Abstract
The shape of urban settlements plays a fundamental role in their
sustainable planning. Properly defining the boundaries of cities is
challenging and remains an open problem in the science of cities. Here,
we propose a worldwide model to define urban settlements beyond their
administrative boundaries through a bottom-up approach that takes into
account geographical biases intrinsically associated with most societies
around the world, and reflected in their different regional growing
dynamics. The generality of the model allows one to study the scaling
laws of cities at all geographical levels: countries, continents and the
entire world. Our definition of cities is robust and holds to one of the
most famous results in social sciences: Zipf's law. According to our
results, the largest cities in the world are not in line with what was
recently reported by the United Nations. For example, we find that the
largest city in the world is an agglomeration of several small
settlements close to each other, connecting three large settlements:
Alexandria, Cairo and Luxor. Our definition of cities opens the doors to
the study of the economy of cities in a systematic way independently of
arbitrary definitions that employ administrative boundaries.
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