## 5 Experiments
### Frequent Approximate Subgraphs Mined by the Proposed Algorithm
#### 5.2.2 Comparison Regarding the Number of Frequent Approximate Subgraphs Mined and Runtime  
In this experiment, we compared the performance of REAFUM and our proposed algorithm (AGCM-SLV) with a real-world dataset (PTC-FM [64]). We evaluated how the variation in the parameters \(\alpha\) and \(\beta\) impacts the number of frequent subgraphs mined and the runtime. _PTC-FM_ is a dataset that contains compounds labeled according to carcinogenicity in female mice. This dataset includes 349 graphs where nodes represent atoms labeled by atom type, and edges represent chemical bonds and are labeled by bond type. This experiment uses specific portions of the PTC-FM dataset based on its size. Table 8 shows the datasets built from _PTC-FM_ for our experiment. Figure 7(a) shows how the number of frequent approximate subgraphs mined is affected by varying the dissimilarity threshold, with the support threshold set constant at 90%. The figure contains three horizontal plots showing the number of frequent approximate subgraphs mined, each plot corresponding to a specific value of the dissimilarity threshold (1, 2, and 3). The colored bars represent the number of frequent approximate subgraphs \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Dataset** & **Total Graphs** & **Average Nodes** & **Average Edges** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 8: Datasets built from PTC-FM for our experiment. Figure 7: Expansion process of REAFUM and the proposed algorithm (AGCM-SLV) in the frequent approximate subgraph (highlighted in blue) within graph \(g_{3}\). mined for the different cases (both, only REAFUM, and only AGCM-SLV). It is important to emphasize that each plot has a different number of frequent subgraphs on the y-axis scale. In the first plot, when the dissimilarity threshold is 1, the number of frequent approximate subgraphs is up to 100; in the second plot, when the dissimilarity threshold is 2, the number of frequent approximate subgraphs is up to 310; and in the third plot, when the dissimilarity threshold is 3, the number of frequent approximate subgraphs extends up to 800. We need to focus on each plot to compare the number of frequent approximate subgraphs mined by both algorithms. The results reveal that while both algorithms mine most of the frequent subgraphs represented by a blue-colored bar, there are also cases where an algorithm mines additional frequent subgraphs represented by a cyan-colored bar for our proposed algorithm and a red-colored bar for REAFUM. Notice that the red-colored bars representing REAFUM in Figure 8a are not easily seen (see, for example, the second graph of Figure 8a in the last column corresponding to 121-150), since there are a few cases where a small number of frequent approximate subgraphs are mined only by REAFUM. To observe how varying the dissimilarity threshold impacts the number of frequent subgraphs mined, we compare the increase in frequent subgraphs mined across the three plots. The results show that both algorithms mine more frequent approximate subgraphs as the dissimilarity threshold increases. Figure 8: Number of frequent approximate subgraphs mined and runtime of AGCM-SLV and REAFUM varying the dissimilarity threshold \((\beta)\) with constant support threshold \((\alpha)\) of 90%. **(a)** Number of frequent approximate subgraphs; **(b)** Runtime. Figure 8b shows the corresponding runtime in which the frequent approximate subgraphs of Figure 8a were mined by both algorithms. This figure also contains three horizontal plots, which, in this case, show the runtime of mining the frequent approximate subgraphs for both algorithms. Each plot corresponds to a dissimilarity threshold value (1, 2, and 3); the number of frequent approximate subgraphs mined is represented by colored bars for the different cases (both, only REAFUM, and only AGCM-SLV), and the runtime is represented by different line colors for each algorithm (REAFUM and AGCM-SLV). It is important to emphasize that each plot has a different time scale on the y-axis.