Skip to main content
Figure 2 | EPJ Data Science

Figure 2

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

Figure 2

Heaps’ law for countries. (a), Zipf’s Law: PDF (y-axis) of city sizes X (x-axis) for all cities in Europe, America, Asia and Africa. The darker regions correspond to cities with population \(X > 10^{5}\), above which the distributions are a power law with exponent \(\beta = 1+\alpha \) given in Table 1. The dashed lines correspond to \(y = x^{-\beta }\). Distributions have been shifted in the y-axis for clarity.(b)–(c) and (e)–(f), Heaps’ law for America, Europe, Africa and Asia. The following information is displayed for each country: population (x-axis), number of cities with more than 100 k inhabitants (y-axis), logarithm of the area (marker size) and population density (color). The black line is a power law fit of the scaling relationship between the number of cities and the total population; Heaps exponents γ are reported in Table 1. (d), The exponent of the Zipf PDF, β (y-axis) and the corresponding exponent γ of Heaps’ law for Europe, America, Asia and Africa. Marker size corresponds to the minimum city population used in determining the values of γ and β: values used are \(10^{3}, 5 \times 10^{3}, 10^{4}\) and 105, where 103 is represented by the smallest marker and 105 by the largest. Increasing the minimum city population corresponds to a decrease in the amount of data used to fit γ and β: for a given continent, each point represents the same data set but restricted to a different range of X values. The black dashed line corresponds to the relationship between the exponents, \(\beta = \gamma + 1\)

Back to article page