If cities are considered as 'superorganisms', then disorders of their metabolic processes cause something analogous to an 'urban disease'. It is therefore helpful to identify the causes of such disorders by analyzing the inner mechanisms that control urban metabolic processes. Combining input-output analysis with ecological network analysis lets researchers study the functional relationships and hierarchy of the urban metabolic processes, thereby providing direct support for the analysis of urban disease. In this paper, using Beijing as an example, we develop a model of an urban metabolic system that accounts for the intensity of the embodied ecological elements using monetary input-output tables from 1997, 2000, 2002, 2005, and 2007, and use this data to compile the corresponding physical input-output tables. This approach described the various flows of ecological elements through urban metabolic processes and let us build an ecological network model with 32 components. Then, using two methods from ecological network analysis (flow analysis and utility analysis), we quantitatively analyzed the physical input-output relationships among urban components, determined the ecological hierarchy of the components of the metabolic system, and determined the distribution of advantage-dominated and disadvantage-dominated relationships, thereby providing scientific support to guide restructuring of the urban metabolic system in an effort to prevent or cure urban 'diseases'.