<｜begin▁of▁sentence｜>### Instruction:
Given a Newman-Watts-Strogatz graph with 100 nodes, each connected to 10 neighbors, and a rewiring probability of 0.5, how can the MNMF model ('Community Preserving Network Embedding' from AAAI ‘17) be used to generate node embeddings, cluster centers, and node cluster memberships with custom dimensionality and clustering parameters?
### Response:
import networkx as nx
from karateclub import MNMF

# Create a synthetic graph
G = nx.newman_watts_strogatz_graph(100, 10, 0.5)

# Instantiate the MNMF model with custom parameters
model = MNMF(dimensions=64, clusters=5, lambd=0.2, alpha=0.05, beta=0.05, iterations=100, lower_control=1e-15, eta=5.0, seed=42)

# Fit the model on the synthetic graph
model.fit(G)

# Get the embeddings and memberships
embeddings = model.get_embedding()
cluster_centers = model.get_cluster_centers()
memberships = model.get_memberships()

# Output the results
print('Embeddings: ', embeddings)
print('Cluster Centers: ', cluster_centers)
print('Memberships: ', memberships)
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