We propose a graph-based framework for privacy preserving data publication, which is a systematic abstraction of existing anonymity approaches and privacy criteria. Graph is explored for dataset representation, background knowledge specification, anonymity operation design, as well as attack inferring analysis. The framework is designed to accommodate various datasets including social networks, relational tables, temporal and spatial sequences, and even possible unknown data models. The privacy and utility measurements of the anonymity datasets are also quantified in terms of graph features. Our experiments show that the framework is capable of facilitating privacy protection by different anonymity approaches for various datasets with desirable performance.