<｜begin▁of▁sentence｜>### Instruction:
Within the context of a grant coordination task, imagine that your organization is reviewing various collaborative projects, each represented by a network of partnerships. Suppose we analyze these networks as if they're random graphs constructed according to the Erdős-Rényi model—a common approach to represent connections where each possible link has the same likelihood of being formed. To refine our understanding of these operational networks, could you determine the likelihood of any two potential partners collaborating based on the observed frequency of partnerships in the current project network? Using this inferred likelihood, would you be able to simulate a new project collaboration network that reflects the original model? 

Moreover, as part of assessing the accuracy of our network model, it would be beneficial to calculate the Mean Squared Error (MSE) between the actual collaboration network and the probability matrix generated by the inferred partnership likelihood. This will help us gauge how well the estimated model captures the actual complexity of the inter-organizational collaborations. To assist you with this analysis, consider utilizing the NetworkX library, an API that facilitates the creation, manipulation, and study of the structure, dynamics, and functions of complex networks.
### Response:
import numpy as np
from graspologic.models import EREstimator
import networkx as nx

# Create a random graph using networkx
G = nx.erdos_renyi_graph(n=100, p=0.05)

# Initialize the EREstimator
er_estimator = EREstimator(directed=False, loops=False)

# Fit the ER model to the graph
er_estimator.fit(G)

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

# Sample a new graph from the estimated ER model
sampled_graph = er_estimator.sample(n_samples=1)[0]

# Convert the sampled adjacency matrix back to a networkx graph
sampled_nx_graph = nx.from_numpy_array(sampled_graph)

# Optional: Calculate the Mean Squared Error of the model
mse = er_estimator.mse(graph=nx.to_numpy_array(G))
print('MSE of the model:', mse)
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