In this paper, we describe a one-class classification method based on Support Vector Data Description, which exploits multiple graph structures in its optimization process. We derive in a generic solution which can be employed for supervised one-class classification tasks. The devised method can produce linear or non-linear decision functions, depending on the adopted kernel function. In our experiments, we simultaneously adopted two graphs that describe local and global geometric training data relationships, respectively. We evaluated the proposed classifier in publicly available datasets, where its performance compared favorably against closely related methods.