<｜begin▁of▁sentence｜>### Instruction:
As a policy analyst, I've been examining the potential for data-driven strategies to inform network-related policies, particularly focusing on how seemingly random connections within two distinct groups might influence overall structural behavior and outcomes. Within this context, we've modeled two separate but related communities, with one group consisting of 50 individuals and the other comprising 60 individuals. Each individual has an equal chance of forming a connection with any other individual within their respective group, mirroring the structure of an Erdős-Rényi graph.

The crux of our study is determining whether the underlying patterns or tendencies for connections—what we might call the 'latent social tendencies'—are fundamentally the same between these two groups. In essence, this boils down to a statistical question: Can we utilize Graspologic's `latent_distribution_test` (employing algorithms that imitate the distributions of these social tendencies) to discern whether the social structures of our two modeled groups are statistically indistinguishable? This test hinges on using 'distance correlation' as our metric of choice—a statistical measure that captures a variety of dependencies—and we would attempt to corroborate our findings through 500 repetitions of this test to account for variability.

Incorporating this approach, we aim to understand if policy interventions designed for one group would be applicable to the other, based on the assumption that similar latent distributions suggest analogous responses to such interventions. This understanding could pave the way for more efficient allocation of resources, allowing us to tailor interventions to the specificities of each group's social dynamics only when necessary.
### Response:
import numpy as np
import networkx as nx
from graspologic.inference import latent_distribution_test

# Generate two random graphs with different numbers of vertices
G1 = nx.erdos_renyi_graph(n=50, p=0.2)
G2 = nx.erdos_renyi_graph(n=60, p=0.2)

# Perform a latent distribution test to determine if the graphs have the same distributions of latent positions
p_value, test_statistic = latent_distribution_test(A1=nx.to_numpy_array(G1), A2=nx.to_numpy_array(G2),
                                                    test='dcorr', metric='euclidean', n_bootstraps=500, size_correction=True)

# Print the test statistic and p-value
print(f'Test Statistic: {test_statistic}')
print(f'p-value: {p_value}')
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