# FSOpt_k: Finding the Optimal Anonymization Level for a Social Network Graph
## 6 Experimental Results
### Information Loss Metrics
#### 6.2.2 General Properties of Graph Analysis
What is clear is that although FSopt_k used better criteria for selecting edges than UMGA in the graph modification process, the accuracy of the algorithm is reduced in some cases. In other words, UMGA uses an optimal partitioning graph to find the best grouping of graph nodes. Therefore, the accuracy of UMGA is very high. However, the proposed algorithm can find the best partitioning of graph nodes using an optimization algorithm with low runtime. Since the purpose of the proposed algorithm in this paper is to reduce the runtime of the anonymization algorithm, it is reasonable to reduce the accuracy of the algorithm. However, as shown in the evaluation results, this decrease in the accuracy of the algorithm is low and does not have much effect on the utility of the anonymous graph. Figure 8: Comparison of error values of the algorithms on Dolphins dataset for (a): \(\mathcal{L}=0.05\), (b): \(\mathcal{L}=0.1\), and (c): \(\mathcal{L}=0.2\). Figure 9: Comparison of error values of the algorithms on netscience dataset for (a): \(\mathcal{L}=0.05\), (b): \(\mathcal{L}=0.1\), and (c): \(\mathcal{L}=0.2\). Figure 11: Comparison of error values of the algorithms on polbooks dataset for (**a**): \(\mathcal{L}=0.05\), (**b**): \(\mathcal{L}=0.1\), and (**c**): \(\mathcal{L}=0.2\). Figure 10: Comparison of error values of the algorithms on power grid dataset for (**a**): \(\mathcal{L}=0.05\), (**b**): \(\mathcal{L}=0.1\), and (**c**): \(\mathcal{L}=0.2\). Figure 9 shows the results of the evaluation of the proposed algorithm on the netscience dataset for values of \(\mathcal{L}=0.05\), \(\mathcal{L}=0.1\), and \(\mathcal{L}=0.2\). As can be deduced from this figure, the proposed algorithm has improved in most cases over the existing algorithms. This improvement is more visible for \(\mathcal{L}=0.1\) and \(\mathcal{L}=0.2\). As mentioned earlier, a slight decrease in the accuracy of the proposed algorithm is acceptable. In fact, the cost we pay to speed up to anonymize the graph is a reduction in algorithm accuracy. However, in most cases, we see an increase in the accuracy of the algorithm as a result of using PL and coreness criteria in selecting the best edges to remove and add. The FSopt_k algorithm evaluation results are compared to other algorithms on the power grid dataset for different values of \(\mathcal{L}\) in \[APL(G)=\frac{1}{n(n-1)}*\sum_{i\
eq j}d(v_{i},v_{j}),\]0 Evaluation results on this dataset show that in the APL and modularity criteria, the accuracy of the proposed algorithm is increased. This increased accuracy is due to the use of coreness and PL criteria in selecting the most appropriate edges in the graph modification process. However, the results of evaluating the algorithms on this dataset show that in the two criteria, ACC and T, the accuracy of the proposed algorithm is reduced. The results of evaluating the proposed method on the polbooks dataset are shown in \[APL(G)=\frac{1}{n(n-1)}*\sum_{i\
eq j}d(v_{i},v_{j}),\]1 This figure shows an improvement in general criteria due to using coreness and PL in finding the best edges to be changed in the graph. The increase in error of \(\mathcal{L}=0.2\) is due to calculating the k value more than what has been obtained in UMGA. In general, the anonymous graph has more than the one obtained by UMGA. In order to conclude the evaluation results presented in this section, the mean of the errors was obtained for each criterion. The result can be seen in \[APL(G)=\frac{1}{n(n-1)}*\sum_{i\
eq j}d(v_{i},v_{j}),\]2 This figure illustrates the improvement of the proposed algorithm over existing algorithms in terms of general graph criteria. This improvement is the result of using appropriate criteria to select the best edges in the graph modification step to be added or removed. In the case of the ACC criterion, the UMGA algorithm performs better than FSopt_k. However, the results of the evaluation of the two algorithms FSopt_k and UMGA are close together. As already explained, the accuracy of the proposed algorithm is reduced.