What do you mean by select the largest? I think if you want the longest line, you can simply connect every edge.

Maybe you mean connect in a similar way but choose the longest?

@Szabolcs is there any way to extract graphics primitives from GraphElementData? E.g>: GraphElementData["VertexShapeFunction"] "ConcaveDiamond".

@Kuba I think I tried once and didn't succeed. I didn't try very hard though. Specifically, I did not try to Trace what Graph does what it evaluates to obtain the shapes.

@Kuba Got it! Spelunk[GraphComputation`GraphElementDataDump`Shape2DVertex] will take you there.

More specifically, look at the definitions of GraphComputation`GraphElementDataDump`shape2d

@Szabolcs Thanks :D

@Kuba Do you know of a builtin way to convert a directed graph to undirected and preserve only bidirectional edges?

@Szabolcs bidirected edge is a pair of directed edges?

@Kuba Yes, a -> b, b -> a. Of course there are fairly simple ways to do it but I just wanted to make sure there's nothing built in that I missed that already does it in one step.

@Szabolcs no sorry, only manual approaches come to my mind.

Solving the "Easy Cube" game with Mathematica

community.wolfram.com/groups/-/m/t/870698