Due to COVID-19, the shipping market has faced uncertainty, and the possibility of changes in port routes has increased. The purpose of this study was to analyze the network of container liner shipping routes between Asia and Europe. In particular, this research focused on a global risky situation—the COVID-19 pandemic. The data examined encompassed Asia–Europe route schedules from January 2018 to October 2021, which exhibited significant fluctuations due to the COVID-19 pandemic originating in 2019. To access this problem, utilizing concepts of centrality from social network analysis (SNA), namely degree centrality and betweenness centrality, this analysis incorporated route capacity as a weighted factor. The findings revealed that the port of Rotterdam held the highest degree of centrality in 2018, 2019, and 2021, while Shanghai claimed the highest degree of centrality in 2020. Singapore exhibited the highest betweenness centrality. Asian ports wielded greater influence during the COVID-19 pandemic compared to European ports. Furthermore, Singapore emerged as a pivotal mediator in the Asia–Europe routes, playing a significant role within the global supply chain. Results showed that the port could be put into an unstable situation. Therefore, the managers of port and shipping companies should be ready to minimize risk. From an academic perspective, it is difficult to integrate and analyze container liner schedules as they are monthly updated. This study therefore analyzed continuous schedules to examine dynamic changes in schedules. By adopting SNA, we presented changes in connectivity over multiple periods. This study addressed questions stakeholders may have had about route changes during the global crisis, contributing to sustainable container transportation. This study provides a general understanding of Asia–Europe container scheduling for decision makers. Using market schedules, this research analyzed the connections, and evaluated and compared each port.