  In this paper, we develop a novel approach to measuring urban sprawl based on
street nodes and naturally defined urban boundaries, both extracted from
massive volunteered geographic information OpenStreetMap databases through some
data-intensive computing processes. The street nodes are defined as street
intersections and ends, while the naturally defined urban boundaries constitute
what we call natural cities. We find that the street nodes are significantly
correlated with population of cities. Based on this finding, we set street
nodes as a proxy of population to measure urban sprawl. We further find that
street nodes bear a significant linear relationship with city areal extents. In
the plot with the x axis representing city areal extents, and the y axis street
nodes, sprawling cities are located below the regression line. We verified the
approach using urban areas and population from the US census, and then applied
the approach to three European countries: France, Germany, and the United
Kingdom for the categorization of natural cities into three classes: sprawling,
compact, and normal. This categorization sets a uniform standard for cross
comparing sprawling levels across an entire country.
  Keywords: Street networks, openstreetmap, volunteered geographic information,
GIS
