<｜begin▁of▁sentence｜>### Instruction:
Imagine we're examining a biological system with interactions between two different types of molecules represented by two groups of nodes [0, 1] for type A and [2, 3] for type B. Our dataset, encapsulated within a NetworkX graph object 'B', models the interactions between these molecule types with four relationships (edges), each with an interaction strength of 1 to 4.

In our study, we need to focus on the interactions within type A molecules only. To achieve this, we're interested in creating a new interaction map, a graph 'G', which represents the interplay between type A molecules based on their shared connections to type B molecules.

We plan to use the 'generic_weighted_projected_graph' function from NetworkX to construct this new graph 'G'. However, to properly represent the interaction strength between two type A molecules (let's say 'u' and 'v'), we want to employ a custom weight function 'shared_weight'. This function will define the interaction strength between 'u' and 'v' based on the number of common type B molecules they both interact with in our initial system 'B'.

How do we apply this custom function 'shared_weight' to obtain the weighted projection onto the nodes [0, 1] in the projected graph 'G', while maintaining the biological relevance of the interaction strength as described?
### Response:
import networkx as nx
from networkx.algorithms import bipartite

# Define a custom weight function
def shared_weight(G, u, v):
    u_nbrs = set(G[u])
    v_nbrs = set(G[v])
    return len(u_nbrs & v_nbrs)

# Create a complete bipartite graph B with a set of edges with weights
B = nx.complete_bipartite_graph(2, 2)
for i, (u, v) in enumerate(B.edges()):
    B.edges[u, v]['weight'] = i + 1

# Use the custom weight function to create a weighted projected graph
G = bipartite.generic_weighted_projected_graph(B, [0, 1], weight_function=shared_weight)

# Print the edges with their weights in the projected graph
print(list(G.edges(data=True)))
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