6-DoF object grasping is a crucial skill for embodied intelligent robots. Previous methods often rely on large-scale networks for feature extraction, followed by grasp pose prediction, which increases the network's parameter count and overlooks the geometric and graph features of the point cloud. To address these challenges, we propose GraphGrasp, a graph-guided 6-DoF grasping pose prediction method. It performs graph analysis from the perspectives of scene, object, and grasping graphs. First, we introduce a graph feature embedding method based on local-global features to model the scene graph effectively. Then, we use a graph transformer strategy to represent spatial relationships between objects in the object graph. Finally, we propose a multi-metric, multi-level grasp pose evaluation algorithm to predict and explore graspable points, enabling effective construction of grasp graphs and accurate grasp pose evaluation. We test GraphGrasp on the GraspNet-1Billion dataset, and the results show that, compared to previous methods, it achieves nearly the same performance with about $\frac{1}{5}$ of the parameters of state-of-the-art methods, significantly improving grasp pose prediction speed. Additionally, in real-world robot grasping scenarios, GraphGrasp outperforms previous methods in practical grasp pose prediction tasks.