<｜begin▁of▁sentence｜>### Instruction:
As the overseer of our laboratory's data management operations, imagine we have acquired a dataset concerning genetic marker sequences that share common subsequences. Our dataset includes the following sequences: ['can', 'cane', 'cant', 'cat', 'dog', 'dot']. Your task is to structure this dataset into a hierarchical representation using NetworkX to create a prefix tree, which is a data structure that allows us to efficiently organize and search through these sequences by their shared prefixes.

Could you devise a method to construct this prefix tree within NetworkX and then demonstrate a strategy for extracting a list of all the interconnections, which in this context would be equivalent to the network’s edges? Additionally, we require a procedure to pinpoint the terminal elements of this hierarchy, commonly referred to as leaf nodes, as they represent the end of a sequence in our dataset.

Furthermore, once the prefix tree is functional, we will need a reliable technique to traverse the structure backwards to effectively retrieve the original sequences from the conglomerate hierarchy. I trust in your expertise to incorporate our sequence data into this NetworkX structure with precision, allowing for a streamlined analysis and retrieval of genetic markers in our ongoing research endeavors.
### 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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