Graph-Mamba is a novel graph model that integrates a selective state space model (SSM) with a data-dependent node selection mechanism to enhance long-range context modeling in graph networks. The SSM, specifically Mamba, is adapted to handle non-sequential graph data by formulating graph-centric node prioritization and permutation strategies. This approach captures long-range dependencies more effectively than traditional attention mechanisms, which suffer from quadratic computational costs in large graphs. Extensive experiments on ten benchmark datasets demonstrate that Graph-Mamba outperforms state-of-the-art methods in long-range graph prediction tasks, achieving linear-time computational complexity and significantly reduced GPU memory consumption. The code and models are publicly available at <https://github.com/bowang-lab/Graph-Mamba>.Graph-Mamba is a novel graph model that integrates a selective state space model (SSM) with a data-dependent node selection mechanism to enhance long-range context modeling in graph networks. The SSM, specifically Mamba, is adapted to handle non-sequential graph data by formulating graph-centric node prioritization and permutation strategies. This approach captures long-range dependencies more effectively than traditional attention mechanisms, which suffer from quadratic computational costs in large graphs. Extensive experiments on ten benchmark datasets demonstrate that Graph-Mamba outperforms state-of-the-art methods in long-range graph prediction tasks, achieving linear-time computational complexity and significantly reduced GPU memory consumption. The code and models are publicly available at <https://github.com/bowang-lab/Graph-Mamba>.