# FSOpt_k: Finding the Optimal Anonymization Level for a Social Network Graph
## 6 Experimental Results
### Information Loss Metrics
#### 6.2.3 Analysis of Community Structure Metrics  
In order to evaluate the proposed algorithm in this section, the graph community criteria are used, which include the variation of information (VI) [53], normalized mutual information [53] (NMI), the split-join distance [54], the Rand index [55], and the adjusted Rand index [56], to evaluate NaFa4 KDA algorithm. When the community structure of the two graphs is alike, the VI and split-join metrics are zero, and the other metrics are one. Figure 12: Average of the obtained error values on all datasets. The parameters that their best value is one are reversed to provide a better understanding of the evaluation outcomes. Thus, lower values for all metrics in this section indicate better algorithm efficiency. Given that VA and KDVEM include fake nodes in the social network graph, the number of vector members is different for the two graphs. Therefore, these algorithms are neglected when this condition occurs. Evaluation Results of Community Structure Metrics  
Figure 13 shows the results of the evaluation of the algorithms on the Dolphins dataset for different \(\mathcal{L}\) values. As can be seen in this figure, in most cases, the evaluation results show the improvement of the proposed algorithm in terms of structural graph criteria. These results show that in addition to the proposed algorithm being able to find the optimal value of k in a short time, it is able to preserve the structural properties of the social network graph. In other words, in addition to partitioning the graph nodes close to the UMGA algorithm, the use of PL and coreness parameters has further preserved the graph structure after the anonymization operation. However, the evaluation results on this dataset for \(\mathcal{L}\) = 0.2 indicate an increase in the error of the proposed algorithm compared to UMGA. We had the same result for the T criterion in this figure. These results show that by applying the FSopt_k algorithm to this dataset for only \(\mathcal{L}\) = 0.2, the structure of the anonymous graph is more modified than the UMGA algorithm. We obtained similar results for structural graph metrics on the co-authorship dataset. These results are shown in Figure 14. As we infer from these results, the use of the proposed algorithm on this dataset has led to an increase in the utility of the anonymous graph. The results show that the proposed algorithm is able to preserve the properties of the social network graph in addition to finding the optimal value of k at low runtime. Figure 13: Evaluated values of community structure metrics on Dolphins for (a): \(\mathcal{L}=0.05\), (b): \(\mathcal{L}=0.1\), and (c): \(\mathcal{L}=0.2\). The results of the evaluation of FSopt_k on the power grid dataset are shown in Figure 15. As shown in this figure, the error generated in the structural features of the social network graph is less than the UMGA algorithm when applying the FSopt_k algorithm on the graph. Therefore, it can be concluded that the proposed algorithm was effective in reducing the number of changes to the social network graph after anonymization. Figure 14: Evaluated values of community structure metrics on netscience for (**a**): \(\mathcal{L}=0.05\), (**b**): \(\mathcal{L}=0.1\), and (**c**): \(\mathcal{L}=0.2\). Figure 15: Evaluated values of community structure metrics on power grid for (**a**): \(\mathcal{L}=0.05\), (**b**): \(\mathcal{L}=0.1\), and (**c**): \(\mathcal{L}=0.2\). Figure 16 denotes the evaluation results of the proposed algorithm on the polbooks dataset. The evaluation results indicate an improvement in anonymous graph utility, which is the result of using more effective criteria to change the graph. Figure 17 shows the mean values of errors obtained for each criterion on all datasets. As shown in this figure, on average, employing the proposed algorithm on the dataset leads to fewer changes in the social network graph.