<｜begin▁of▁sentence｜>### Instruction:
Imagine you're working in a large healthcare network with several departments, each represented as a node in a system database. These departments are interconnected, and the connection strength is defined by a 'weight' value. Here are the details of each department, including their operational load (node weight): Department 1 (operational load: 2), Department 2 (operational load: 1), Department 3 (operational load: 1), Department 4 (operational load: 1), and Department 5 (operational load: 3).

Their connections are as follows: Department 1 is connected to Department 2 with a cooperation level (edge weight) of 3.0, to Department 3 with a cooperation level of 2.0, while Department 3 also connects to Department 4 and 5 with cooperation levels of 4.0 and 1.0, respectively.

Your task is to organize these departments into smaller networks, or 'clusters', so that each cluster's combined operational load doesn't exceed 4 to maintain efficiency. Additionally, when splitting these clusters, you aim to preserve the strongest cooperative connections as much as possible, thus minimizing the weight of the connections you disrupt.

You're to approach this by applying a method similar to the Lukes algorithm, which optimizes for both cluster sum constraints and the minimization of cut connection weights. Can you rework the system by reassigning departments into these efficient clusters with the details provided, while also keeping cooperation loss to a minimum?
### Response:
import networkx as nx
from networkx.algorithms import tree

# Create a weighted tree
T = nx.Graph()
T.add_nodes_from([(1, {'weight': 2}), (2, {'weight': 1}), (3, {'weight': 1}), (4, {'weight': 1}), (5, {'weight': 3})])
T.add_weighted_edges_from([(1, 2, {'weight': 3.0}), (1, 3, {'weight': 2.0}), (3, 4, {'weight': 4.0}), (3, 5, {'weight': 1.0})])

# Partition the tree using the Lukes algorithm
max_partition_size = 4
partition = tree.lukes_partitioning(T, max_partition_size, 'weight', 'weight')

print(partition)
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