<｜begin▁of▁sentence｜>### Instruction:
As an online moderator, consider this scenario: you're tasked with managing a community network to ensure efficient communication and collaboration among its members. The network is currently organized according to relationships defined by pairs of members who directly interact, such as exchanging messages or collaborating on projects. These interactions are captured as edges in a graph: [(1, 2), (2, 3), (3, 4), (4, 5), (1, 5), (2, 4)].

To improve the structure and flow of the community network, it's proposed to reorganize the interactions by applying a network analysis technique called treewidth decomposition. This process will use the Minimum Fill-in heuristic to streamline the network, making the oversight of community interactions more manageable.

Could you explore the implementation of this technique on the given network? Specifically, we aim to determine the treewidth after reorganization and identify any new pairs of interactions that would result from the decomposition. Your findings will aid in planning better strategies for network management and possibly enhance user engagement on the platform.
### Response:
import networkx as nx
from networkx.algorithms.approximation.treewidth import treewidth_min_fill_in

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

# Get treewidth decomposition using Minimum Fill-in heuristic
treewidth, decomposed_graph = treewidth_min_fill_in(G)

print('Treewidth:', treewidth)
print('Decomposed Graph:', decomposed_graph.edges())
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