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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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# minimum weighted distance sum - find the weighted distance sum that is the lowest. The corresponding city is the centroid city;
 
# minimum weighted distance sum - find the weighted distance sum that is the lowest. The corresponding city is the centroid city;
 
# add cities - more cities can be added to see whether the found centroid city is correct. For this recommence on step 1;
 
# add cities - more cities can be added to see whether the found centroid city is correct. For this recommence on step 1;
 +
 +
=== Spreadsheet ===
 +
The recipe described above has been implemented in a Google spreadsheet. For each country (territory) a separate spreadsheet needs to be created (just copy an existing) one. Each spreadsheet has multiple worksheets.
 +
* population worksheet: this worksheet lists the largest cities and their population (as columns), ordered by the population. The fraction is calculated from the data;
 +
* 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;
 +
* 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 ==
 
This recipe has been applied on the following countries:
 
This recipe has been applied on the following countries:
 
{| class="wikitable sortable"
 
{| class="wikitable sortable"
 
|-
 
|-
! Country !! Centroid city !! quality !! spreadsheet
+
! Country !! Centroid city !! Runnerup city !! quality !! spreadsheet
 +
|-
 +
| Albania || Tirana || Kamëz || 13 || link
 +
|-
 +
| Algeria || Algers || Blida || 15 || link
 +
|-
 +
| Austria || Vienna || Baden bei Wien || 61  || [https://docs.google.com/spreadsheets/d/1joXvrjWDmabsyFqf4V6bBsmCJHp0fhCB5oAy8nOStRU link]
 +
|-
 +
| Belgium || Brussels || Antwerp ||  0.7 || [https://docs.google.com/spreadsheets/d/1-_DRQi9VUrV2o5oVRL01DUBz9iT3ZvVPlvxvz9O_ZLg link]
 +
|-
 +
| Bosnia and Herzegovina || Zenica || || 0.6 || link
 +
|-
 +
| Bulgaria - provinces || Stara Zagora || Plovdiv || 44 || [https://docs.google.com/spreadsheets/d/193RBhO4Dnd4ZwPbepP2oeyF5PkOMDeoxszSNuMW8VrQ link]
 +
|-
 +
| Croatia || Zagreb || Velika Gorica || 30 || [https://docs.google.com/spreadsheets/d/1aWRYBN87i9pO8GbbxcemB38LIexrWnDgZMVqXOAwRaA link]
 +
|-
 +
| Czech Republic || Prague || ||  9  || [https://docs.google.com/spreadsheets/d/1QlsggBo0dOK-gvXR3-wOeeIQOLDSQ6J9TAGijCZ0ENg/ link]
 
|-
 
|-
| Austria || Vienna || || [https://docs.google.com/spreadsheets/d/1joXvrjWDmabsyFqf4V6bBsmCJHp0fhCB5oAy8nOStRU/ link]
+
| Denmark || Copenhagen || Roskilde || 5  || [https://docs.google.com/spreadsheets/d/1uB0MooOA0xT8z9bRfZ1iaKxNph1FQgeUby0HmXSOrKw link]
 
|-
 
|-
| Belgium || Brussels || 296 || [https://docs.google.com/spreadsheets/d/1-_DRQi9VUrV2o5oVRL01DUBz9iT3ZvVPlvxvz9O_ZLg link]
+
| Estonia || Tallinn || Maardu || 12 || [https://docs.google.com/spreadsheets/d/1nhs-FE32-n0taDLiNHxZ71VBGC2mYrBHjLlwI_PNMsQ/ link]
 
|-
 
|-
| Czech Republic || Prague || || [https://docs.google.com/spreadsheets/d/1QlsggBo0dOK-gvXR3-wOeeIQOLDSQ6J9TAGijCZ0ENg/ link]
+
| Finland || Helsinki || || 5 || [https://docs.google.com/spreadsheets/d/1OXHdXZDUJ9So5oSP67ZWzkDdSaQADQdZbDMnp7ekXcU/ link]
 
|-
 
|-
| Denmark || Copenhagen || || [https://docs.google.com/spreadsheets/d/1uB0MooOA0xT8z9bRfZ1iaKxNph1FQgeUby0HmXSOrKw link]
+
| France || Paris || Lyon || 7 || [https://docs.google.com/spreadsheets/d/1-G7VVZDE7xH6yzhsVYpmTTnu3rtgvadMC7WX9yIJqPc link]
 
|-
 
|-
| Estonia || Tallinn || || [https://docs.google.com/spreadsheets/d/1nhs-FE32-n0taDLiNHxZ71VBGC2mYrBHjLlwI_PNMsQ/ link]
+
| Germany - cities || Hannover || Bielefeld || 19 || [https://docs.google.com/spreadsheets/d/1HSNFq2sJiRxarSvY_mHtEOiSIq9fwFAyTh9lA4DfgF4 link]
 
|-
 
|-
| Finland || Helsinki || || [https://docs.google.com/spreadsheets/d/1OXHdXZDUJ9So5oSP67ZWzkDdSaQADQdZbDMnp7ekXcU/ link]
+
| Germany - states || Hesse || Thuringia || 2 || [https://docs.google.com/spreadsheets/d/1HSNFq2sJiRxarSvY_mHtEOiSIq9fwFAyTh9lA4DfgF4 link]
 
|-
 
|-
| France || Paris || || [https://docs.google.com/spreadsheets/d/1-G7VVZDE7xH6yzhsVYpmTTnu3rtgvadMC7WX9yIJqPc link]
+
| Greece || Athens || || || [https://docs.google.com/spreadsheets/d/1RN6YIwDWLgLrultpRt49D83s3UCeAuQErZb4Orriv-Q link]
 
|-
 
|-
| Germany || Hannover || || [https://docs.google.com/spreadsheets/d/1HSNFq2sJiRxarSvY_mHtEOiSIq9fwFAyTh9lA4DfgF4 link]
+
| Hungary || Budapest ||  || || [https://docs.google.com/spreadsheets/d/16VZjIhacrZqKWNp95POnc2qKuLgpfTcIgs8Ygt6nxPI link]
 
|-
 
|-
| Ireland || Dublin || || [https://docs.google.com/spreadsheets/d/15KY_dUl_3PB_taWZNkfdhcv9RhX7YgcyUC21aNADOdE link]
+
| Iceland || Reykjavik || Kópavogur || 10 || [https://docs.google.com/spreadsheets/d/1skWHDUfRtpaUkjXy-WiCWhqGBI8st-FB9sjcMaIRiCc link]
 
|-
 
|-
| Italy || Rome || || [https://docs.google.com/spreadsheets/d/19GxxwjgUrsMB522Vv_3zUCg-bJVyg054WwMK5S3tkP0 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 || Jonava || [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]
 +
|-
 +
| Romania || Bucharest || Ploiești || 4 || [https://docs.google.com/spreadsheets/d/1V-39ygo6LszL2PWHUVi8VFtci1CExjpQLN7Y2w-nUXQ link]
 +
|-
 +
| Serbia - districts || Belgrad || Srem || 5 || [https://docs.google.com/spreadsheets/d/1ComqBolNvRQ7xYrvO4mMsKfcD39b4h6p4MwN7PAEqac/edit?usp=sharing link]
 
|-
 
|-
| Slovakia || Banská Bystrica || [https://docs.google.com/spreadsheets/d/1lTXNbUIM5ATG1C0TpzsgmtGnHFBqt0m2PBtRvVul0XE/ link]
+
| Slovakia || Banská Bystrica || Nitra || 0.3 || [https://docs.google.com/spreadsheets/d/1lTXNbUIM5ATG1C0TpzsgmtGnHFBqt0m2PBtRvVul0XE/ link]
 
|-
 
|-
| Slovenia || Ljubljana || [https://docs.google.com/spreadsheets/d/1CVV7NGr2XZ-iYhE4c48Vm7WBhXPOxa79XrdV5GVck5E/ link]
+
| Slovenia || Ljubljana || Domžale || 74 || [https://docs.google.com/spreadsheets/d/1CVV7NGr2XZ-iYhE4c48Vm7WBhXPOxa79XrdV5GVck5E/ link]
 
|-
 
|-
| Netherlands || Utrecht || [https://docs.google.com/spreadsheets/d/1x8Vfb2ZIjsTmb0lRrO-8YHC6NKmgc58HtP_cNSjeOQY link]
+
| Spain || Madrid || Barcelona || 1.1 || [https://docs.google.com/spreadsheets/d/1Zf0ks3MiWOHbh9CSNiZQwW3yy9jW3l7qFahGYBH-uc8 link]
 
|-
 
|-
| Norway || Skien || [https://docs.google.com/spreadsheets/d/1e3vPPWMyJu6k5rdbqDC9EGgOCgmAmsGZ2JO1oMrCbXw/edit link]
+
| Sweden || Nörrköping || Stockholm || 3 || [https://docs.google.com/spreadsheets/d/16kjE6_IIoqiOHdFB-x1rpJiEesRbNqhwXSv8HTyy_NQ link]
 
|-
 
|-
| Poland || Łódź || [https://docs.google.com/spreadsheets/d/1wBNuc3qItIouZHKLI-c9TrJcL2skF-T6sw_Yh1gPxM4 link]
+
| Switzerland || Olten || Solothurn || 6  || [https://docs.google.com/spreadsheets/d/1VJ08fAdkbvnKAFDnn1RnNXQxWn9nzTK1y5GJ5AJFa1Y link]
 
|-
 
|-
| Portugal || Lisboa || [https://docs.google.com/spreadsheets/d/1DBTu9pNtdLhf0hBPGqnYbLYXnxhAkX0f7eDcRBIrZGU link]
+
| Tunisia || Tunis || || || link
 
|-
 
|-
| Spain || Madrid || [https://docs.google.com/spreadsheets/d/1Zf0ks3MiWOHbh9CSNiZQwW3yy9jW3l7qFahGYBH-uc8 link]
+
| United Kingdom || Coventry || Leicester || 12 || [https://docs.google.com/spreadsheets/d/1xbNe-QDLIZt6h1HvLAa4jzTQoyifdLaiTr4UgaqbHNk link]
 
|-
 
|-
| Sweden || Nörrköping || [https://docs.google.com/spreadsheets/d/16kjE6_IIoqiOHdFB-x1rpJiEesRbNqhwXSv8HTyy_NQ link]
+
| European Union - cities || Munich || Prague || 0.3 || [ link]
 
|-
 
|-
| Switzerland || Olten || [https://docs.google.com/spreadsheets/d/1VJ08fAdkbvnKAFDnn1RnNXQxWn9nzTK1y5GJ5AJFa1Y link]
+
| European Union - countries || Luxemburg || Germany || 29 || [https://docs.google.com/spreadsheets/d/13OGmvv8BMbShdGuncfYYCjs3_YpKeC8wVftFVb1pbHk/edit link]
 
|-
 
|-
| United Kingdom || Leicester || [https://docs.google.com/spreadsheets/d/1xbNe-QDLIZt6h1HvLAa4jzTQoyifdLaiTr4UgaqbHNk 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.
Line 81: Line 130:  
* 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 ==
 
The city population centroids have been found a step by step process. This allows to see how the centroid changes after a city has been added. In general the largest city dominates the position of the centroid. And if that city is also close to the geographic centroid, it will be the centroid in the end (Belgium, Spain). If a large city is surrounded by other cities, then one of those can become the centroid (Norway, Switzerland). The layout of motorways can influence the selection between two cities (France).
 
The city population centroids have been found a step by step process. This allows to see how the centroid changes after a city has been added. In general the largest city dominates the position of the centroid. And if that city is also close to the geographic centroid, it will be the centroid in the end (Belgium, Spain). If a large city is surrounded by other cities, then one of those can become the centroid (Norway, Switzerland). The layout of motorways can influence the selection between two cities (France).
   −
Some individual country observations:
+
In general we see that the largest city is also the centroid city, when it is really much larger than the other cities.
* ''Austria'' - did not know Vienna is so large;
+
 
 +
Some exceptions to this:
 
* ''Belgium'' - the runnerup is Mechelen, so if more cities are added, the centroid might move towards that city along the motorway;
 
* ''Belgium'' - the runnerup is Mechelen, so if more cities are added, the centroid might move towards that city along the motorway;
* ''Czech Republic'' - the country is dominated by Prague
  −
* ''Denmark'' - no surprise that this is Copenhagen. This is by far the largest city of Denmark. And thus much different from the geographic centroid;
  −
* ''Finland'' - the country is dôminated by Helsinki;
   
* ''France'' - the centroid lies along the motorway between Paris and Lyon. There are no cities that are large enough in the top 20 to push the centroid away from Paris towards Lyon. Adding Dijon did not help. Probably due to a lack of motorways to the west from Dijon;
 
* ''France'' - the centroid lies along the motorway between Paris and Lyon. There are no cities that are large enough in the top 20 to push the centroid away from Paris towards Lyon. Adding Dijon did not help. Probably due to a lack of motorways to the west from Dijon;
 
* ''Germany'' - the country is dominated by Berlin. Only thanks to the existence of a large town to the west, the centroid could be moved there (Hannover);
 
* ''Germany'' - the country is dominated by Berlin. Only thanks to the existence of a large town to the west, the centroid could be moved there (Hannover);
 
* ''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;
* ''Ireland'' - the centroid is dominated by Dublin;
  −
* ''Latvia'' - dominated by Riga;
   
* ''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;
 
* ''Poland'' - largest cities are spread out, so Łódź lies in between;
 
* ''Poland'' - largest cities are spread out, so Łódź lies in between;
* ''Portugal'' - the centroid is dominated by Lisbon and surrounding cities;
   
* ''Slovakia'' - there are several small towns fighting to centroid. Banská Bystrica was able to fend them off;
 
* ''Slovakia'' - there are several small towns fighting to centroid. Banská Bystrica was able to fend them off;
* ''Slovenia'' - although Ljubljana is not large, the other towns are even smaller;
   
* ''Spain'' - Madrid is very well placed centrally in the country. Madrid and Barcelona are the greatest influencers on the centroid. The cities on the Canaries have been removed, but the Baleares have been kept.
 
* ''Spain'' - Madrid is very well placed centrally in the country. Madrid and Barcelona are the greatest influencers on the centroid. The cities on the Canaries have been removed, but the Baleares have been kept.
* ''Sweden'' - the country is dominated by the Oslo and surrounded cities. Due to the cities close to Denmark, the centroid is moved to the south.
+
* ''Sweden'' - the country is dominated by the Stockholm and surrounded cities. Due to the cities close to Denmark, the centroid is moved to the south.
 
* ''Switzerland'' - Olten is one of the smaller towns in the valleys around Zurich, which dominates the centroid. Note that for transport a route through Italy is sometimes more advantageous.
 
* ''Switzerland'' - Olten is one of the smaller towns in the valleys around Zurich, which dominates the centroid. Note that for transport a route through Italy is sometimes more advantageous.
* ''United Kingdom'' - Although the UK is dominated by London, there are a lot of large cities to the north. This is the reason Leicester is the centroid.
+
* ''United Kingdom'' - Although the UK is dominated by London, there are a lot of large cities to the north. This is the reason Coventry is the centroid.
    
== Quality ==
 
== Quality ==
Line 121: Line 166:     
=== Actual accuracy ===
 
=== Actual accuracy ===
Can the accuracy of the centroid city be determined from the actual calculations, or their development? Every time another city is added, the centroid might change. But how likely is it that this happens. That depends on the size and relative population of the added city. And it depends on weighted distance to the runnerup centroid city. If the weighted distance is very larger, adding other cities will nut budge the winner city.
+
Can the accuracy of the centroid city be determined from the actual calculations, or their development? Every time another city is added, the centroid might change. But how likely is it that this happens. That depends on the size and relative population of the added city. And it depends on weighted distance to the runnerup centroid city. If the weighted distance is very large, adding other cities will not budge the winner city.
 +
 
 +
So calculate the difference in weighted distance between the winner centroid city and the runner-up centroid city. Divide this by the fractional size of the latest city added. This will result in a dethroning distance. This dethroning distance is the distance required to dethrone the winner city. (In practice this required distance will be much larger)
 +
 
 +
If this dethroning distance is larger than the size of the country, the winner centroid is ok. If the dethroning distance is smaller, then we have to take a closer look. As the dethroning distance will be much larger, we should only look at cases where the dethroning distance is smaller than the actual distance.
 +
 
 +
In the calculated centroids, this implies:
 +
* France (between Paris and Lyon)
 +
* Norway (between Oslo and Skien)
 +
* Portugal (between Lisboa and Odivelas)
 +
* United Kingdom (between Leicester and London)
 +
 
 +
Should we bother from transportation score point of view? Not for Norway and Portugal. For France and United Kingdom more cities should be added.
 +
 
 +
* United Kingdom the centroid moved to Coventry after adding the city;
 +
* France stays difficult, adding another 5 cities caused a switch from Paris to Lyon. Adding cities in between (Auxerre, Chalons) did not help.
    
== Observations ==
 
== Observations ==
 
Can this approach also be used to get an indication of country size?
 
Can this approach also be used to get an indication of country size?

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