# Exploring Graph Mamba: A Comprehensive Survey on State-Space Models for Graph Learning

arXiv: https://arxiv.org/abs/2412.18322 · HTML: https://mlsanity.com/paper/2412.18322/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Video, motion and generative Mamba models, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 45 of its 104 references that are in the map.
- First posted on arXiv 24 Dec 2024.

## Placed in

- State-space sequence models (S4, Mamba) / [Video, motion and generative Mamba models](https://mlsanity.com/ssm/video-motion-and-generative-mamba-models/)

## Builds on (most cited first, 30 of 45)

- [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)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Embodied Hands: Modeling and Capturing Hands and Bodies Together](https://mlsanity.com/paper/2201.02610/) (2022)
- [Do We Really Need Complicated Model Architectures For Temporal Networks?](https://mlsanity.com/paper/2302.11636/) (2023)
- [Graph-Mamba: Towards Long-Range Graph Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2402.00789/) (2024)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Brain Network Transformer](https://mlsanity.com/paper/2210.06681/) (2022)
- [A Generalization of ViT/MLP-Mixer to Graphs](https://mlsanity.com/paper/2212.13350/) (2022)
- [FBNETGEN: Task-aware GNN-based fMRI Analysis via Functional Brain Network Generation](https://mlsanity.com/paper/2205.12465/) (2022)
- [Mamba-360: Survey of State Space Models as Transformer Alternative for Long Sequence Modelling: Methods, Applications, and Challenges](https://mlsanity.com/paper/2404.16112/) (2024)
- [State Space Model for New-Generation Network Alternative to Transformers: A Survey](https://mlsanity.com/paper/2404.09516/) (2024)
- [A Survey on Graph Neural Networks and Graph Transformers in Computer Vision: A Task-Oriented Perspective](https://mlsanity.com/paper/2209.13232/) (2022)
- [Vision Mamba: A Comprehensive Survey and Taxonomy](https://mlsanity.com/paper/2405.04404/) (2024)
- [Knowledge Graphs Meet Multi-Modal Learning: A Comprehensive Survey](https://mlsanity.com/paper/2402.05391/) (2024)
- [Hamba: Single-view 3D Hand Reconstruction with Graph-guided Bi-Scanning Mamba](https://mlsanity.com/paper/2407.09646/) (2024)
- [A Survey of Mamba](https://mlsanity.com/paper/2408.01129/) (2024)
- [A Comprehensive Survey of Dynamic Graph Neural Networks: Models, Frameworks, Benchmarks, Experiments and Challenges](https://mlsanity.com/paper/2405.00476/) (2024)
- [Modeling Multivariate Biosignals With Graph Neural Networks and Structured State Space Models](https://mlsanity.com/paper/2211.11176/) (2022)
- [Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systems](https://mlsanity.com/paper/2410.19892/) (2024)
- [STG-Mamba: Spatial-Temporal Graph Learning via Selective State Space Model](https://mlsanity.com/paper/2403.12418/) (2024)
- [Mamba in Vision: A Comprehensive Survey of Techniques and Applications](https://mlsanity.com/paper/2410.03105/) (2024)
- [DyG-Mamba: Continuous State Space Modeling on Dynamic Graphs](https://mlsanity.com/paper/2408.06966/) (2024)

## Built on by (most cited first, 2 of 2)

- [pLSTM: parallelizable Linear Source Transition Mark networks](https://mlsanity.com/paper/2506.11997/) (2025)
- [GLADMamba: Unsupervised Graph-Level Anomaly Detection Powered by Selective State Space Model](https://mlsanity.com/paper/2503.17903/) (2025)

## Abstract (arXiv)

Graph Mamba, a powerful graph embedding technique, has emerged as a cornerstone in various domains, including bioinformatics, social networks, and recommendation systems. This survey represents the first comprehensive study devoted to Graph Mamba, to address the critical gaps in understanding its applications, challenges, and future potential. We start by offering a detailed explanation of the original Graph Mamba architecture, highlighting its key components and underlying mechanisms. Subsequently, we explore the most recent modifications and enhancements proposed to improve its performance and applicability. To demonstrate the versatility of Graph Mamba, we examine its applications across diverse domains. A comparative analysis of Graph Mamba and its variants is conducted to shed light on their unique characteristics and potential use cases. Furthermore, we identify potential areas where Graph Mamba can be applied in the future, highlighting its potential to revolutionize data analysis in these fields. Finally, we address the current limitations and open research questions associated with Graph Mamba. By acknowledging these challenges, we aim to stimulate further research and development in this promising area. This survey serves as a valuable resource for both newcomers and experienced researchers seeking to understand and leverage the power of Graph Mamba.