TreePlot does not give a "binary-looking" tree for a binary tree

Question

I use the following code to generate a binary tree with root 1.

TreePlot[{1 -> 2, 1 -> 3, 2 -> 4, 2 -> 5, 3 -> 6, 3 -> 7, 4 -> 8, 
  4 -> 9, 5 -> 10, 5 -> 11, 6 -> 12, 6 -> 13, 7 -> 14, 7 -> 15, 
  8 -> 16, 8 -> 17, 10 -> 18, 10 -> 19, 11 -> 20, 11 -> 21, 13 -> 22, 
  13 -> 23, 15 -> 24, 18 -> 25, 18 -> 26, 19 -> 27, 19 -> 28, 
  25 -> 29, 25 -> 30, 26 -> 31, 31 -> 32, 31 -> 33}, 
 VertexLabeling -> True]

However, it generates a non-binary-looking tree with 2 as the "root".

Anyone has solution for this? Thank you!

Answer 1

The documentation says:

TreePlot[g] attempts to choose the root so as to make trees have as few layers as possible.

What it does not say is that edge directions are ignored when determining the root node. The result is that TreePlot rejects the expected tree rooted at 1 because it has eight layers as opposed to the seven layers obtained with 2 as the root.

While this behaviour might be less than useful, the good news is that if we explicitly specify the proper root node then the tree is rendered nicely:

TreePlot[
  { 1 -> 2, 1 -> 3, 2 -> 4, 2 -> 5, 3 -> 6, 3 -> 7, 4 -> 8
  , 4 -> 9, 5 -> 10, 5 -> 11, 6 -> 12, 6 -> 13, 7 -> 14, 7 -> 15
  , 8 -> 16, 8 -> 17, 10 -> 18, 10 -> 19, 11 -> 20, 11 -> 21
  , 13 -> 22, 13 -> 23, 15 -> 24, 18 -> 25, 18 -> 26, 19 -> 27
  , 19 -> 28, 25 -> 29, 25 -> 30, 26 -> 31, 31 -> 32, 31 -> 33
  }
, Top
, 1
, VertexLabeling -> True
]

Note the addition of the arguments Top and 1 which indicate that the tree should be rooted at the top of the diagram and that the root node should be 1.