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.


g = GraphData["DodecahedralGraph"];

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

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

IGLayoutCircle @ IGReorderVertices[FindHamiltonianCycle[FindHamiltonianCycle[FindHamiltonianCycle[FindHamiltonianCycle[g][[1, All, 1]], g]

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