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[FEATURE] Test if a graph is edge-weighted

Szabolcs Horvát
Posted 9 years ago
POSTED BY: Szabolcs Horvát
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The solution above suffers from bad performance, unfortunately. Here's a faster, but complicated version:

https://mathematica.stackexchange.com/a/163247/12

edgeWeightedQ[g_?EmptyGraphQ] := False (* avoid error with First if graph has no edges but is vertex weighted *)
edgeWeightedQ[g_] :=
    WeightedGraphQ[g] &&
    With[{weights = Developer`ToPackedArray@GraphComputation`WeightValues[g]},
      If[First[weights] === 1 && MinMax[weights] === {1, 1},
        PropertyValue[g, EdgeWeight] =!= Automatic,
        True
      ]
    ]

A similar implementation is included in IGraph/M as IGEdgeWeightedQ.
POSTED BY: Szabolcs Horvát

Originally I wrote that the best I could come up with was

 PropertyValue[wg, EdgeWeight] =!= Automatic

but I was not confident that this would work in every situation.

Perpahs some thought that this was nitpicking. It wasn't:

g = Graph[{}, {}];

PropertyValue[g, EdgeWeight]
(* $Failed *)

It does not work on the null graph.

So in case someone else wants to test if a graph is edge-weighted, let me rewise that to 

WeightedGraphQ[wg] &&  PropertyValue[wg, EdgeWeight] =!= Automatic

(keeping in mind that && is short circuiting)

If anyone finds a problem with this variant, let me know.
POSTED BY: Szabolcs Horvát
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