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I'm trying to find a code that can quantify the proximity of countries in Europe, taking into account shared borders and I am completely stumped.

So ideally, countries that share a border have a high number and then countries where you have to pass through several borders have a significantly lower score.

Is there also a code which could tell me how many borders one would have to cross to get from country A to country B?

Any help would be greatly appreciated!

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    $\begingroup$ By "borders", do you mean geographical borders? $\endgroup$ – J. M.'s technical difficulties Mar 12 '18 at 16:06
  • $\begingroup$ Yes, the shared geographical borders. $\endgroup$ – user09320290 Mar 12 '18 at 16:08
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Update

Inspired by J.M.'s comment I will give a more compact and more functional solution here:

euCountries = CountryData["Europe"];

edges = Inner[
    Function[ {c, listbc}, Sort @ UndirectedEdge[ c, # ]& /@ listbc ],
    euCountries,
    Map[ CountryData[ #, "BorderingCountries" ]&, euCountries ],
    Union
];

g = Graph[ euCountries, edges, VertexLabels -> "Name", ImageSize -> Large ];

Original Solution

A quick an dirty go at this is maybe to build a graph for say Europe with an edge connecting two countries meaning that they are neighbors.

countriesInEurope = CountryData[ "Europe" ];

We then find the neighbors for each country and store them together with the country itself in a list of strings:

listNeighbors = (({#}~Join~CountryData[#, "BorderingCountries"]) & /@ 
countriesInEurope) /. e_Entity :> CountryData[e, "Name"];

We now construct the edges for the graph with taking care of duplicates, so that two countries will only be connected by a single undirected edge:

countryEdges[ list_ ] := With[
   {
     country = First @ list,
     neighbors = Rest @ list
   } ,
   If[ neighbors === {}, Return[Nothing] ];
   Map[ country \[UndirectedEdge] # &, neighbors ]
];

edges = Map[ countryEdges, listNeighbors ] // RightComposition[
   Flatten,
   ReplaceAll[ UndirectedEdge[ a_, b_] :> UndirectedEdge @@ Sort@{a, b}],
   DeleteDuplicates

];

Now we can have our graph:

g = Graph[ Flatten @ listNeighbors, edges, VertexLabels -> "Name" , ImageSize -> Large]

enter image description here

Working With the Graph

We see that there are two countries in between Germany and Croatia:

FindShortestPath[ g, "Germany", "Croatia"]

{"Germany", "Austria", "Hungary", "Croatia"}

We can also have a CountryDistance that would give the number of borders to cross:

countryDistance[a_ , b_ ] := FindShortestPath[ g, a, b] // Length // # - 1 &

countryDistance[ "Germany", "Morocco" ]

3

So with a bit of work more can be done in this line...

|improve this answer|||||
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    $\begingroup$ Here's a compact version: euCountries = CanonicalName[CountryData["Europe"]]; edges = Union[Flatten[Table[Sort[UndirectedEdge[bord, #]], {bord, CanonicalName[CountryData[#, "BorderingCountries"]]}] & /@ euCountries]]; g = Graph[euCountries, edges, ImageSize -> Large, VertexLabels -> "Name"] $\endgroup$ – J. M.'s technical difficulties Mar 13 '18 at 4:58
  • $\begingroup$ @J.M. Interestingly, one may drop CanonicalName completely in your version as VertexLabels -> "Name" takes care of it. $\endgroup$ – gwr Mar 13 '18 at 11:07
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    $\begingroup$ I know, I just preferred storing strings instead of Entity[] objects in the vertices. $\endgroup$ – J. M.'s technical difficulties Mar 13 '18 at 12:39

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