we refine hyperbolic representations to enhance graph semantics. Since tree contrastive learning is non-trivial and costs quadratic complexity, we advance our theory by discovering that structural entropy bounds the tree contrastive loss. Finally, we approach graph clustering through a novel augmented structural information learning (ASIL), which offers an efficient objective to integrate hyperbolic partitioning tree construction and contrastive learning. With a provable improvement in graph conductance, ASIL achieves effective debiased graph clustering in linear complexity. Extensive experiments show ASIL outperforms 20 strong baselines by an average of +12.42% in NMI on the Citeseer dataset.