  Zipfs Law states that rank-size distributions of city populations follow a
power law with an exponent of -1. The assertion of a universal power law is
controversial because the linearity and slope appear to vary over time and
among countries. We compare census enumerations and night light luminance as
proxies for population density and intensity of development in the contiguous
United States. Treating population density and development intensity as
continuous quantities allows for the definition of spatial networks based on
the level of spatial connectivity. The resulting distributions of spatial
network components (subsets of connected nodes) vary with degree of
connectivity, but maintain consistent scaling over a wide range of network
sizes. At continental scales, spatial network rank-size distributions obtained
from both population density and night light brightness are well-fit by power
laws with exponents near -1 for a wide range of density and luminance
thresholds. However, the largest components (10,000 - 100,000 sq.km) are far
larger than individual cities and represent spatially contiguous agglomerations
of urban, suburban and periurban development. Projecting county-level numbers
of confirmed cases of SARS-CoV-2 for the US onto spatial networks of population
and development allows the spatiotemporal evolution of the epidemic to be
quantified as propagation within networks of varying connectivity.. The results
show an abrupt transition from slow increases in confirmed cases in a small
number of network components to rapid geographic dispersion to a larger number
of components before mobility reductions occurred in March 2020.
