A worldwide model for boundaries of urban settlements.

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.