Graph data has emerged as a critical resource due to its rich structural and semantic information. Anonymization is essential for preventing node re-identification during graph data sharing or publishing. Different users have diverse privacy requirements, motivating research on personalized anonymization. In practice, multiple data analysts may demand different levels of privacy protection for the same graph, requiring regeneration of anonymized graphs for distinct privacy requirements. Existing personalized anonymization methods suffer from high computational overhead when supporting diverse, scenario-specific requirements. To address this inefficiency, we formulate a personalized k2-anonymity model to protect both node degrees and attribute information. Then we design a Hierarchical Personalized Graph Anonymization (HPGA) algorithm to efficiently generate multi-scenario anonymized graphs under varying privacy requirements. HPGA constructs a reusable hierarchical structure and incorporates an efficient privacy requirement matching mechanism for anonymization. It applies edge modification and attribute generalization strategies to generate anonymized graphs. Experimental results on real-world datasets show that HPGA significantly reduces 99% computation time compared to the existing method. In addition, HPGA maintains good data utility.
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