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1,277 bytes added ,  09:08, 1 March 2021
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In practice this approach is not feasible. It is just to much work to (to do by hand a least). So we need a way to get a reasonable approximation. For the calculation of the centroids a limited number of cities are used. We could try to extrapolate this data to get the transportation country size.
 
In practice this approach is not feasible. It is just to much work to (to do by hand a least). So we need a way to get a reasonable approximation. For the calculation of the centroids a limited number of cities are used. We could try to extrapolate this data to get the transportation country size.
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== Practice ==
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== Approach ==
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In the figure the results for Maroc are shown.
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The cumulative population weighted distances are plotted against the cumulative population ratios. Each added city adds a point, increasing the cumulative population ratio and the cumulative distance. If the cumulative population ratio is 1, we have covered the entire population. And the corresponding cumulative distance is the value we are looking for.
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Instead of adding all the cities, we could fit a line to the data of a few city points. The cumulative distance of the fit at a population ratio of 1, is then again the value we are looking for.
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The function to fit must behave nicely with extrapolations. This excludes complex functions with many parameters. A simple linear of logarithmic function should be sufficient. A logarithmic function is preferred, as you expect that as smaller cities are added, the contribution to the distance is also smaller (not sure this logic is correct).
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In the graph for Maroc a logarithmic function is used. The largest cities are not used in the fit calculation, as these ones seem not to follow the curve. They would bias the fit to much, when we use so few points. The fit will result in a transportation size of 419 km. Compare this to a maximum actual distance of about 1000 km.
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