<｜begin▁of▁sentence｜>### Instruction:
In the realm of understanding and resolving conflicts within community networks, a mediator has encountered two groups, each comprising 100 individuals subdivided equally into smaller factions. The mediator suspects that the underlying relationship patterns within and across these factions are remarkably similar, suggesting a potential for harmonized integration or conflict resolution strategies. To substantiate this intuition with empirical evidence, the mediator considers employing a sophisticated analytical approach, specifically the latent distribution test available through graspologic, an advanced tool designed for such investigations. This method will facilitate a rigorous comparison of the networks' structures, aiming to confirm or refute the hypothesis of their structural equivalence. The inquiry is rooted in leveraging graspologic alongside networkx to execute a two-sample hypothesis test, evaluating if the observed networks indeed share comparable distributions of latent positions—a scientific endeavor that might illuminate pathways toward enhanced cohesion and understanding between the groups.
### Response:
import networkx as nx
import numpy as np
from graspologic.inference import latent_distribution_test

# Generate two random graphs G1 and G2 using the stochastic block model
n_communities = [50, 50]
p_matrix = [[0.5, 0.05], [0.05, 0.5]]
G1 = nx.stochastic_block_model(n_communities, p_matrix, seed=42)
G2 = nx.stochastic_block_model(n_communities, p_matrix, seed=43)

# Perform the latent distribution test
result = latent_distribution_test(G1, G2, test='dcorr', metric='euclidean', n_bootstraps=200, random_state=42)
p_value = result['p']

# Print the p-value
print(f'P-value of the latent distribution test: {p_value}')
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