<｜begin▁of▁sentence｜>### Instruction:
As a Survey Researcher, let's imagine you're constructing a study on the interconnectedness of certain social groups, categorized as 'A', 'B', 'C', and 'D'. The interactions between these groups are as follows: 'A' interacts with both 'B' and 'C', 'B' also interacts with 'C', and 'C' further reaches out to 'D'. These connections could be visualized in a network graph for a clear understanding of the social dynamics involved.

You're interested in simplifying this network structure to enable a more efficient analysis. Specifically, you intend to determine the complexity of the network by calculating its treewidth—a measure that can give you insights into how closely these groups are related. To do this, you plan to apply a network analysis technique known as the Minimum Fill-in heuristic.

Could you outline how one might utilize the Minimum Fill-in heuristic to ascertain the treewidth of this network? Additionally, what would be the form of the resulting decomposed tree that elucidates the interactions among the groups 'A', 'B', 'C', and 'D'? This decomposed tree would then serve as a useful tool for your survey data analysis by revealing the underlying structure in a simplified manner.
### Response:
import networkx as nx

# Create a graph
G = nx.Graph()
G.add_edges_from([('A', 'B'), ('A', 'C'), ('B', 'C'), ('C', 'D')])

# Use the treewidth_min_fill_in heuristic
treewidth, tree = nx.treewidth_min_fill_in(G)

print('Treewidth:', treewidth)
print('Decomposed tree:')
for edge in tree.edges():
    print(edge)
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