<｜begin▁of▁sentence｜>### Instruction:
An analyst is working on understanding social interaction patterns within a small community. By modelling the community's social network as a Random Dot Product Graph (RDPG), they want to estimate latent positions that explain the probability of connection between individuals. The analyst plans to use the graspologic.models.RDPGEstimator to estimate these latent positions and then sample a new graph from the fitted model to predict potential future links. The community consists of 100 individuals with given relationship data represented as a graph with 100 nodes. Can the analyst estimate the latent positions and sample a new graph using graspologic?
### Response:
import numpy as np
import networkx as nx
from graspologic.models import RDPGEstimator
from graspologic.embed import AdjacencySpectralEmbed

# Generate a synthetic graph using NetworkX
G = nx.fast_gnp_random_graph(100, 0.5)

# Convert to adjacency matrix
A = nx.to_numpy_array(G)

# Instantiate the RDPG estimator
rdpg_estimator = RDPGEstimator(loops=False, n_components=2, diag_aug_weight=1, plus_c_weight=1)

# Fit the model to the adjacency matrix A
rdpg_estimator.fit(A)

# Get the latent positions
latent_positions = rdpg_estimator.latent_tuple_

# Generate a new graph from the estimated model
new_graph = rdpg_estimator.sample(1)[0]

# Convert the sampled adjacency array to a NetworkX graph
new_G = nx.from_numpy_array(new_graph)

# Output the number of nodes and edges in the new graph
print('Number of nodes:', new_G.number_of_nodes())
print('Number of edges:', new_G.number_of_edges())
<|EOT|>
