def _delete_nonterminal_leaves(edges, terminals):
r"""Prunes all non-terminal leaves from the tree.
Given the edges of a tree and a set of terminal vertices, this method
removes all non-terminal leaves and returns the new tree edges.
Parameters
----------
edges : list
A list of the edges of the tree.
terminals : set
A set of the terminal vertices.
Returns
-------
tree_edges : list
A list of the edges of the pruned tree.
Notes
-----
This method deletes all non-terminal leaves from the tree. This process
is repeated until all leaves are terminals. There is room to improve
this algorithm.
"""
# Form a graph from the edge list.
tree = Graph()
for (u, v) in edges:
tree.add_edge(u, v)
# Now delete all leaves that are not terminals
while True:
leaves = tree.leaves()
changed = False
for leaf in leaves:
if leaf not in terminals:
tree.delete_vertex(leaf)
changed = True
if not changed:
break
return tree.edges()
