<｜begin▁of▁sentence｜>### Instruction:
Imagine you're a director piecing together a compelling narrative about a virtual society, visualized as a network of a hundred characters. This society is split into two distinct groups, or 'communities,' each with 50 members. As part of the story, you notice that members within the same community interact much more frequently than with those from the other group, hinting at an intricate subplot of relationships.

To give depth to your story, you decide to analyze this virtual society using a sophisticated technique akin to character development in filmmaking. You opt for the Degree-corrected Stochastic Block Model (DCSBM), a tool that helps you understand not only the community dynamics but also the unique prominence of each character within these groups.

Using an advanced method analogous to special effects in your film production toolkit, you plan to utilize the DCSBMEstimator from graspologic to breathe life into this analysis. This tool will reveal the underlying structure of interactions between the communities, represented as a block probability matrix. Moreover, it will unveil the grand design of connections across the entire network, through an overall probability matrix. 

Your ultimate goal, much like finalizing the cast for your movie, is to assign each character to their correct community, based on the model’s insights. In the realm of your narrative analysis, this means gathering the predicted community assignments for each node, ensuring each character in your virtual society plays a role that fits the plot you are crafting.
### Response:
import numpy as np
from graspologic.models import DCSBMEstimator
from graspologic.simulations import sbm

# Simulate a graph using SBM
n = [50, 50]  # 100 nodes divided into 2 blocks
B = np.array([[0.5, 0.05], [0.05, 0.5]])  # block matrix
G = sbm(n, B)

# Fit the DCSBM model
model = DCSBMEstimator(directed=False, degree_directed=False)
model.fit(G)

# Extract estimated parameters
block_p = model.block_p_
p_mat = model.p_mat_
vertex_assignments = model.vertex_assignments_

print('Block probability matrix:\n', block_p)
print('Probability matrix for the fit model:\n', np_mat)
print('Predicted block assignments for each node:\n', vertex_assignments)
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