Europe Data set:> eurodist                 Athens Barcelona…

July 3, 2010
By

(This article was first published on Human Mathematics, and kindly contributed to R-bloggers)



Europe

Data set:
> eurodist
                Athens Barcelona Brussels Calais Cherbourg Cologne Copenhagen
Barcelona         3313                                                      
Brussels          2963      1318                                            
Calais            3175      1326      204                                   
Cherbourg         3339      1294      583    460                            
Cologne           2762      1498      206    409       785                  
Copenhagen        3276      2218      966   1136      1545     760          
Geneva            2610       803      677    747       853    1662       1418
Gibraltar         4485      1172     2256   2224      2047    2436       3196
Hamburg           2977      2018      597    714      1115     460        460
Hook of Holland   3030      1490      172    330       731     269        269
Lisbon            4532      1305     2084   2052      1827    2290       2971
Lyons             2753       645      690    739       789     714       1458
Madrid            3949       636     1558   1550      1347    1764       2498
Marseilles        2865       521     1011   1059      1101    1035       1778
Milan             2282      1014      925   1077      1209     911       1537
Munich            2179      1365      747    977      1160     583       1104
Paris             3000      1033      285    280       340     465       1176
Rome               817      1460     1511   1662      1794    1497       2050
Stockholm         3927      2868     1616   1786      2196    1403        650
Vienna            1991      1802     1175   1381      1588     937       1455
                Geneva Gibraltar Hamburg Hook of Holland Lisbon Lyons Madrid
Barcelona                                                                  
Brussels                                                                   
Calais                                                                     
Cherbourg                                                                  
Cologne                                                                    
Copenhagen                                                                 
Geneva                                                                     
Gibraltar         1975                                                     
Hamburg           1118      2897                                           
Hook of Holland    895      2428     550                                   
Lisbon            1936       676    2671            2280                   
Lyons              158      1817    1159             863   1178            
Madrid            1439       698    2198            1730    668  1281      
Marseilles         425      1693    1479            1183   1762   320   1157
Milan              328      2185    1238            1098   2250   328   1724
Munich             591      2565     805             851   2507   724   2010
Paris              513      1971     877             457   1799   471   1273
Rome               995      2631    1751            1683   2700  1048   2097
Stockholm         2068      3886     949            1500   3231  2108   3188
Vienna            1019      2974    1155            1205   2937  1157   2409
                Marseilles Milan Munich Paris Rome Stockholm
Barcelona                                                  
Brussels                                                   
Calais                                                     
Cherbourg                                                  
Cologne                                                    
Copenhagen                                                 
Geneva                                                     
Gibraltar                                                  
Hamburg                                                    
Hook of Holland                                            
Lisbon                                                     
Lyons                                                      
Madrid                                                     
Marseilles                                                 
Milan                  618                                 
Munich                1109   331                           
Paris                  792   856    821                    
Rome                  1011   586    946  1476              
Stockholm             2428  2187   1754  1827 2707         
Vienna                1363   898    428  1249 1209      2105

Multi-dimensional scaling of the distances:

> cmdscale(eurodist)
                        [,1]        [,2]
Athens           2290.274680  1798.80293
Barcelona        -825.382790   546.81148
Brussels           59.183341  -367.08135
Calais            -82.845973  -429.91466
Cherbourg        -352.499435  -290.90843
Cologne           293.689633  -405.31194
Copenhagen        681.931545 -1108.64478
Geneva             -9.423364   240.40600
Gibraltar       -2048.449113   642.45854
Hamburg           561.108970  -773.36929
Hook of Holland   164.921799  -549.36704
Lisbon          -1935.040811    49.12514
Lyons            -226.423236   187.08779
Madrid          -1423.353697   305.87513
Marseilles       -299.498710   388.80726
Milan             260.878046   416.67381
Munich            587.675679    81.18224
Paris            -156.836257  -211.13911
Rome              709.413282  1109.36665
Stockholm         839.445911 -1836.79055
Vienna            911.230500   205.93020

Plot

     require(stats)
     loc <- cmdscale(eurodist)
     rx <- range(x <- loc[,1])
     ry <- range(y <- -loc[,2])
     plot(x, y, type="n", asp=1, xlab="", ylab="")
     abline(h = pretty(rx, 10), v = pretty(ry, 10), col = "light gray")
     text(x, y, labels(eurodist), cex=0.8)

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