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I have a bunch of high dimensional data and I want to use a graph to plot relationships among that data. To keep things small, say the data is

d[x_, y_] := Total[Abs[x - y]];
data = RandomReal[{0, 1}, {10, 5}];
RelationGraph[0.2 < d[#1, #2] < 1.5 &, data, data]

This draws a nice graph of all the elements whose distance apart is between 0.2 and 1.5. If I want to label the graph with the index number, then

RelationGraph[0.2 < d[#1, #2] < 1.5 &, dist, dist, VertexLabels -> "Index"]

works fine. But if I want to use my own labels, Mathematica does not draw the graph and simply returns the input unchanged. For example, neither of these:

RelationGraph[0.2 < d[#1, #2] < 1.5 &, dist, dist, 
              VertexLabels -> {1 -> "this", 2 -> "that"}]

RelationGraph[0.2 < d[#1, #2] < 1.5 &, dist, dist, 
              VertexLabels -> Table[i -> Subscript[v, i], {i, 5}]]

return any graph. Is there a trick to using VertexLabels? Or do I need to search for another way to draw the graphs?

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    $\begingroup$ You need Table[dist[[i]] -> Subscript[v, i], {i, 5}] - it takes the element's value not the position. $\endgroup$
    – flinty
    Commented Jul 1, 2020 at 22:07

1 Answer 1

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RelationGraph[0.2 < d[#1, #2] < 1.5 &, data, data, 
 VertexLabels -> {data[[1]] -> "this", data[[2]] -> "that"}]

enter image description here

RelationGraph[0.2 < d[#1, #2] < 1.5 &, data, data, 
 VertexLabels -> MapIndexed[# -> Subscript[v, #2[[1]]] &, data]]

enter image description here

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