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graphs and networks - Edge Labels with distance between vertices


I am trying to make traveling salesman type graph using the locations of NFL stadiums as the vertices. I need to get the EdgeLabels to appear was the distance between the vertices. I was able to slightly modify some code from


Building graph based on the cities connection?


but I am still unsure about how to incorporate the distances.


stateConnections = {{"TEN", "CAR"}, {"NYGJ", "PIT", "DET"}, {"SEA", 
"MIN" }, {"SFO", "SEA", "SDO"}, {"ARZ", "HOU"}, {"DAL", 
"STL"}, {"PHI", "MIA", "KCY"}, {"OAK", "ARZ", "DEN"}, {"DEN", 
"DAL"}, {"GBY", "CIN", "CHI"}, {"MIN", "MIA"}, {"NOR", "TEN", 
"HOU"}, {"DET", "KCY"}, {"BUF", "CLE"}, {"CLE", "NWE"}, {"NWE", 
"TBY"}, {"TBY", "STL"}, {"PIT", "BAL"}, {"JAC", "ATL"}, {"IND", 

"BAL", "CHI"}, {"ATL", "CIN"},  {"JAC", "BUF"}, {"WAS", "CAR", 
"JAC"}, {"SDO", "ARZ"}};


stateData = {"TEN,36.1665,-86.7713", "NYGJ,40.8122,-74.077", "PIT,40.4468,-80.0158", "CAR,35.2258,-80.8529", "BAL,39.278,-76.6228", "TBY,27.976,-82.5033", 
"IND,39.7601,-86.1638", "MIN,44.9739,-93.2581", 
"ARZ,33.5277,-112.263", "DAL,32.7478,-97.0928", 
"ATL,33.7576,-84.401", "NYGJ,40.8122,-74.077", 
"DEN,39.7439,-105.02", "MIA,25.9579,-80.2388", 
"PHI,39.9008,-75.1675", "CHI,41.8623,-87.6167", 

"NWE,42.0909,-71.2643", "WAS,38.9077,-76.8645", 
"GBY,44.5013,-88.0622", "SDO,32.7831,-117.12", 
"NOR,29.9509,-90.0814", "HOU,29.6848,-95.411", 
"BUF,42.7737,-78.787", "SFO,37.7135,-122.386", 
"JAC,30.3239,-81.6374", "CLE,41.506,-81.6996", 
"OAK,37.7514,-122.201", "KCY,39.0489,-94.484", 
"STL,38.633,-90.1885", "SEA,47.5952,-122.332", 
"CIN,39.0954,-84.516", "DET,42.3402,-83.0458"};

stateAbbreviations = Union[Flatten[stateConnections]];

stateToNumber = MapThread[Rule, {stateAbbreviations, Range[Length[stateAbbreviations]]}];
numberToState = MapThread[ Rule, {Range[Length[stateAbbreviations]], stateAbbreviations}];
allConnections = Flatten[Function[e, Map[UndirectedEdge[First[e], #] &, Rest[e]]] /@ stateConnections];
connections = Union[Sort /@ allConnections];
stateCenters = First[StringSplit[#, ","]] -> ToExpression /@ RotateLeft@Rest[StringSplit[#, ","]] & /@ stateData;
stateCoords = (# & /@ stateAbbreviations) /. stateCenters;
temp = Graph[connections /. stateToNumber];
vertexCoordinates = stateCoords[[VertexList[temp]]];
g = Graph[connections /. stateToNumber, VertexCoordinates -> vertexCoordinates, VertexLabels -> numberToState, VertexShapeFunction -> "Circle", VertexSize -> 1, VertexLabelStyle -> Directive[Black, 7]];


Show[Graphics[{LightGray, CountryData["USA", "Polygon"]}], g, ImageSize -> 1000]

Answer



In Mathematica 10 it is easy to do with GeoDistance. Simply replace your g with the following lines


stateToLocation = 
  Rule[First[#], ToExpression[Rest[#]]] & /@ (StringSplit[stateData, 
     ","]);
edgeLabels = 
  Thread[Rule[
    EdgeList[g], (EdgeList[g] /. numberToState /. stateToLocation) /. 
     UndirectedEdge -> GeoDistance]];

g = Graph[connections /. stateToNumber, 
   VertexCoordinates -> vertexCoordinates, 
   VertexLabels -> numberToState, VertexShapeFunction -> "Circle", 
   VertexSize -> 1, VertexLabelStyle -> Directive[Black, 7], 
   EdgeLabels -> edgeLabels];

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