<｜begin▁of▁sentence｜>### Instruction:
Imagine we're observing a community of felines, mapping out their interactions as an intricate web of social connections—a cat community network, if you will. In such a network, each cat has an unseen 'social space' influencing their likelihood to fraternize with others. In this scenario, how might we deduce these hidden social spaces, effectively estimating the invisible spots each cat occupies, which in turn dictate their social engagements within our mapped kitty society?
### Response:
import networkx as nx
from graspologic.models import RDPGEstimator

# Step 1: Construct an undirected social network graph as a NetworkX object
G = nx.fast_gnp_random_graph(n=100, p=0.1)

# Convert the graph to an adjacency matrix
adjacency_matrix = nx.to_numpy_array(G)

# Step 2: Initialize and fit the RDPGEstimator to estimate latent positions
# that represent the probability of connection between nodes
rdpg_estimator = RDPGEstimator(loops=False, n_components=2)
rdpg_estimator.fit(adjacency_matrix)

# Get the latent positions
latent_positions = rdpg_estimator.latent_tuple_

# Get the estimated probability matrix
probability_matrix = rdpg_estimator.p_mat_

# Print the shapes of the latent positions and probability matrix
print('Latent Positions Shape:', latent_positions[0].shape)
print('Probability Matrix Shape:', probability_matrix.shape)
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