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In practice it will be quite difficult to solve this for all towns in an area. But can we do it for the largest towns? And how many towns should we incorporate?
 
In practice it will be quite difficult to solve this for all towns in an area. But can we do it for the largest towns? And how many towns should we incorporate?
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== Recipe ==
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Using the above considerations we can setup a recipe:
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# Largest cities - find the largest cities (by population size) for a country. Star with the 5 largest cities;
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# Population - list the population size for each of the largest cities, and calculate the fraction of the total population of all largest cities;
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# distances - calculate the distances between all the largest cities. We can use the directions of OpenStreetMap for this;
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# weighted distance - calculate the weighted distances, i.e. the distance times the city fraction;
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# weighted distance sum - add all the weighted fractions for a specific city (the centroid city);
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# minimum weighted distance sum - find the weighted distance sum that is the lowest. The corresponding city is the centroid city;
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# add cities - more cities can be added to see whether the found centroid city is correct. For this recommence on step 1;
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== Result ==
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This recipe has been tried on the following countries:
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{| class="wikitable sortable"
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|-
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! Country !! Centroid city !! spreadsheet
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|-
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| Belgium || Brussels || [https://docs.google.com/spreadsheets/d/1-_DRQi9VUrV2o5oVRL01DUBz9iT3ZvVPlvxvz9O_ZLg link]
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|-
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| France || Paris || [https://docs.google.com/spreadsheets/d/1-G7VVZDE7xH6yzhsVYpmTTnu3rtgvadMC7WX9yIJqPc link]
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|}
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