visualization – I want to place the edges of a Hamiltonian cycle (Graph, GraphLayout)

From Mathematica 11.3, GraphLayout -> "CircularEmbedding" place the vertices around a circle in the same order they appear in vertexList[graph].

Thus, you must rearrange the vertices according to the Hamiltonian cycle.

Example:

g = GraphData["DodecahedralGraph"];

Graphic[
 FindHamiltonianCycle[g][[1, All, 1]],
EdgeList[g],
GraphLayout -> "CircularEmbedding"
]

enter the description of the image here


How to do IGraph / M is as follows, if you prefer:

Needs["IGraphM`"]
IGLayoutCircle @ IGReorderVertices[FindHamiltonianCycle[FindHamiltonianCycle[FindHamiltonianCycle[FindHamiltonianCycle[g][[1, All, 1]], g]

enter the description of the image here

IGReorderVertices preserve the properties of the graphic (including style) when reordering vertices.