There is no y coordinate for the tree nodes but you can get the x (branch length) like this:

from Bio import Phylo

tree = Phylo.read("example.nwk", "newick")

#all nodes:
print(tree.depths())

# only terminals nodes:
print(tree.get_terminals())

Thanks Simon. I don't think I asked my question in the quite right way. Although a newick tree is a just a mathematical object with no representation in 2D space, some drawing algorithm must have been used to render that object onto two (x,y) dimensions on a graph. So I am wondering 1) what algorithm(s) can render a newick tree object into a 2D graph like in the image below, and 2) how can I grab the coordinates of the nodes and edges?

Thanks!