Is there a curved EdgeShapeFunction that has arrowheads?

Question

The undocumented "CurvedArc" EdgeShapeFunction draws edges as curves (instead of straight lines). However, it does not draw arrowheads for directed graphs.

Is there a built-in EdgeShapeFunction specification that draws directed edges as curved arcs, with a consistent curve direction relative to the edge direction, and visible arrowheads?

I could certainly create my own edge shape function that does this. But this is such a frequently needed edge shape function that I am hoping that it is already built in, just not documented (just like "CurvedArc").

---

Example of a graph where this would be useful, and CurvedArc fails.

RelationGraph[MemberQ[{1, 2, 4}, Mod[#1 - #2, 7]] &, Range[0, 6],
 EdgeShapeFunction -> "CurvedArc"]

Note that this is a directed graph.

Edge shape function that would work better with this graph:

rot[{x_, y_}] := {-y, x}
arc = Function[{pts, edge},
  Module[{s = First[pts], t = Last[pts]},
   {Arrowheads[{{Automatic, 2/3}}], 
    Arrow@BezierCurve[{s, s + (t - s)/2 + 1/8 rot[t - s] , t}]}
   ]
  ]

All edge shape function specs should be listed by GraphElementData["EdgeShapeFunction"] but they aren't.

Answer 1

We can check if Graph calls GraphElementData during the drawing stage:

With[{g = Graph[{1 -> 2}, GraphLayout -> "GravityEmbedding"]},
 TracePrint[MakeBoxes[g], _GraphElementData, TraceInternal -> True]
];

GraphElementData[CurvedEdge]

   GraphElementData[{CurvedEdge,0.0183437}]

And so:

RelationGraph[MemberQ[{1, 2, 4}, Mod[RandomChoice[{Abs, Identity}][#1 - #2], 7]] &, 
  Range[0, 6], EdgeShapeFunction -> "CurvedEdge"]