  A city (or an urban cluster) is not an isolated spatial unit, but a
combination of areas with closely linked socio-economic activities. However, so
far, we lack a consistent and quantitative approach to define multi-level urban
clusters through these socio-economic connections. Here, using granular
population distribution and flow data from China, we propose a bottom-up
aggregation approach to quantify urban clusters at multiple spatial scales. We
reveal six 'phases' (i.e., levels) in the population density-flow diagram, each
of which corresponds to a spatial configuration of urban clusters from large to
small. Besides, our results show that Zipf's law appears only after the fifth
level, confirming the spatially dependent nature of urban laws. Our approach
does not need pre-defined administrative boundaries and can be applied
effectively on a global scale.
