  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 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.
