Gangs are closely knit groups that pose a significant threat to law and social security. They are able to do this because of the strong bonds that exist between their members, as well as the internal and external factors that constrain them. In the past, most academic research on gangs has relied on sociological methods. However, this paper proposes a new approach that uses mathematical models and information technology (IT). This approach is based on the following four core functions of an archival system: 1. Data acquisition, 2. Archive construction, 3. Data maintenance, 4. Application. The proposed approach has several advantages over traditional sociological methods. First, it is more dynamic and can be used to track the changing structure and activities of gangs. Second, it is more comprehensive and can be used to collect data from a wider range of sources. Third, it is more accurate and can be used to identify patterns and trends in gang activity. The paper uses a case study of a criminal gang in Taiwan to illustrate the application of the proposed approach. The case study shows how the gang's organizational structure, leadership, and activities have changed over time. It also shows how the gang has been able to expand its geographical reach and influence. The proposed approach is a new and innovative way to study gangs. It has the potential to provide law enforcement agencies with a more comprehensive and accurate understanding of gang activity. This information can then be used to develop more effective strategies for combating gangs and protecting society.