## 5 Experiments
### Analysis of the Performance of AGCM-SLV  
We evaluated the performance of our proposed algorithm, AGCM-SLV, on the real-world _PTC_ dataset [64] by analyzing how variations in the dissimilarity threshold (\(\beta\)) and support threshold (\(\alpha\)) impact both the number of frequent approximate subgraphs mined and the runtime. The _PTC_ dataset [64] contains compounds labeled according to carcinogenicity in male mice (MM), male rats (MR), female mice (FM), and female rats (FR). In these four graph collections, the nodes represent atoms and are labeled by atom type, and the edges represent chemical bonds and are labeled by bond type. Table 9 shows the number of graphs in each graph collection and the average number of nodes and edges for the four _PTC_ graph collections. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Dataset** & **Total Graphs** & **Average Nodes** & **Average Edges** \\ \hline PTC-FM & 349 & 14.11 & 14.48 \\ PTC-FR & 351 & 14.56 & 15.00 \\ PTC-MM & 336 & 13.97 & 14.32 \\ PTC-MR & 344 & 14.29 & 14.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Description of PTC datasets. Figure 9: Number of frequent approximate subgraphs mined and runtime of AGCM-SLV and REAFUM varying the dissimilarity threshold (\(\beta\)) with a constant support threshold (\(\alpha\)) of 80%. (**a**) Number of frequent approximate subgraphs; (**b**) Runtime. Figure 10a shows the impact of varying the dissimilarity and support thresholds on the number of frequent approximate subgraphs mined. This figure contains three vertical plots showing the number of frequent approximate subgraphs mined across the four graph collections of PTC (FM, FR, MM, and MR). Each plot corresponds to a specific dissimilarity threshold value (1, 2, or 3). In each plot, the colored bars represent the number of frequent approximate subgraphs mined for each support threshold (70%, 80%, and 90%). To observe the impact of varying the dissimilarity threshold, we compare the increase in the number of frequent approximate subgraphs across the three plots. The results show that as the dissimilarity threshold increases, the number of frequent approximate subgraphs mined also increases. This is because allowing more modifications increases the number of occurrences per candidate subgraph that fulfills the dissimilarity threshold, leading to more frequent approximate subgraphs being mined. On the other hand, to observe the impact of varying the support threshold, we compare the variation within each plot with the different colored bars. The results reveal that the number of frequent approximate subgraphs mined increases as the support threshold decreases. This is because it is more likely for a frequent approximate subgraph to appear in fewer graphs within the graph collection. Figure 10b shows the corresponding runtime for mining the frequent approximate subgraphs shown in Figure 10a. This figure also contains three vertical plots, which indicate the runtime of mining the frequent approximate subgraphs across the four graph collections of PTC (FM, FR, MM, and MR). Each plot corresponds to a specific dissimilarity threshold value (1, 2, or 3). The colored lines represent the runtimes for each support threshold (70%, 80%, and 90%). To observe the impact of varying the dissimilarity threshold on runtime, we need to compare the increase in the runtime across the three plots. It is important to emphasize that each plot has a different timescale on the y-axis. In the first plot, the runtime is less than 3 min with a dissimilarity threshold of 1; in the second plot, it is less than 28 min with a dissimilarity threshold of 2; and in the third plot, it extends up to 7 h with a dissimilarity threshold of 3. As the dissimilarity threshold increases, the runtime also increases because of the rise in the number of frequent approximate subgraphs mined. Figure 10: Number of frequent approximate subgraphs mined and runtime of AGCM-SLV varying the support threshold from 70% to 90% and the dissimilarity threshold from 1 to 3.