<｜begin▁of▁sentence｜>### Instruction:
Imagine you're an Innovation Strategist working in the vibrant world of tech startups, tasked with fostering collaboration between different departments to boost creativity and innovation. You've spotted an opportunity to analyze and enhance cross-departmental collaboration within your company. You've gathered data representing different departments (labeled 'A', 'B', 'C') and their collaborative efforts on various projects (numbered 1, 2, 3, 4). The collaborations are captured as interactions where departments have worked together on the same project, leading to connections such as: working together on project 1 (departments 'A' and 'B'), project 2 features a collaboration between 'B' and another department, and so on, resulting in a set of interactions [('A', 1), ('B', 1), ('B', 2), ('C', 3), ('A', 4), ('C', 4)].

Your task, leveraging this scenario, is to analyze the network of departmental collaborations to understand how tightly knit these connections are. The aim is to project this bipartite network of departments and projects onto a simplified model where only departments are nodes. This model will reflect the intensity of collaboration between departments not through direct linkages, but through their shared projects, quantified in a meaningful way. 

Could you transform this network into a weighted graph where each edge's weight signifies the strength of collaboration between two departments based on their joint projects? This would involve creating a weighted projected graph focusing solely on the departments 'A', 'B', and 'C', and summarizing their interconnectedness through calculated weights that embody the extent of their collaborations. 

How do we proceed with constructing this projected graph to illuminate the pattern of collaborative interactions among departments, effectively guiding strategies to enhance interdisciplinary innovation and creativity within the company?
### Response:
import networkx as nx
from networkx.algorithms import bipartite

# Create a bipartite graph B
B = nx.Graph()
B.add_nodes_from(['A', 'B', 'C'], bipartite=0)  # Add the node attribute "bipartite"
B.add_nodes_from([1, 2, 3, 4], bipartite=1)
B.add_edges_from([('A', 1), ('B', 1), ('B', 2), ('C', 3), ('A', 4), ('C', 4)])

# Nodes to project onto (bottom nodes)
bottom_nodes = ['A', 'B', 'C']

# Create the weighted projected graph
G = bipartite.collaboration_weighted_projected_graph(B, bottom_nodes)

# Print out the edges with weights
for edge in sorted(G.edges(data=True)):
    print(edge)
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