Open Access

REVIEW

Graph-Mamba: A Survey of Selective State Space Models for Graph Learning

Guangyu Xu^1,2,*

1 Future Tech Institute, Guangzhou Huashang University, Guangzhou, China
2 School of the Environment, The University of Queensland, Brisbane, QLD, Australia

* Corresponding Author: Guangyu Xu. Email:

(This article belongs to the Special Issue: The Collection of the Latest Reviews on Advances and Challenges in AI)

Computer Modeling in Engineering & Sciences 2026, 148(2), 6 https://doi.org/10.32604/cmes.2026.084644

Received 27 April 2026; Accepted 28 July 2026; Issue published 28 August 2026

Abstract

The fusion of GNNs and SSMs is creating a new era in the realm of dynamical learning with structures. Graph-Mamba is one of the most promising works in this fast-moving field. With its unique capability to incorporate graph topology and selective dynamics in a stable manner, Graph-Mamba has demonstrated its ability to model intricate relationships. However, the existing research on Graph-Mamba has not been compiled into a coherent form; the theoretical basis and practical implementation of the framework have not been synthesized systematically across different domains. First, we demonstrate the theoretical connection between graph propagation and state space evolution and articulate Graph-Mamba as a hybrid dynamical system defined through selective propagation. We further discuss the particular developments made possible within each application area to which the model is relevant. Regardless of whether spatio-temporal and physical systems, biomedical networks, or heterogeneous graphs are in question, we articulate how selective propagation can be adapted to address specific structural and temporal requirements. In light of this discussion, we formulate the overarching theoretical framework for understanding how Graph-Mamba facilitates selective evolution of graph connectivity and state space evolution through the mediation of contextual selectivity. This survey goes beyond summarizing empirical results and focuses on a more profound methodological change. Specifically, we make a case for viewing Graph-Mamba as a promising paradigm that transforms graph-based learning from a static topological approach to a controllable dynamic one. Essentially, this indicates the convergence of graph theory and dynamical systems that will most likely inspire generalized sequence-structure architectures. Ultimately, Graph-Mamba offers not merely a model design, but a foundational direction for understanding the interplay between selective sequence scanning and structured relational dynamics.

---

Keywords

---