The population sizes of Mexican cities follow a power-law distribution

Geography, for example because of the presence of rivers, ravines, or peaks, can subdivide a city. These subdivisions raise the question of identifying the area occupied by the city, of deciding whether or not they are aggregates of distinct built-up areas, and whether or not geographical separations are merely asperities in a certain continuum of built-up areas. The city as a union of administrative units allows for jurisdictional practices, but for public policy in health for example, identification by built-up areas is more operational. The study of urban populations thus requires that cities be circumscribed on objective criteria. Circumscribing a city requires knowledge of commuting flows, but in the absence of this piece of information, circumscribing it relies on the fact that it is made up of close built-up areas. This is reflected in the intersection of the convex envelopes of the spatial extent of these built-up areas. The algorithm treats coordinates of the vertices of polygons encompassing built-up areas provided by the Census Bureau for the United States or the National Institute of Statistics and Geography for Mexico. It allows for computing whether convex hulls of polygons intersect or not. If they do, then the built-up areas circumscribed by these polygons are part of the same city. The result is that cities now reflect the geographic extent of urban areas rather than their administrative areas. With this delineation method applied to Mexico’s 2020 census data, the population sizes of urban areas with at least 2,126 inhabitants follow a power law, with exponent 0.954 (standard deviation = 0.016), whereas this is no longer the case when considering only the administrative extents of cities with more than 15,000 inhabitants.