<｜begin▁of▁sentence｜>### Instruction:
Given a weighted tree with nodes {1, 2, 3, 4} having weights {3, 1, 4, 2} respectively and edges {(1, 2, 1.0), (1, 3, 2.0), (3, 4, 3.0)}, how can you use the Lukes partitioning algorithm in NetworkX to divide the tree into clusters so that the sum of the node weights in each cluster does not exceed 5 and the weight of the cut edges is minimized?
### Response:
import networkx as nx
from networkx.algorithms import tree

# Create a weighted tree
T = nx.Graph()
T.add_nodes_from([(1, {'weight': 3}), (2, {'weight': 1}), (3, {'weight': 4}), (4, {'weight': 2})])
T.add_weighted_edges_from([(1, 2, {'weight': 1.0}), (1, 3, {'weight': 2.0}), (3, 4, {'weight': 3.0})])

# Perform Lukes partitioning on the tree
max_partition_weight = 5
partition = tree.lukes_partitioning(T, max_size=max_partition_weight, edge_weight='weight', node_weight='weight')

print('Partition:', partition)
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