There are overwhelming proofs of how urbanization contributes to the increase of carbon emissions. However, it has been unclear how structural and functional changes in urban carbon flows evolve with socioeconomic development in a long run, which is important for a more systemic and efficient carbon mitigation policy. The present study probes into the interaction between urban carbon metabolism and socioeconomic activities from a systems perspective. Taking Beijing as a case study, we model the dynamics between the changing carbon metabolism and variation in socioeconomic conditions over 1985-2030, based on a collection of system-based indicators from ecological network analysis. We find an "inverted V curve" carbon transition in Beijing, and the turning point occurred around 2010. This transition is widely observed in the variation in total embodied emission, total system throughflow, boundary flow and system capacity. Continuing improvement in efficiency is expected to lessen the pressure from carbonization in 2020 and 2030 without sacrificing the diversity of economic activities. We suggest that network analysis has a unique potential in unfolding the interplay between carbon transition and socioeconomic development that most "accounting approaches" fail to penetrate.