The COVID-19 pandemic has brought a brand-new challenge to the design and management of the air transportation network (ATN). Many countries have partially or entirely shut down their international flights during this period to contain the spread of COVID-19. However, the changes in the international connectivity of different countries during this period varied greatly, as the ATNs of different countries have different structures. Accordingly, this paper studies the impact of network topology on the international robustness of a country's ATN to pandemic-induced disruptions. Therein, a Weighted International Efficiency metric is proposed to evaluate a country's connectivity to other countries, followed by deriving an International Robustness metric that measures the ability of a country's ATN to maintain international connections during pandemics. Further, three internal and external topological metrics are defined to characterize the structure of an ATN. The results of correlation and regression analysis show that the proportion of international airports inside a country is the most important factor in determining its international robustness to pandemics, followed by the density of the domestic connections. Surprisingly, the number of directly connected foreign cities has little effect on international robustness. The analysis demonstrates the importance of studying ATN topology during emergencies.