Just a quick note for those who may be looking to make binary tree graphs in Sage. In the end you may be better off using Graphviz for more complex graphing needs. However, if you are determined to use sage here is some example code for a binary tree. I will try and put some more in depth graphs later using NetworkX:
BinaryTree={‘ROOT’:[1],1:[2,3],2:[4,5,6],3:[7,8,9]}
T=DiGraph(BinaryTree)
TREE=T.plot(graph_border=True,vertex_size=120, layout=”tree”,
tree_orientation=”down”,tree_root=’ROOT’,edge_colors=”red”,vertex_labels=True)
TREE.show()
The syntax here is fairly self explanatory. If you need more details remember you can hit the tab key at different points and a better description will be produced. Here is an example view of what you would see after hitting the tab key left of the T. variable (after assigning it to the DiGraph class) . Try hitting the tab key in a variety of areas and you may be surprised what helpful information might pop up. Remember this will work in python as well.

sage binary tree
For more practical use of nodes and graphs check out NetworkX.