<｜begin▁of▁sentence｜>### Instruction:
Imagine you're a Rehabilitation Counselor working with an individual who enjoys solving puzzles as a form of cognitive therapy. To create an engaging problem for them, you have developed a puzzle representing a network of tasks and dependencies, depicted by a series of connections, or 'edges', between 'nodes'. The puzzle is drawn out as a graph with specific relationships: (1 connects to 2), (2 connects to 3), (3 connects to 4), (4 connects back to 1), (1 also connects to 3), and (2 connects to 4). 

Your goal is to guide them through an exercise that involves finding an efficient way to organize these tasks, allowing a balanced distribution without overwhelming any single point in the network. This is akin to calculating the 'treewidth' of the graph, which serves to measure how tree-like the network is. Specifically, you seek to use a method known as the 'Minimum Fill-in heuristic,' which helps in obtaining the most streamlined arrangement, known as a 'tree decomposition,' without actually altering the puzzle's connections. 

The challenge for your client is not only to understand the complexity of the network but also to apply a strategic approach to simplify the relationships between the tasks. By presenting the treewidth calculation as a puzzle objective, you aim to stimulate your client's problem-solving skills and aid their cognitive rehabilitation process. How would you go about determining the treewidth and achieving the tree decomposition using the 'Minimum Fill-in heuristic' for this graph?
### Response:
import networkx as nx

# Create a graph
G = nx.Graph()
G.add_edges_from([(1, 2), (2, 3), (3, 4), (4, 1), (1, 3), (2, 4)])

# Use the Minimum Fill-in heuristic to find the treewidth
treewidth, tree_decomp = nx.treewidth_min_fill_in(G)

print('Treewidth:', treewidth)
print('Tree decomposition:', tree_decomp.edges())
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