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Information hiding allows us to hide secret information into digital objects such as images without significantly distorting the objects. The object containing hidden information will be transmitted to a data receiver via a probably insecure channel. To securely transmit the object carrying hidden information, the distortion caused by data embedding should be as low as possible, which is referred to as the ratedistortion optimization problem. Many conventional methods optimize the data embedding procedure by a heuristic fashion, which may be not optimal in terms of the rate-distortion performance. In this chapter, we introduce novel approaches that use graph theory for information hiding. These graph models are general and can be used for improving the rate-distortion performance of information hiding systems. In addition to rate-distortion optimization, recent graph models used for system design of information hiding will be also reviewed. This chapter is intended as a tutorial introducing advanced graph models applied to information hiding.