Most hyperspectral anomaly detection algorithms are based on various hypothetical models justified by different methods. The closer to the real-world scene distribution a hypothetical model is, the better detection performance usually results, albeit at the expense of increased model complexity. There is also a challenge in most of the detection methods that anomalous components cannot be completely separated from the background due to the difference between hypothetical models and the real-world scene. To address this problem, a novel strategy based on graph theory and the multiple support vector machines technique is proposed in this paper. Firstly, a graphical connected point-based estimation is utilized as a preprocessing procedure to separate potential anomalies from robust backgrounds of the image. Second, without building a hypothetical model, the hyperspectral image is classified into several categories by a clustering method according to the different characteristics of materials. Consequently, for each category, the support vector machine is used to classify anomalous components and background components belonging to specific categories, and the result map of each classification is obtained. Finally, all maps corresponding to various categories are fused by an effective fusion strategy, and the detection result is generated by our method. In the subsequent experiments, we use several state-of-art anomaly detection algorithms in a comparison with our method using both simulated and real-world HSI datasets. The experimental results demonstrate that the proposed method outperforms others.