## 4 Performance Evaluation  
The performance of the proposed scheme was evaluated against that of some of the existing methods to demonstrate its excellence and validity. An experiment was conducted with two main focuses. First, a dataset with repeated patterns was created following [27] to verify if the proposed scheme could identify patterns necessary for compression. Second, the experiment was conducted on various real-world graph sets. Table 1 presents the experimental environment. The proposed graph stream compression method is implemented in Python 3.8, leveraging key libraries such as NumPy 1.21 and SciPy 1.7 for efficient numerical computations. NetworkX 2.6 is used for graph data structures and algorithms, and python-igraph 0.9.6 is used for fast graph processing. The core algorithms for pattern mining, dictionary maintenance, and compression are built from scratch, while the above libraries are used for data preprocessing, result analysis, and performance comparison. Equation (2) calculates the size of the compressed graph compared with that of the original one. Using this equation, the extent of compression relative to the size of the original data can be determined. The performance evaluation assesses changes in compression time and rate depending on the pattern dictionary size in a graph stream environment. \begin{table}
\begin{tabular}{c c} \hline \hline
**HW/SW** & **Description** \\ \hline CPU & Intel(R) Core (TM) i7-12700K \\ \hline RAM & 32 GB \\ \hline Python & 3.8.10 \\ \hline Igraph & 0.9.1 \\ \hline networkX & 3.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental environment. Additionally, the change in compression rate based on the size of the batch can be examined; thus, the performance of the proposed scheme can be verified and validated under various conditions. \[\textit{Compression ratio}=\textit{Compressed graph size}/\textit{Original graph size} \tag{2}\]  
Finally, the experiments in this study were conducted with a window size, \(W_{batch}\), of 3, a threshold, \(\gamma\), of 2, and an \(\alpha\) of 0.5. First, an experiment was conducted to verify if the proposed scheme could find the subgraphs it sought. The patterns of each dataset presented in Table 2 include three-clique, four-clique, four-star, four-path, five-path, and eight-tree, i.e., a total of six patterns. In this experiment, experimental datasets with a desired frequency were created following [27]. The data used in the experiment consisted of 1000 vertices and 10,000 edges. \"Cov.\" (coverage) in Table 2 indicates the extent to which the pattern constituted the entire graph. The experimental results show that the proposed scheme, while generally taking more time than GraphZip [11], accurately found all the subgraph patterns. Furthermore, the proposed scheme was able to find accurate subgraph patterns faster than SUBDUE [27]. In this experiment, when the experiment time exceeded 10 min (600 s), it was deemed erroneous and marked as timed-over. Table 2 summarizes the experimental results on several synthetic graph datasets, each including a specific type of subgraph pattern (e.g., three-clique, four-path). \"Cov.\" stands for coverage, indicating the percentage of the dataset covered by the corresponding pattern. \"Accuracy\" measures the ratio of correctly identified patterns over the total number of true patterns. The proposed scheme achieves 100% accuracy for all tested datasets, demonstrating its ability to thoroughly detect the embedded patterns, which is crucial for effective compression.