Social networks have become integral to daily life, allowing users to connect and share information. The efficient analysis of social networks benefits fields such as epidemiology, information dissemination, marketing, and sentiment analysis. However, the direct publishing of social networks is vulnerable to privacy attacks such as typical 1-neighborhood attacks. This attack can infer the sensitive information of private users using users’ relationships and identities. To defend against these attacks, the k-anonymity scheme is a widely used method for protecting user privacy by ensuring that each user is indistinguishable from at least k−1 other users. However, this approach requires extensive modifications that compromise the utility of the anonymized graph. In addition, it applies uniform privacy protection, ignoring users’ different privacy preferences. To address the above challenges, this paper proposes an anonymity scheme called TCα-PIA (Tree Clustering and α-Partial Isomorphism Anonymization). Specifically, TCα-PIA first constructs a similarity tree to capture subgraph feature information at different levels using a novel clustering method. Then, it extracts the different privacy requirements of each user based on the node cluster. Using the privacy requirements, it employs an α-partial isomorphism-based graph structure anonymization method to achieve personalized privacy requirements for each user. Extensive experiments on four public datasets show that TCα-PIA outperforms other alternatives in balancing graph privacy and utility.