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[[Category:Eco-Score]]
The [https://en.wikipedia.org/wiki/Centroid centroid] of a country (or area) can de defined in multiple ways. On the earth surface it is more useful to speak of the [https://en.wikipedia.org/wiki/Geographical_centre geographical center]. It is possible to find lists of these centers for area's on earth. ([[Eco-score transport - en|parent page]])
The [https://en.wikipedia.org/wiki/Centroid centroid] of a country (or area) can de defined in multiple ways. On the earth surface it is more useful to speak of the [https://en.wikipedia.org/wiki/Geographical_centre geographical center]. It is possible to find lists of these centers for area's on earth. ([[Eco-score transport - en|parent page]])


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* distance worksheet: this worksheet contains the distances between the cities noted on the population spreadsheet. The distances are taken from OpenStreetMap. Only the fields above the diagonal need to be filled. The fields below the diagonal are filled subsequently;
* distance worksheet: this worksheet contains the distances between the cities noted on the population spreadsheet. The distances are taken from OpenStreetMap. Only the fields above the diagonal need to be filled. The fields below the diagonal are filled subsequently;
* weighted sum: this worksheet is calculated based on the two worksheets mentioned above. The row at the bottom (the one without a city) is the sum of a column. The column with the smallest sum is the city we are looking for. To determine the quality of this city, the entries weighted dethroning distance, dethroning distance and real distance need to be changed. The weighted dethroning distance should have the weighted sum of the runnerup city minus the weighted sum of the centroid city. The dethroning distance is the weighted dethroning distance divided by the population fraction of the latest city that has been added. And the real distance is a reference to the real distance between the centroid and runnerup city. The larger the difference betzeen dethroning distance and real distance, the better the quality;
* weighted sum: this worksheet is calculated based on the two worksheets mentioned above. The row at the bottom (the one without a city) is the sum of a column. The column with the smallest sum is the city we are looking for. To determine the quality of this city, the entries weighted dethroning distance, dethroning distance and real distance need to be changed. The weighted dethroning distance should have the weighted sum of the runnerup city minus the weighted sum of the centroid city. The dethroning distance is the weighted dethroning distance divided by the population fraction of the latest city that has been added. And the real distance is a reference to the real distance between the centroid and runnerup city. The larger the difference betzeen dethroning distance and real distance, the better the quality;
* growth worksheet: this worksheet allows to see how the weighted sums grow with each added city. Especially to see what happens between the centroid and runnerup city;
* size worksheet: this worksheet allows to estimate the transportation size of a country. The cumulative weighted sum is plotted against the cumulative population fraction. A logarithmic fit is made, and the transportation size is estimated at a population fraction of 1, i.e. the entire population;


== Result ==
== Result ==
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{| class="wikitable sortable"
{| class="wikitable sortable"
|-
|-
! Country !! Centroid city !! quality !! spreadsheet
! Country !! Centroid city !! Runnerup city !! quality !! spreadsheet
|-
|-
| Austria || Vienna || 2680 || [https://docs.google.com/spreadsheets/d/1joXvrjWDmabsyFqf4V6bBsmCJHp0fhCB5oAy8nOStRU/ link]
| Albania || Tirana || Kamëz || 13 || link
|-
|-
| Belgium || Brussels || 296 || [https://docs.google.com/spreadsheets/d/1-_DRQi9VUrV2o5oVRL01DUBz9iT3ZvVPlvxvz9O_ZLg link]
| Algeria || Algers || Blida || 15 || link
|-
|-
|- Bulgaria || Sofia || 739 || [https://docs.google.com/spreadsheets/d/193RBhO4Dnd4ZwPbepP2oeyF5PkOMDeoxszSNuMW8VrQ link]
| Austria || Vienna || Baden bei Wien || 61  || [https://docs.google.com/spreadsheets/d/1joXvrjWDmabsyFqf4V6bBsmCJHp0fhCB5oAy8nOStRU link]
|-
|-
| Czech Republic || Prague || 1685 || [https://docs.google.com/spreadsheets/d/1QlsggBo0dOK-gvXR3-wOeeIQOLDSQ6J9TAGijCZ0ENg/ link]
| Belgium || Brussels || Antwerp ||  0.7 || [https://docs.google.com/spreadsheets/d/1-_DRQi9VUrV2o5oVRL01DUBz9iT3ZvVPlvxvz9O_ZLg link]
|-
|-
| Denmark || Copenhagen || 1759 || [https://docs.google.com/spreadsheets/d/1uB0MooOA0xT8z9bRfZ1iaKxNph1FQgeUby0HmXSOrKw link]
| Bosnia and Herzegovina || Zenica || || 0.6 || link
|-
|-
| Estonia || Tallinn || 2348 || [https://docs.google.com/spreadsheets/d/1nhs-FE32-n0taDLiNHxZ71VBGC2mYrBHjLlwI_PNMsQ/ link]
| Bulgaria - provinces || Stara Zagora || Plovdiv || 44 || [https://docs.google.com/spreadsheets/d/193RBhO4Dnd4ZwPbepP2oeyF5PkOMDeoxszSNuMW8VrQ link]
|-
|-
| Finland || Helsinki || 986 || [https://docs.google.com/spreadsheets/d/1OXHdXZDUJ9So5oSP67ZWzkDdSaQADQdZbDMnp7ekXcU/ link]
| Croatia || Zagreb || Velika Gorica || 30 || [https://docs.google.com/spreadsheets/d/1aWRYBN87i9pO8GbbxcemB38LIexrWnDgZMVqXOAwRaA link]
|-
|-
| France || Paris || 253 || [https://docs.google.com/spreadsheets/d/1-G7VVZDE7xH6yzhsVYpmTTnu3rtgvadMC7WX9yIJqPc link]
| Czech Republic || Prague || ||  9  || [https://docs.google.com/spreadsheets/d/1QlsggBo0dOK-gvXR3-wOeeIQOLDSQ6J9TAGijCZ0ENg/ link]
|-
|-
| Germany || Hannover || 3800 || [https://docs.google.com/spreadsheets/d/1HSNFq2sJiRxarSvY_mHtEOiSIq9fwFAyTh9lA4DfgF4 link]
| Denmark || Copenhagen || Roskilde || 5  || [https://docs.google.com/spreadsheets/d/1uB0MooOA0xT8z9bRfZ1iaKxNph1FQgeUby0HmXSOrKw link]
|-
|-
| Greece || Athens || 66 || [https://docs.google.com/spreadsheets/d/1RN6YIwDWLgLrultpRt49D83s3UCeAuQErZb4Orriv-Q link]
| Estonia || Tallinn || Maardu || 12 || [https://docs.google.com/spreadsheets/d/1nhs-FE32-n0taDLiNHxZ71VBGC2mYrBHjLlwI_PNMsQ/ link]
|-
|-
| Hungary || Budapest || 1424 || link
| Finland || Helsinki || || 5 || [https://docs.google.com/spreadsheets/d/1OXHdXZDUJ9So5oSP67ZWzkDdSaQADQdZbDMnp7ekXcU/ link]
|-
|-
| Iceland || Reykjavik || 30 || [https://docs.google.com/spreadsheets/d/1skWHDUfRtpaUkjXy-WiCWhqGBI8st-FB9sjcMaIRiCc link]
| France || Paris || Lyon || 7 || [https://docs.google.com/spreadsheets/d/1-G7VVZDE7xH6yzhsVYpmTTnu3rtgvadMC7WX9yIJqPc link]
|-
|-
| Ireland || Dublin || 1913 || [https://docs.google.com/spreadsheets/d/15KY_dUl_3PB_taWZNkfdhcv9RhX7YgcyUC21aNADOdE link]
| Germany - cities || Hannover || Bielefeld || 19 || [https://docs.google.com/spreadsheets/d/1HSNFq2sJiRxarSvY_mHtEOiSIq9fwFAyTh9lA4DfgF4 link]
|-
|-
| Italy || Rome || 394 || [https://docs.google.com/spreadsheets/d/19GxxwjgUrsMB522Vv_3zUCg-bJVyg054WwMK5S3tkP0 link]
| Germany - states || Hesse || Thuringia || 2 || [https://docs.google.com/spreadsheets/d/1HSNFq2sJiRxarSvY_mHtEOiSIq9fwFAyTh9lA4DfgF4 link]
|-
| Greece || Athens || || || [https://docs.google.com/spreadsheets/d/1RN6YIwDWLgLrultpRt49D83s3UCeAuQErZb4Orriv-Q link]
|-
| Hungary || Budapest ||  || || [https://docs.google.com/spreadsheets/d/16VZjIhacrZqKWNp95POnc2qKuLgpfTcIgs8Ygt6nxPI link]
|-
| Iceland || Reykjavik || Kópavogur || 10 || [https://docs.google.com/spreadsheets/d/1skWHDUfRtpaUkjXy-WiCWhqGBI8st-FB9sjcMaIRiCc link]
|-
| Ireland || Dublin || 56  || || [https://docs.google.com/spreadsheets/d/15KY_dUl_3PB_taWZNkfdhcv9RhX7YgcyUC21aNADOdE link]
|-
| Italy || Rome || Florence || 0.6 || [https://docs.google.com/spreadsheets/d/19GxxwjgUrsMB522Vv_3zUCg-bJVyg054WwMK5S3tkP0 link]
|-
| Kosovo - districts || Pristina || Ferizaj || 2 || [https://docs.google.com/spreadsheets/d/1vZLvWIn1DKnzpRC37v4LVUSdiaO7k6HOJw23f12GpH4/edit?usp=sharing link]
|-  
|-  
| Latvia || Riga || 593 || [https://docs.google.com/spreadsheets/d/1Ls57Onx80PpDggjztZgjOMDc0ikybXH2Rv7hsIIIav8/ link]
| Latvia || Riga || || 25 || [https://docs.google.com/spreadsheets/d/1Ls57Onx80PpDggjztZgjOMDc0ikybXH2Rv7hsIIIav8/ link]
|-  
|-  
| Lithuania || Kaunas || 34 || [https://docs.google.com/spreadsheets/d/1gz49-FMuaVvFIro2QgoIaxot24ysm1k_2fn6RJJxLF4 link]
| Lithuania || Kaunas || || || [https://docs.google.com/spreadsheets/d/1gz49-FMuaVvFIro2QgoIaxot24ysm1k_2fn6RJJxLF4 link]
|-
| Montenegro || Podgorica || Tuzi || 5 || [https://docs.google.com/spreadsheets/d/1GyGKUNo1OVRjRAAWNjHCJnFYKMmuxoVYT-2FdkZv3og/edit?usp=sharing link]
|-
| Morocco || Temara || Rabat || 2.8 || link
|-
| Netherlands - cities || Utrecht || Amsterdam || 4  || [https://docs.google.com/spreadsheets/d/1x8Vfb2ZIjsTmb0lRrO-8YHC6NKmgc58HtP_cNSjeOQY link]
|-
| Netherlands - provinces || Utrecht || Zuid-Holland || 15  || [https://docs.google.com/spreadsheets/d/1uyw9WAFAPtyx-hRyJ4j3PyLSVrEB48fhMUZD28VhzfI/edit?usp=sharing link]
|-
| North Macedonia || Skopje || Vardar ||  0.1 || [https://docs.google.com/spreadsheets/d/1EAb2rOX7l2SkcBhKNCpvHPGXsExJKjtzPDiTDnWlNcY/edit?usp=sharing link]
|-
| Norway || Skien || Oslo ||  0.7 || [https://docs.google.com/spreadsheets/d/1e3vPPWMyJu6k5rdbqDC9EGgOCgmAmsGZ2JO1oMrCbXw/edit link]
|-
| Poland || Łódź || Warschau || 24 || [https://docs.google.com/spreadsheets/d/1wBNuc3qItIouZHKLI-c9TrJcL2skF-T6sw_Yh1gPxM4 link]
|-
| Portugal || Loures || Lissabon || 1.1 || [https://docs.google.com/spreadsheets/d/1DBTu9pNtdLhf0hBPGqnYbLYXnxhAkX0f7eDcRBIrZGU link]
|-
|-
| Netherlands || Utrecht || 139 || [https://docs.google.com/spreadsheets/d/1x8Vfb2ZIjsTmb0lRrO-8YHC6NKmgc58HtP_cNSjeOQY link]
| Romania || Bucharest || Ploiești || 4 || [https://docs.google.com/spreadsheets/d/1V-39ygo6LszL2PWHUVi8VFtci1CExjpQLN7Y2w-nUXQ link]
|-
|-
| Norway || Skien || 91 || [https://docs.google.com/spreadsheets/d/1e3vPPWMyJu6k5rdbqDC9EGgOCgmAmsGZ2JO1oMrCbXw/edit link]
| Serbia - districts || Belgrad || Srem || 5 || [https://docs.google.com/spreadsheets/d/1ComqBolNvRQ7xYrvO4mMsKfcD39b4h6p4MwN7PAEqac/edit?usp=sharing link]
|-
|-
| Poland || Łódź || 805  || [https://docs.google.com/spreadsheets/d/1wBNuc3qItIouZHKLI-c9TrJcL2skF-T6sw_Yh1gPxM4 link]
| Slovakia || Banská Bystrica || Nitra || 0.3 || [https://docs.google.com/spreadsheets/d/1lTXNbUIM5ATG1C0TpzsgmtGnHFBqt0m2PBtRvVul0XE/ link]
|-
|-
| Portugal || Lisboa || 12 || [https://docs.google.com/spreadsheets/d/1DBTu9pNtdLhf0hBPGqnYbLYXnxhAkX0f7eDcRBIrZGU link]
| Slovenia || Ljubljana || Domžale || 74 || [https://docs.google.com/spreadsheets/d/1CVV7NGr2XZ-iYhE4c48Vm7WBhXPOxa79XrdV5GVck5E/ link]
|-
|-
| Romania || Bucharest || 1370 || [https://docs.google.com/spreadsheets/d/1V-39ygo6LszL2PWHUVi8VFtci1CExjpQLN7Y2w-nUXQ link]
| Spain || Madrid || Barcelona || 1.1 || [https://docs.google.com/spreadsheets/d/1Zf0ks3MiWOHbh9CSNiZQwW3yy9jW3l7qFahGYBH-uc8 link]
|-
|-
| Slovakia || Banská Bystrica || 44 || [https://docs.google.com/spreadsheets/d/1lTXNbUIM5ATG1C0TpzsgmtGnHFBqt0m2PBtRvVul0XE/ link]
| Sweden || Nörrköping || Stockholm || 3 || [https://docs.google.com/spreadsheets/d/16kjE6_IIoqiOHdFB-x1rpJiEesRbNqhwXSv8HTyy_NQ link]
|-
|-
| Slovenia || Ljubljana || 917 || [https://docs.google.com/spreadsheets/d/1CVV7NGr2XZ-iYhE4c48Vm7WBhXPOxa79XrdV5GVck5E/ link]
| Switzerland || Olten || Solothurn || 6  || [https://docs.google.com/spreadsheets/d/1VJ08fAdkbvnKAFDnn1RnNXQxWn9nzTK1y5GJ5AJFa1Y link]
|-
|-
| Spain || Madrid || 4579 || [https://docs.google.com/spreadsheets/d/1Zf0ks3MiWOHbh9CSNiZQwW3yy9jW3l7qFahGYBH-uc8 link]
| Tunisia || Tunis || || || link
|-
|-
| Sweden || Nörrköping || 600 || [https://docs.google.com/spreadsheets/d/16kjE6_IIoqiOHdFB-x1rpJiEesRbNqhwXSv8HTyy_NQ link]
| United Kingdom || Coventry || Leicester || 12 || [https://docs.google.com/spreadsheets/d/1xbNe-QDLIZt6h1HvLAa4jzTQoyifdLaiTr4UgaqbHNk link]
|-
|-
| Switzerland || Olten || 248 || [https://docs.google.com/spreadsheets/d/1VJ08fAdkbvnKAFDnn1RnNXQxWn9nzTK1y5GJ5AJFa1Y link]
| European Union - cities || Munich || Prague || 0.3 || [ link]
|-
|-
| United Kingdom || Coventry || 587 || [https://docs.google.com/spreadsheets/d/1xbNe-QDLIZt6h1HvLAa4jzTQoyifdLaiTr4UgaqbHNk link]
| European Union - countries || Luxemburg || Germany || 29 || [https://docs.google.com/spreadsheets/d/13OGmvv8BMbShdGuncfYYCjs3_YpKeC8wVftFVb1pbHk/edit link]
|-
|-
| European Union || Prague || 646 || link
| Bouches du Rhône || Marseille || Les Pennes Mirabeau || 30 || link
|}
|}
This approach of finding a centroid seems to give good results. For Belgium there is not a large difference with the geographic centroid, which is expected for a densely populated country. For Norway it is much closer to the population area's.
This approach of finding a centroid seems to give good results. As more cities are added the centroid does not change for most countries.


For small countries, it is clear that the major city should be used as Centroid. Think of Andorra, Liechtenstein, Monaco and San Marino.
For small countries, it is clear that the major city should be used as Centroid. Think of Andorra, Liechtenstein, Monaco and San Marino.
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* green pins - geographic centroids
* green pins - geographic centroids
* red pins - wikipedia centroids (barycenters)
* red pins - wikipedia centroids (barycenters)
* dots - cities in second place


== Country Remarks ==
== Country Remarks ==
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* ''Italy'' - the centroid is dominated by Rome, but might move upwards towards Florence, when more cities in the populous north are added;
* ''Italy'' - the centroid is dominated by Rome, but might move upwards towards Florence, when more cities in the populous north are added;
* ''Lithuania'' - the medium sized cities Kaunas;
* ''Lithuania'' - the medium sized cities Kaunas;
* ''Morocco'' - the centroid lies along the coast between the large cities Casablanca and Rabat;
* ''Netherlands'' - as expected in Utrecht. This is in the center of the country and also a center of motorways;
* ''Netherlands'' - as expected in Utrecht. This is in the center of the country and also a center of motorways;
* ''Norway'' - the centroid is in Skien, but could have been in Oslo, or in between these two cities. The centroid is much lower than the actual geographic centroid;
* ''Norway'' - the centroid is in Skien, but could have been in Oslo, or in between these two cities. The centroid is much lower than the actual geographic centroid;
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