## 2 Related Work  
This section explains techniques focused on the structure of graphs and techniques for compressing frequent patterns in graphs within the realm of existing graph compression research. Some of the previous studies proposed focusing on the graph's structural characteristics. StarZIP [13] performs structural compression by identifying and reordering only sub-graph sets in a star shape, applying an encoding technique for compression, and incrementally processing the graphs. It also uses snapshots to create graph stream objects, which are then shattered to transform undirected graphs into directed ones. GraphZIP [22] compresses graph streams using clique-shaped sub-graphs. This technique decomposes the original graph into a set of cliques and then compresses each set of clique graphs. During this process, it focuses on minimizing the disk I/O by using efficient graph representation structures, such as CSC (compressed sparse column) or CSR (compressed sparse row). The main goal of these methods is to maximize space efficiency by compressing the graph as much as possible, not considering frequent or important patterns. Research on compressing frequent patterns in graphs utilizes graph mining techniques. Graph mining is a process of extracting useful information and patterns from graphs, used for analyzing large volumes of complex network data. During this process, various algorithms and techniques are applied to consider the relationships among vertices and edges, graph structure, and dynamic changes. Frequent pattern mining [1, 5, 6, 7, 11, 15, 21] is a method of extracting meaningful information or patterns from data, used in various fields, such as pattern analysis, anomaly detection, and recommendation services. FP-Growth is a method that efficiently finds frequent patterns using an FP-tree structure [32, 33]. In this method, minimum support is applied to find patterns that appear more than a certain number of times, and the support represents the proportion of the data that include a specific pattern out of the total data. The FP-tree starts with a null root node (vertex), storing the item and its repetition count in each vertex, and the final FP-tree is constructed after reading all transactions. However, unlike frequent pattern mining in static environments, the same in-graph stream environments become more complex owing to dynamic data changes and in information overflow. FP-streaming [14] dynamically detects frequent patterns over time to solve the problem of time-varying data input amounts. In these methods, the construction process of the pattern tree is similar to that of the FP-tree. The tree is constructed using a given similarity and support, managing time and support information in a table to detect all frequent patterns. GraphZip [11] proposes a dictionary-based compression method that increases compression efficiency by utilizing frequent patterns in graph streams. This technique applies dictionary-based compression along with the minimum description length principle to identify the maximum compression patterns in the graph stream. The input data comprise vertices, edges, and their labels; the process starts with storing vertex information and then processing edge information in a stream format. It sets a batch size to process vertices in bulk, and starts with a single edge to expand and generate patterns. Scores are assigned to the generated patterns, and all patterns are scored taking into account the occurrence frequency at the time of appearance and the total number of edges. Then, they are sorted in descending order to remove patterns that exceed the dictionary size. For each batch, the collected patterns are compressed and the information is recorded in a file. This process is repeated to complete the compression. However, a limitation of GraphZip [11] is that it does not utilize time-related information in pattern management.