Skip to main content
Figure 4 | EPJ Data Science

Figure 4

From: Testing Heaps’ law for cities using administrative and gridded population data sets

Figure 4

Scaling properties of urban clusters. (a), Portion of the GRUMP dataset representing the distribution of population in a region of the Midwestern United States. The color denotes the logarithm of the population: light yellow for high population, dark blue for low population. (b)–(d), Urban clusters in the region depicted in panel (a) obtained applying the City Clustering Algorithm for different values of the minimum population parameter: m= 28 in (b), 129 in (c), 599 in (d). (e), Scaling relationship between area and population of clusters. The different colors denote different values of the CCA parameter m (see the legend of panel (f) for the m values). The points indicate the average area of clusters with a given rescaled population. Data are fit to the power law in Equation (3) and the legend reports the values of the scaling exponent ω for the various m. (f), Counter Cumulative Distribution Functions of cluster areas. The different colors denote different values of the CCA parameter m (see the legend for the m values). The grey line is a power law with exponent −1 as a guide for the eye. (g), Counter Cumulative Distribution Functions of cluster populations, x (dashed curves), and rescaled populations, \((x/m)^{\omega (m)}\) (solid curves). The grey line is a power law with exponent −1 as a guide for the eye

Back to article page