<｜begin▁of▁sentence｜>### Instruction:
Given a tree with edge set [(0, 1), (1, 2), (1, 3), (3, 4), (3, 5)] where all nodes have a weight of 1, how can you partition this tree into clusters with a maximum weight of 3 using the Lukes partitioning algorithm?
### Response:
import networkx as nx
from networkx.algorithms.tree import lukes_partitioning

# Create a tree
T = nx.Graph()
T.add_edges_from([(0, 1), (1, 2), (1, 3), (3, 4), (3, 5)])

# Set node weights
for node in T.nodes():
    T.nodes[node]['weight'] = 1

# Partition the tree
max_size = 3
partition = lukes_partitioning(T, max_size, edge_weight=None, node_weight='weight')

print('Partition:', partition)
<|EOT|>
