<｜begin▁of▁sentence｜>### Instruction:
In a Mixed Membership Stochastic Block Model with 6 nodes, how do you sample a graph where nodes have a high probability of belonging to the second community, using a block probability matrix with intra-community connection probability of 0.5 for the first community and 1 for the second community, and mixed-membership vectors sampled from a Dirichlet distribution with alpha parameters [0.05, 1000]?
### Response:
import numpy as np
from graspologic.simulations import mmsbm

# Set random seed for reproducibility
rng = np.random.default_rng(1)
# Define the number of nodes and the block probability matrix
n = 6
p = [[0.5, 0], [0, 1]]
# Define the Dirichlet distribution parameter alpha for mixed-membership vectors
alpha = [0.05, 1000]
# Sample a graph from the MMSBM
A, labels = mmsbm(n, p, alpha, rng=rng, return_labels=True)
print('Adjacency Matrix:\n', A)
print('Membership Labels:\n', labels)
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