Urban metabolism is a useful framework for characterizing human manipulation of energy and material flows in cities, but little attention has been paid to interactions among different flows. In this study, we examine the coupling of energy and carbon flows associated with cities. To do this, a time-series dataset of carbon and energy flows with 66 urban samples of various geographic and economic conditions is developed, dating back to 1865. We assess correlation between energy consumption and carbon emissions with consideration of urban size and population density. By focusing on Beijing and Issaquah as two case cities, we model the coupling of energy and carbon metabolism at urban scale from a network perspective. The energy-carbon nexus is evaluated for its impact on carbon intensities associated with economic sectors. We find energy-use and carbon emissions of 1865-2014 are strongly coupled, for both large and small cities of varying population densities. A closer look into the impact of the energy-carbon nexus on carbon intensities is important for emissions control. We suggest that more comprehensive and up-to-date monitoring of the nexus in urban energy and carbon flows be initiated immediately in order to search for ideal options of low-carbon pathways for cities at global scale.