<｜begin▁of▁sentence｜>### Instruction:
Imagine you are a biomedical engineer working on a project to understand the interconnectivity within a cellular network. You wish to create a simplified model of this network to study its growth patterns and connectivity probabilities that could resemble the behavior of cellular connections in biological tissues.

Your current objective is to construct a biomimetic graph model that starts with a foundational cluster of three interconnected cells, analogous to an initial clique in graph theory. As the model progresses, it will incorporate additional 'cells' (new nodes) into the network, each mimicking the duplication of a pre-existing cell. The duplication process is defined by two critical probabilities: each newcomer 'cell' has a 50% probability to form connections with the neighboring cells of its progenitor cell, simulating shared intercellular communication pathways. Additionally, there's a 30% chance for the new cell to form a direct link back to the original cell it is replicating, reflecting a self-referential communication link.

Your task is to digitally synthesize this cellular network until it reaches a total of 10 nodes, while assuring the stochastic nature of the connections is consistent across simulations. For this reason, you must utilize a fixed randomization seed of 42, ensuring the reproducibility of your network, which is vital for subsequent analysis and peer validation.

In practical terms, you would be creating a graph theoretical representation of this biological phenomenon, which could potentially be saved as a 'networkx' GML graph file for easy storage and manipulation. Nevertheless, in this scenario, the name of the GML file has not been provided, and you would have to create and name it according to your project's naming conventions. The emulation of this developmental cellular process using the partial duplication model could offer valuable insights into the structural evolution of biological networks.
### Response:
import networkx as nx

# Generate a random graph using the partial duplication model
N = 10  # Total number of nodes
n = 3   # Number of nodes in the initial clique
p = 0.5 # Probability of joining neighbors
q = 0.3 # Probability of joining the source node
seed = 42 # Seed for random number generator

# Create the graph
pd_graph = nx.partial_duplication_graph(N, n, p, q, seed)

# Draw the graph
import matplotlib.pyplot as plt
nx.draw(pd_graph, with_labels=True)
plt.show()
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