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Figure 1 | EPJ Data Science

Figure 1

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

Figure 1

Theoretical prediction. Relationship between the expected number of cities and the total population for the null model, which assumes a Zipf law with exponent \(\alpha = 0.75\) and minimum city size \(m=10^{2}\) for the distribution of city sizes and no spatial correlations between cities. The thin blue lines are 100 realisations of the model and the blue circles denote the average number of cities, \(\langle C|N \rangle \), for a fixed value of the total population, N. The solid red line is the theoretical prediction of Equation (1) and the dashed black line is Heaps’ law, \(\langle C|N \rangle \sim N^{\alpha }\), which holds in the limit of very large population \(N \gg m\)

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