# LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering

arXiv: https://arxiv.org/abs/2405.11801 · HTML: https://mlsanity.com/paper/2405.11801/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 61 references that are in the map.
- First posted on arXiv 20 May 2024.

## Builds on (most cited first, 30 of 40)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Towards Unsupervised Deep Graph Structure Learning](https://mlsanity.com/paper/2201.06367/) (2022)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Deep Graph Clustering via Dual Correlation Reduction](https://mlsanity.com/paper/2112.14772/) (2021)
- [Multi-view Contrastive Graph Clustering](https://mlsanity.com/paper/2110.11842/) (2021)
- [ProGCL: Rethinking Hard Negative Mining in Graph Contrastive Learning](https://mlsanity.com/paper/2110.02027/) (2021)
- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [Structural Entropy Guided Graph Hierarchical Pooling](https://mlsanity.com/paper/2206.13510/) (2022)
- [Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs](https://mlsanity.com/paper/2104.02228/) (2021)
- [Dink-Net: Neural Clustering on Large Graphs](https://mlsanity.com/paper/2305.18405/) (2023)
- [SE-GSL: A General and Effective Graph Structure Learning Framework through Structural Entropy Optimization](https://mlsanity.com/paper/2303.09778/) (2023)
- [Graph Communal Contrastive Learning](https://mlsanity.com/paper/2110.14863/) (2021)
- [A Self-supervised Mixed-curvature Graph Neural Network](https://mlsanity.com/paper/2112.05393/) (2021)
- [Self-Supervised Continual Graph Learning in Adaptive Riemannian Spaces](https://mlsanity.com/paper/2211.17068/) (2022)
- [Pseudo-Riemannian Graph Convolutional Networks](https://mlsanity.com/paper/2106.03134/) (2021)
- [ACE-HGNN: Adaptive Curvature Exploration Hyperbolic Graph Neural Network](https://mlsanity.com/paper/2110.07888/) (2021)
- [Stop using the elbow criterion for k-means and how to choose the number of clusters instead](https://mlsanity.com/paper/2212.12189/) (2022)
- [A Self-supervised Riemannian GNN with Time Varying Curvature for Temporal Graph Learning](https://mlsanity.com/paper/2208.14073/) (2022)
- [Hyperbolic Geometric Graph Representation Learning for Hierarchy-imbalance Node Classification](https://mlsanity.com/paper/2304.05059/) (2023)

## Built on by (most cited first, 21 of 21)

- [RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry](https://mlsanity.com/paper/2502.03251/) (2025)
- [Spiking Graph Neural Network on Riemannian Manifolds](https://mlsanity.com/paper/2410.17941/) (2024)
- [Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models](https://mlsanity.com/paper/2510.17457/) (2025)
- [Transformers versus the EM Algorithm in Multi-class Clustering](https://mlsanity.com/paper/2502.06007/) (2025)
- [Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Models](https://mlsanity.com/paper/2603.00618/) (2026)
- [ASIL: Augmented Structural Information Learning for Deep Graph Clustering in Hyperbolic Space](https://mlsanity.com/paper/2504.09970/) (2025)
- [Unsupervised Graph Clustering with Deep Structural Entropy](https://mlsanity.com/paper/2505.14040/) (2025)
- [KAT-Coder-V2.5 Technical Report](https://mlsanity.com/paper/2607.05471/) (2026)
- [Hyperbolic Continuous Structural Entropy for Hierarchical Clustering](https://mlsanity.com/paper/2512.00524/) (2025)
- [Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger](https://mlsanity.com/paper/2603.00599/) (2026)
- [Structural Entropy Guided Probabilistic Coding](https://mlsanity.com/paper/2412.08841/) (2024)
- [StarEmbed: Benchmarking Time Series Foundation Models on Astronomical Observations of Variable Stars](https://mlsanity.com/paper/2510.06200/) (2025)
- [Towards LLM-Empowered Knowledge Tracing via LLM-Student Hierarchical Behavior Alignment in Hyperbolic Space](https://mlsanity.com/paper/2602.22879/) (2026)
- [Beyond the Academic Monoculture: A Unified Framework and Industrial Perspective for Attributed Graph Clustering](https://mlsanity.com/paper/2603.20829/) (2026)
- [Riemannian Geometry Speaks Louder Than Words: From Graph Foundation Model to Next-Generation Graph Intelligence](https://mlsanity.com/paper/2603.21601/) (2026)
- [Towards Effective, Efficient and Unsupervised Social Event Detection in the Hyperbolic Space](https://mlsanity.com/paper/2412.10712/) (2024)
- [Human-Centric Community Detection in Hybrid Metaverse Networks with Integrated AI Entities](https://mlsanity.com/paper/2502.10750/) (2025)
- [FTSCommDetector: Discovering Behavioral Communities through Temporal Synchronization](https://mlsanity.com/paper/2510.00014/) (2025)
- [Parameter-Free Clustering via Self-Supervised Consensus Maximization (Extended Version)](https://mlsanity.com/paper/2511.09211/) (2025)
- [Hierarchical Textual Knowledge for Enhanced Image Clustering](https://mlsanity.com/paper/2604.11144/) (2026)
- [Riemannian Graph Tokenizer for Structural Knowledge Transfer](https://mlsanity.com/paper/2610.15427/) (2026)

## Abstract (arXiv)

Graph clustering is a fundamental problem in machine learning. Deep learning methods achieve the state-of-the-art results in recent years, but they still cannot work without predefined cluster numbers. Such limitation motivates us to pose a more challenging problem of graph clustering with unknown cluster number. We propose to address this problem from a fresh perspective of graph information theory (i.e., structural information). In the literature, structural information has not yet been introduced to deep clustering, and its classic definition falls short of discrete formulation and modeling node features. In this work, we first formulate a differentiable structural information (DSI) in the continuous realm, accompanied by several theoretical results. By minimizing DSI, we construct the optimal partitioning tree where densely connected nodes in the graph tend to have the same assignment, revealing the cluster structure. DSI is also theoretically presented as a new graph clustering objective, not requiring the predefined cluster number. Furthermore, we design a neural LSEnet in the Lorentz model of hyperbolic space, where we integrate node features to structural information via manifold-valued graph convolution. Extensive empirical results on real graphs show the superiority of our approach.