(Tree) Graph Layout

Question

I am trying to draw a graph in a tree-like form. I can't use TreeGraph because what I am drawing is not properly a tree (has loops) so TreeGraph won't draw it. Here is the code:

Graph[{1 -> 3, 1 -> 4, 1 -> 5, 3 -> 7, 3 -> 8, 4 -> 6, 4 -> 7, 5 -> 8,6 -> 12, 7 -> 12, 8 -> 12},
GraphLayout -> "LayeredEmbedding",
VertexLabels -> "Name"]

and this is the output:

My question: is it possible to move vertex 6 to the left of vertex 7, i.e. to achieve a LayeredLeft effect?

If vertex 3 were the same distance from 4 as 4 is from 5 that would be even better, i.e. some kind of grid effect.

Thanks in advance

Answer 1

You can manually set the VertexCoordinates. The order of the coordinates are

Graph[
  {1 -> 3, 1 -> 4, 1 -> 5, 3 -> 7, 3 -> 8, 4 -> 6, 4 -> 7, 5 -> 8, 6 -> 12, 
   7 -> 12, 8 -> 12}] // VertexList

{1, 3, 4, 5, 7, 8, 6, 12}

Graph[
 {1 -> 3, 1 -> 4, 1 -> 5, 3 -> 7, 3 -> 8, 4 -> 6, 4 -> 7, 5 -> 8, 6 -> 12, 
  7 -> 12, 8 -> 12},
 VertexLabels -> "Name",
 VertexCoordinates -> {
   {1, 1.5}, {1, 1}, {0, 1}, {2, 1}, {1, .5}, {2, .5}, {0, .5}, {1, 0}}]

Alternatively, change the order of entry of the edges

Graph[{1 -> 4, 4 -> 6, 4 -> 7, 1 -> 3, 1 -> 5, 3 -> 7, 3 -> 8, 5 -> 8, 
  6 -> 12, 7 -> 12, 8 -> 12},
 VertexLabels -> "Name"]

Answer 2

Simply use Sorted vertex list as the first argument of Graph to avoid manual modification of vertex coordinates or of the edge list:

g1 = Graph[{1 -> 3, 1 -> 4, 1 -> 5, 3 -> 7, 3 -> 8, 4 -> 6, 4 -> 7, 
    5 -> 8, 6 -> 12, 7 -> 12, 8 -> 12}, 
   GraphLayout -> "LayeredEmbedding", VertexLabels -> "Name", ImageSize -> 300];

g2 = Graph[Sort[VertexList[g1]], EdgeList[g1], VertexLabels -> "Name", ImageSize -> 300];

Row[{g1, g2}, Spacer[10]]