## 4 Tc\(\alpha\)-PIa
### Node Clustering Based on Similarity Tree
\[ACC=\frac{1}{|N|}\sum_{i=1}^{|N|}C_{i}\] (8) where \(|N|\) is the number of nodes in the graph and \(C_{i}\) is the local clustering coefficient of node \(i\). * **Average Shortest Path Length (APL)**. The average shortest path length is the average length of the shortest path between any two nodes in the graph. By comparing the average shortest path length of the original and anonymous graphs, we can understand the influence of anonymization on graph connectivity. \[APL=\frac{\sum_{i\
eq j}path(v_{i},v_{j})}{|N|(|N|-1)}\] (9) where \(path(v_{i},v_{j})\) is the length of the shortest path between nodes \(v_{i}\) and \(v_{j}\). * **Eigenvector Centrality (EC)**. Eigenvector centrality is used to measure the importance of nodes in a network structure. Analyzing the change in eigenvector centrality can provide insight into changes in the importance and influence of nodes caused by anonymization. ### Comparison and Analysis of Experimental Results

**Implementation. ** The experimental setup consists of a device manufactured by Lenovo located in Beijing, China, equipped with an AMD Ryzen 5 5600H processor with Radeon Graphics clocked at 3.30 GHz and 16 GB RAM. The operating system used is Windows 10 Home, and the programming language used for the implementation is Python 3.7. **Comparison. ** To demonstrate the effectiveness of our proposed TC\(\alpha\)-PIA scheme, we performed the following experimental comparisons: (1) We compared the TC\(\alpha\)-PIA scheme with the GPPS [16] introduced in Section 1. For a fair comparison, we used consistent \(\alpha\) values for uniform anonymity and compared them with the GPPS scheme. In addition, wecompared the results under different \(\alpha\) values (referred to as TC\(\alpha\)-PIA\({}_{\text{second}}\)), with those of the GPPS scheme. Note that the results of GPPS are averaged over several experiments under non-isomorphic conditions, while the TC\(\alpha\)-PIA\({}_{\text{second}}\) results are the average of several experiments with different \(\alpha\) values required by different users. (2) To validate the effectiveness of tree clustering based on the combined criterion, we compared it with traditional clustering based on Euclidean similarity within the same anonymity scheme. **Experimental settings. ** We set \(k=5\), 10, 15, 20, 25. For TCA-PIA, we set three \(\alpha\) values: \(\alpha_{1}=100\%\), \(\alpha_{2}=50\%\), and \(\alpha_{3}=10\%\). #### 5.3.1 Comparison of the Overall Performance of Schemes

This experiment was performed on both complete and random graphs. For random graphs, we followed the method in reference [13] and randomly extracted 500 to 2000 nodes and their edges from the larger Ca-CondMat dataset to construct four random graph datasets for further experimental comparison with the GPPS scheme [16]. These datasets are denoted as CA-CM\({}_{1}\), CA-CM\({}_{2}\), CA-CM\({}_{3}\), and CA-CM\({}_{4}\), respectively, and contain 500, 1000, 1500, and 2000 nodes and their corresponding edges. Complete graphs
* **Comparison of IL. ** Figure 7a shows the effect of different schemes on the IL in the soc-wiki-Vote dataset. It is evident that as \(\alpha\) decreases, the IL of TC\(\alpha\)-PIA increases, indicating fewer modifications to the original graph and better preservation of the original data. In addition, for the same \(\alpha\), IL decreases as \(k\) increases, suggesting that higher privacy levels result in lower utility of the graph. The lower IL at \(k=15\) compared to \(k=20\) is due to dataset inhomogeneities causing experimental fluctuations. Compared to GPPS, TC\(\alpha\)-PIA(\(\alpha_{1}\)), TC\(\alpha\)-PIA(\(\alpha_{2}\)), and TC\(\alpha\)-PIA(\(\alpha_{3}\)) perform better, as the proposed scheme effectively limits the addition of fake nodes and edges, reducing their impact on the original graph. Unlike TC\(\alpha\)-PIA, TC\(\alpha\)-PIA\({}_{\text{second}}\) considers the different \(\alpha\) requirements of all users.