Urban metabolism research faces difficulties defining ecological trophic levels and analyzing relationships among the metabolic system's energy components. Here, we propose a new way to perform such research. By integrating throughflow analysis with ecological network utility analysis, we used network flows to analyze the metabolic system's network structure and the ecological relationships within the system. We developed an ecological network model for the system, and used four Chinese cities as examples of how this approach provides insights into the flows within the system at both high and low levels of detail. Using the weight distribution in the network flow matrix, we determined the structure of the urban energy metabolic system and the trophic levels; using the sign distribution in the network utility matrix, we determined the relationships between each pair of the system's compartments and their degrees of mutualism. The model uses compartments based on 17 sectors (energy exploitation; coal-fired power; heat supply; washed coal; coking; oil refinery; gas generation; coal products; agricultural; industrial; construction; communication, storage, and postal service; wholesale, retail, accommodation, and catering; household; other consuming; recovery; and energy stocks). Analyzing the structure and functioning of the urban energy metabolic system revealed ways to optimize its structure by adjusting the relationships among compartments, thereby demonstrating how ecological network analysis can be used in future urban system research.