This paper investigates how variations in aviation carbon pricing influence the network choices of airlines and social planner. Beyond the traditional direct-flight (DF) network, hub-and-spoke (HS) network and mixed (MX) network, we incorporate the 2-hub (2 H) network into our analysis. The findings reveal that as carbon pricing costs increase, the optimal network configuration for airlines progresses sequentially through 2 H, MX and DF. This suggests that due to horizontal product differentiation, the inclusion of 2 H in the model renders the HS network—which is widely utilized by numerous major airlines—no longer the optimal choice for airlines. From the perspective of social planner, the optimal network configuration undergoes a progression from HS, 2 H, HS, MX, DF, MX to DF as carbon pricing costs rise. While the HS network may not align with the optimal choice for airlines, it has the potential to be the socially optimal network. Furthermore, the transition of socially optimal networks exhibits discontinuities, resulting in significant deviations from the network decisions made by airlines. Overall, this paper broadens the scope of network choices available to airlines by incorporating the 2 H network and offers theoretical insights for policy formulation by both airlines and society within the context of aviation carbon offset.