6-DoF object-agnostic grasping in unstructured environments is a critical yet challenging task in robotics. Most current works use non-optimized approaches to sample grasp locations and learn spatial features without concerning the grasping task. This paper proposes GraNet, a graph-based grasp pose generation framework that translates a point cloud scene into multi-level graphs and propagates features through graph neural networks. By building graphs at the scene level, object level, and grasp point level, GraNet enhances feature embedding at multiple scales while progressively converging to the ideal grasping locations by learning. Our pipeline can thus characterize the spatial distribution of grasps in cluttered scenes, leading to a higher rate of effective grasping. Furthermore, we enhance the representation ability of scalable graph networks by a structure-aware attention mechanism to exploit local relations in graphs. Our method achieves state-of-the-art performance on the large-scale GraspNet-1Billion benchmark, especially in grasping unseen objects (+11.62 AP). The real robot experiment shows a high success rate in grasping scattered objects, verifying the effectiveness of the proposed approach in unstructured environments.