<｜begin▁of▁sentence｜>### Instruction:
Given a graph whose edge set is [(1, 2), (1, 3), (2, 3), (3, 4), (4, 5), (5, 6), (4, 6)], can you find the subgraph of nodes in the 2-core that have exactly 2 neighbors within the 2-core using the NetworkX library?
### Response:
import networkx as nx

# Create a graph
G = nx.Graph()
G.add_edges_from([(1, 2), (1, 3), (2, 3), (3, 4), (4, 5), (5, 6), (4, 6)])

# Compute the core number for each node (optional step for optimization)
core_numbers = nx.core_number(G)

# Calculate the 2-corona of the graph
two_corona = nx.k_corona(G, 2, core_number=core_numbers)

print('Nodes in the 2-corona:', list(two_corona.nodes()))
print('Edges in the 2-corona:', list(two_corona.edges()))
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