<｜begin▁of▁sentence｜>### Instruction:
Given a set of vertex types and a dictionary of connection probabilities based on vertex types, can you generate a preference graph where vertices are connected based on their types and the defined probabilities? For instance, given vertex types [0, 1, 0, 1, 0] and connection probabilities {(0, 0): 0.1, (0, 1): 0.8, (1, 0): 0.8, (1, 1): 0.1}, create and display such a graph.
### Response:
from igraph import Graph

# Generating a preference graph with type-based connection probabilities
vertex_types = [0, 1, 0, 1, 0] # Define the type of each vertex
type_probabilities = {(0, 0): 0.1, (0, 1): 0.8, (1, 0): 0.8, (1, 1): 0.1} # Define connection probabilities based on types

# Create the preference graph
g = Graph.Preference(len(vertex_types), type_dist=vertex_types, pref_matrix=type_probabilities)

print(g)
<|EOT|>
