## 4 Performance Evaluation
In other words, the proposed scheme generally spends more time effectively managing and allocating more complex patterns than the existing methods do, thereby demonstrating a higher level of graph pattern recognition and compression efficiency. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Batch Size**} & **Average Number of** & **Average Processing** & **Average Compression** \\  & **Patterns** & **Time (Sec)** & **Ratio(\%)** \\ \hline
50 & 24.1 & 10.7 & 24.4 \\ \hline
100 & 45.9 & 29.4 & 41.2 \\ \hline
200 & 84.2 & 51.3 & 55.7 \\ \hline
300 & 125.8 & 67.3 & 69.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average number of patterns and processing time according to batch size. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Mark** & **\# Vertices** & **\# Edges** & **Description** & **Size (KB, Disk)** \\ \hline DBLP & DB & 317,080 & 1,049,866 & Collaboration & 13,605 \\ \hline YouTube & YT & 1,134,890 & 2,987,624 & Social & 37,814 \\ \hline Skitter & SK & 1,696,415 & 11,095,298 & Internet & 145,612 \\ \hline NBER & NB & 3,774,218 & 16,512,783 & Patent Citation & 257,887 \\ \hline LiveJournal & LJ & 3,997,962 & 34,681,189 & Social & 478,799 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Real-world datasets utilized in the experiment. Additionally, experiments on some datasets confirmed that the proposed scheme required less time than the existing methods do. This implies that the proposed scheme can achieve a balance between efficiency and performance depending on the situation. Figure 9 shows the compression rate and time taken for compression as a function of the pattern dictionary size. The left-side plots show the compression rate, while the right-side ones show the compression execution time. Generally, the proposed scheme demonstrated superior performance in most experiments, especially in larger datasets. One of the existing methods, GraphZip [11], assigns value based on size and frequency for each pattern, which may lead to performance degradation if high-scored patterns do not reappear. In contrast, the proposed scheme considers frequency, size, and time for each pattern. Although it takes more time owing to the complex calculations required for each pattern, it maintains more important patterns and deletes less significant ones, thus managing the pattern dictionary more effectively. Figure 10 shows the results of a performance comparison between the proposed scheme and existing incremental graph pattern extraction methods, using the largest dataset, LiveJournal. GRAMI [28] and FSM [10], which are similar to GraphZip [11] and find frequent patterns in graphs in a stream environment, were included in the experiment. The horizontal axis of the figure represents the percentage of batch processing progress in graph stream data. That is, at a value of 5 on the horizontal axis, approximately 5% of the total graph stream will have been processed. The horizontal axis is divided into intervals of 5%. The total execution time is as shown in Figure 9c. For this dataset, with a batch size of 300, approximately 115,000 iterations of processing were performed. The experimental results showed that for up to 70% of the entire process, GraphZip outperformed the proposed scheme in terms of processing time; however, later on, the latter outperformed the former. This indicates that the proposed scheme performs faster computations by eliminating unnecessary patterns. On the other hand, the existing methods GRAMI and FSM saw an exponential increase in the computation time in the latter half as the number of patterns to compare increased. Figure 8: Time requirement for each process step in the complete process: (**a**) proposed scheme; (**b**) GraphZip. Figure 9: This figure shows the compression rates (left column) and runtimes (right column) of the proposed scheme on various real-world datasets, with respect to different pattern dictionary sizes.