<｜begin▁of▁sentence｜>### Instruction:
In the context of a clinical research coordinator overseeing a study involving network analysis of patient interactions, imagine that a colleague in the research team has mapped out a network diagram representing the social interactions within a cohort of 100 patients. This network was constructed based on an undirected, unweighted model that assumes a certain likelihood of interaction between any given pair of patients, following the Erdos-Renyi random graph framework.

The colleague is now interested in deducing the exact likelihood of interaction that was used to generate this network, with the ultimate aim of producing a synthetic representation of these social interactions that faithfully models the observed pattern. To achieve this, the colleague intends to employ a tool known as the 'EREstimator' from the graspologic library, specifically designed to estimate the parameters of an Erdos-Renyi model given an existing network.

The task at hand is to effectively utilize the 'EREstimator' to ascertain the interaction probability that this patient social network was predicated upon, and then to generate a new synthetic network that is statistically comparable based on the estimated model. It is essential that this work complies with the standard methodologies and protocols in statistical network analysis as part of the broader clinical study.
### Response:
import numpy as np
from graspologic.models import EREstimator
import networkx as nx

# Create a simple random (Erdos-Renyi) graph with 100 nodes
n = 100  # Number of nodes
p = 0.05  # Probability of edge creation

# Generate the graph
G = nx.erdos_renyi_graph(n, p, seed=42)

# Initialize the Erdos-Renyi model estimator
er_estimator = EREstimator(directed=False, loops=False)

# Fit the estimator to the graph
er_estimator.fit(G)

# Print the estimated probability of edge creation
print('Estimated probability of edge creation:', er_estimator.p)

# Generate a synthetic graph sample from the estimated model parameters
synthetic_graph = er_estimator.sample()[0]

# Convert the synthetic graph to a NetworkX graph object
synthetic_nx_graph = nx.from_numpy_array(synthetic_graph)
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