TreePlot: arrows on specific lines

Question

I have the following list of rules:

L={1->2,2->3,3->3};

and I want to plot a tree graph:

TreePlot[L,VertexRenderingFunction->({Disk[#,.02],Text[#2,#1+{.15,0}]}&)]

The thing is, I would like to have the arrows only on certain lines, such as the second one, 2->3. To this end, I shall write the rules as

L={{1->2,2->3,3->3},{False,True,False}};

and generate the tree by TreePlot[L[[1]],...]. My question is: how can I get the arrows only at True positions, as in the example above?

I thought I could use directed edges and undirected edges, that is,

L={UndirectedEdge[1,2],DirectedEdge[2,3],UndirectedEdge[3,3]};

but i get the message TreePlot::grph:L is not a valid graph.

How can I make it work?

Answer 1

TreePlot is the old way to plot trees. It has been superseded by Graph and GraphLayout. GraphLayout -> "LayeredEmbedding" can be used for trees. Please check the documentation on how to set various options for this embedding, including specifying the root: GraphLayout. They're a bit hidden down the page.

Mathematica 10 and later supports mixed graphs with both directed and undirected edges. One way to accomplish what you want is to use these. Unfortunately "LayeredGraphEmbedding" doesn't seem to support them. As a workaround we create an undirected graph, compute the vertex coordinates, then apply them to our mixed graph.

g = Graph[{1 <-> 2, 2 -> 3, 3 <-> 3}, VertexLabels -> "Name"]

UndirectedGraph[g, 
   GraphLayout -> {"LayeredEmbedding", "RootVertex" -> 2}]

pts = GraphEmbedding[%];

SetProperty[g, VertexCoordinates -> pts]

Alternatively, this last step could be replaces by custom code that takes pts, the edge list, some directedness specification for the edges, and draws the edges manually, putting the arrowheads where necessary.

Answer 2

If you have to use TreePlot, you can also

Use EdgeRenderingFunction:

TreePlot[L, VertexRenderingFunction -> ({Disk[#, .02], Text[#2, #1 + {.05, .025}]} &), 
 EdgeRenderingFunction -> ({Darker@Red, 
     If[#2 === {2, 3}, {Arrowheads[{0, 0, .05, 0}], Arrow[#]}, Line[#]]} &)]

Post-process selected Lines to Arrows:

TreePlot[L, VertexRenderingFunction -> ({Disk[#, .02], Text[#2, #1 + {.05, .025}]} &)] /. 
 Line[x_] :> (Line /@ x ) /. 
 Line[{2, 3}] :> {Arrowheads[{0, 0, .05, 0}], Arrow[{2, 3}]}