As a popular multimedia representation, 3D Point Clouds (PC) inevitably encounter distortion during their acquisition, processing, coding, and transmission, resulting in visual quality degradation. Therefore, it is critical to propose a Point Cloud Quality Assessment (PCQA) method to perceive the visual quality of PC. In this paper, we propose a no-reference PCQA method through structure sampling and clustering based on graph, which consists of two-stage pre-processing, quality feature extraction, attention-based feature fusion, and feature regression. For pre-processing, considering the Human Visual System (HVS) tendency to perceive distortions in both the global structure and local details of PCs, a two-stage sampling strategy is introduced. Specifically, to adapt to the irregular structure of PCs, it introduces structural key point sampling and local cluster to capture both global and local information, respectively, thereby facilitating more effective learning of distortion features. Then, in quality feature extraction, two modules are designed based on the two-stage pre-processing results (i.e., Global Feature Extraction (GFE) and Local Feature Extraction (LFE)) to respectively extract global and local quality features. Additionally, for attention-based feature fusion, a Unified Feature Integrator (UFI) module is proposed. This module enhances quality perception capability by integrating global features and individual local quality features and introduces the Transformer to interact with the integrated quality features. Finally, feature regression is conducted to map the final features into the quality score. The performance of the proposed method is tested on four publicly available databases, and the experimental results show that the proposed method is superior compared with existing state-of-the-art no-reference PCQA methods in most cases.