<｜begin▁of▁sentence｜>### Instruction:
Given a set of paths ['can', 'cane', 'cant', 'cat', 'dog', 'dot'], create a prefix tree (trie) using NetworkX to represent these paths with common prefixes. Show how to get the list of edges in the tree, identify the leaf nodes, and recover the original paths from the tree.
### Response:
import networkx as nx

# Create a list of paths (strings)
paths = ['can', 'cane', 'cant', 'cat', 'dog', 'dot']

# Generate the prefix tree from the list of paths
T = nx.prefix_tree(paths)

# Output the edges of the prefix tree
print(list(T.edges()))

# Find and print the leaf nodes
NIL = -1
leaf_nodes = list(T.predecessors(NIL))
print('Leaf nodes:', leaf_nodes)

# Recover and print the original paths from the prefix tree
recovered = []
for leaf in leaf_nodes:
    prefix = ''
    current_node = leaf
    while current_node != 0:  # 0 is the root node
        prefix = str(T.nodes[current_node]['source']) + prefix
        current_node = next(T.predecessors(current_node))
    recovered.append(prefix)
print('Recovered paths:', sorted(recovered))
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