## 5 Conclusions  
In this paper, we proposed an incremental frequent pattern-based compression scheme for processing graph streams. It identifies frequent patterns through graph pattern mining, assigns scores to the patterns, and selects reference patterns from among them. Additionally, it utilizes pattern and provenance information to leverage the change history of graphs. The proposed scheme was observed to detect patterns and perform compression faster than the existing techniques. It can be applied to dynamically changing stream graphs, and improve space efficiency by storing only the most efficient patterns in memory. Furthermore, by maintaining the latest patterns, the proposed scheme improves the compression efficiency and processing speed of graph streams that change in real time. Performance evaluation results showed that in environments with repeated patterns, the proposed scheme performed similarly to the existing methods. Despite the promising results, the proposed scheme has some limitations that need to be addressed in future research. One important issue is the lack of consideration for data security and privacy in the proposed graph stream compression method. While the proposed scheme enables the efficient compression of large-scale, ever-growing graph streams, it does not incorporate any specific mechanisms to protect sensitive information that may be present in the data. This could potentially lead to privacy breaches or a misuse of personal data when the compressed graph is stored or processed in various application domains. Furthermore, we did not establish clear criteria or quantitative limits for the formation of new graph vertices. Moreover, the statistical characteristics of the experimental datasets were not analyzed in detail. These aspects should be further investigated to ensure the robustness and generalizability of the proposed compression method. For real-world data, it consistently yielded higher compression rates and faster processing times in most environments. Smaller pattern dictionary sizes used in this scheme facilitate more effective compression, compared with other pattern mining schemes. Especially in real-time processing environments with limited latency, the proposed scheme outperformed other graph compression or graph pattern mining schemes in terms of processing time. However, some areas exist, where it does not significantly excel in compression rate, and guaranteeing performance for more complex patterns or scalability might be difficult. To address these issues, we plan to enhance its performance via techniques utilizing GPUs and conduct experiments with other various stream-based graph compression schemes. Figure 10: Comparison of performance metrics of the proposed scheme and other pattern mining schemes in streaming environments. **Author Contributions:** Conceptualization, H.L., B.S., D.C., J.L., K.B., and J.Y. ; methodology, H.L., B.S., D.C., J.L., K.B., and J.Y. ; validation, H.L., B.S., D.C., J.L., and K.B. ; formal analysis, H.L., B.S., D.C., J.L., and K.B. ; writing--original draft preparation, H.L., B.S., D.C., J.L., and K.B. ; writing--review and editing, J.Y. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT). (No. 2022R1A2B5802002456, 33%), by the MSIT (Ministry of Science and ICT), Korea, under the Grand Information Technology Research Center support program (IITP-2024-2020-0-01462, 34%) supervised by the IITP (Institute for Information & Communications Technology Planning & Evaluation) and with the support of \"Cooperative Research Program for Agriculture Science and Technology Development (Project No. RS-2021-RD010195, 33%)\" Rural Development Administration, Republic of Korea. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The datasets presented in this study are available in Appendix A.