<｜begin▁of▁sentence｜>### Instruction:
Given a set of data points, how can you use the AutoGMMCluster algorithm from graspologic to determine the optimal number of clusters and assign data points to these clusters? Moreover, how can you transform the resulting clusters into a networkx graph where nodes represent data points that share the same cluster?
### Response:
import numpy as np
from graspologic.cluster import AutoGMMCluster
from sklearn.datasets import make_blobs
import networkx as nx

# Generate synthetic data with 3 clusters
X, y = make_blobs(n_samples=300, centers=3, cluster_std=1.0, random_state=42)

# Use AutoGMMCluster to find the best Gaussian mixture model
auto_gmm = AutoGMMCluster(min_components=2, max_components=4, affinity='euclidean', linkage='ward', covariance_type='full')
clusters = auto_gmm.fit_predict(X)

# Construct a graph from the clustered data
G = nx.Graph()
for label in np.unique(clusters):
    nodes = np.where(clusters == label)[0]
    # Adding nodes that share the same cluster label
    for node1 in nodes:
        for node2 in nodes:
            if node1 != node2:
                G.add_edge(node1, node2)

# List nodes in one of the clusters
print(f'Nodes in cluster 0: {list(np.where(clusters == 0)[0])}')
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