<｜begin▁of▁sentence｜>### Instruction:
If a network researcher has three ErdÅ‘s-RÃ©nyi graphs with 50 nodes each and a connection probability of 0.1, and they want to find a common subgraph where every node is part of the largest connected component in all three graphs, how can they use `multigraph_lcc_intersection` from `graspologic.utils` to identify this intersection graph and the indices of the original nodes that are included in this graph?
### Response:
import networkx as nx
from graspologic.utils import multigraph_lcc_intersection
import numpy as np

# Generate synthetic ErdÅ‘s-RÃ©nyi graphs
np.random.seed(42)
G1 = nx.erdos_renyi_graph(n=50, p=0.1)
G2 = nx.erdos_renyi_graph(n=50, p=0.1)
G3 = nx.erdos_renyi_graph(n=50, p=0.1)

# Convert the graphs to adjacency matrices
adj_matrix1 = nx.to_numpy_array(G1)
adj_matrix2 = nx.to_numpy_array(G2)
adj_matrix3 = nx.to_numpy_array(G3)

# Find intersection of largest connected components
graphs = [adj_matrix1, adj_matrix2, adj_matrix3]
intersection_graph, inds = multigraph_lcc_intersection(graphs, return_inds=True)

# Create a new NetworkX graph from the intersection adjacency matrix
G_intersection = nx.from_numpy_array(intersection_graph)

# Print the result
print(f'The intersection graph has {G_intersection.number_of_nodes()} nodes.')
print(f'The indices of original nodes are: {inds}')
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