<｜begin▁of▁sentence｜>### Instruction:
As a network engineer, I work with various types of data and models to design and analyze networks for different purposes. For example, I may use the GraphBase.Establishment method to simulate the growth of a network, where each new node tries to connect to a certain number of existing nodes based on specific probabilities. These probabilities could be influenced by factors such as node types and connection preferences.

For instance, consider a scenario where I need to design a communication network for a new office building. To do this, I may need to simulate the growth of the network over time as different departments and teams are established within the building. Using the GraphBase.Establishment method, along with parameters such as the number of vertices (representing different departments or teams), the desired number of connections per vertex, along with the distribution of department types and the preferences for connections between them, I can generate a model that represents how the network might evolve.

Once the network model is generated, I can then analyze its structure and connectivity to ensure that it meets the communication needs of the different departments while also adhering to specific connectivity preferences and constraints. This can help in identifying potential issues or opportunities for optimizing the network design.

In this scenario, having the ability to generate such graphs and summarize their properties using tools like NetworkX can be highly valuable in the network design and analysis process.
### Response:
from igraph import Graph, GraphBase

# Define parameters for establishment of the graph
n = 100  # Number of vertices in the graph
k = 3    # Number of connections tried in each step
type_dist = [0.5, 0.3, 0.2]  # Distribution of vertex types
pref_matrix = [[0.2, 0.1, 0.05],
               [0.1, 0.3, 0.1],
               [0.05, 0.1, 0.4]]  # Connection probabilities for types
directed = False  # Generate an undirected graph

# Create the graph using the establishment method
g = GraphBase.Establishment(n, k, type_dist, pref_matrix, directed)

# Print summary of the generated graph
print(g.summary())
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