How to make a Tree diagram using images as vertices, that goes left to right

In Graph or TreeGraph, I can make the vertices images, but the tree always starts at the top.

TreeGraph[{1 -> 2, 1 -> 3},
VertexShape -> {1 -> Graphics[RegularPolygon],
2 -> Graphics[RegularPolygon],
3 -> Graphics[RegularPolygon]}, VertexSize -> 0.6] If I use TreePlot instead, then I can make the tree start on the left:

TreePlot[{1 -> 2, 1 -> 3, 3 -> 4, 3 -> 5}, Left] But TreeGraph doesn't have the "Left" option and TreePlot doesn't have the VertexShape option. How can I have images in a tree that goes from left to right?

Graph has the GraphLayout Option, but I couldn't find the one that does what I want.

It's explained on the doc page of GraphLayout. This documentation page is very long, and most of the information is under the Scope section, under specific layout methods.

Graph[{1 -> 2, 1 -> 3, 3 -> 4, 3 -> 5},
GraphLayout -> {"LayeredEmbedding", "RootVertex" -> 1, "Orientation" -> Left}] You do not need to use TreeGraph unless you also want to verify that the graph is indeed a tree. Graph will do. The key is GraphLayout.

With this layout, the root of directed trees is not detected automatically. You can specify it automatically as I did above. With "LayeredDigraphEmbedding", it is detected, but the layout will not be identical.

You can also achieve the same with IGLayoutReingoldTilford from the IGraph/M package.

IGLayoutReingoldTilford[
Graph[{1 -> 2, 1 -> 3, 3 -> 4, 3 -> 5}],
"RootVertices" -> {1}, "Rotation" -> Pi/2
] tg = TreeGraph[{1 -> 2, 1 -> 3},
VertexShape -> {1 -> Graphics[RegularPolygon],
2 -> Graphics[RegularPolygon],
3 -> Graphics[RegularPolygon]}, VertexSize -> 0.6]

SetProperty[tg, VertexCoordinates -> RotationTransform[Pi/2][GraphEmbedding[tg]]] Alternatively, you can use TreePlot with the hidden options "VertexNames", "VertexFrameBackground" and "VertexFrameStyle":

shapes = Graphics[RegularPolygon[#], ImageSize -> 90, Background -> None] & /@
{4, 6, 5};

TreePlot[{1 -> 2, 1 -> 3}, Left,
DirectedEdges -> True, VertexLabeling -> True,
"VertexNames" -> shapes,
"VertexFrameBackground" -> None,
"VertexFrameStyle" -> None] 