## 2 Related Works
This leads to an increase in fake edges and exacerbates the inconsistency between the anonymized and original data. Hence, data availability cannot be guaranteed, and it is difficult to extend this scheme to scenarioswith large \(k\) and complex graph structures. To prevent adversaries from identifying target nodes through neighborhood information, [PERSON] et al. (2019) proposed a \(kt\)-safety method. This method requires each node in the graph to have a candidate set containing at least \(k\) other nodes with the same non-sensitive attributes and similar neighborhood structures, thereby avoiding the unique identification of any node. However, this scheme has further room for improvement in graph utility. **Structure protection. ** The subgraph is essentially private information of the social network and is vulnerable to privacy attacks. To defend against these privacy attacks, researchers have proposed various privacy-preserving techniques, which mainly include structural anonymization through automorphism and isomorphism methods. For anonymization through automorphism, [PERSON] et al. (2019) combined the concepts of \(k\)-neighborhood and automorphism for neighborhood subgraph anonymization, which achieves the anonymous hiding of 1-hop or even 2-hop neighborhood information. This method not only satisfies \(k\)-anonymity, but can also structurally avoid a certain degree of attacks. Based on \(k\)-automorphism, [PERSON] et al. (2019) proposed a method to prevent attacks by adding fake nodes and edges based on degree value and subgraph structure, which decreased the data utility significantly. [PERSON] et al. (2019) designed an \(AK\)-secure privacy preservation model based on graph automorphism. This model first decomposes the original graph into multiple isomorphic graphs and processes each graph using crossing edges. Although these methods achieve a good balance between graph anonymity and data utility automorphism, the problem of query leakage remains. Researchers have leveraged the isomorphism algorithm to address this problem. For isomorphism methods, [PERSON] et al. (2019) proposed a \(k\)-isomorphism anonymization scheme, which achieves \(k\)-isomorphism by partitioning the graph and adding or removing edges. This scheme also introduces a dynamic publication mechanism to defend against structural attacks. However, this method relies on high-quality graph partitioning to form \(k\)-isomorphic subgraphs. Poor graph partitioning can result in significant information loss or failure to achieve \(k\)-anonymity. [PERSON] et al. (2019) proposed a novel \(K^{+}\)-isomorphism method to achieve anonymity for communities or subgraphs. This method first partitions \(m\) communities into \(n\) similar subgraph clusters, and then further anonymizes these clusters to ensure that each cluster contains at least \(k\) isomorphic communities. However, this approach requires pre-detected communities or subgraphs, which may not always be available in practice. Therefore, it is crucial to design anonymization methods that do not rely on pre-detected communities to enhance their applicability in various scenarios. In general, anonymizing social networks while preserving graph utility is critical for the design and implementation of anonymization schemes. However, most existing schemes lack flexibility, and cannot satisfy different requirements. To address these challenges, we propose a novel \(\alpha\) partial isomorphic anonymity scheme based on node clustering. This scheme considers different user privacy requirements and strikes a balance between graph privacy and utility.