<｜begin▁of▁sentence｜>### Instruction:
Given an undirected graph created from the karate club dataset, and assuming that all the edges have a capacity of 1, how can we use the `gomory_hu_tree` function to find the minimum cut value between any pair of nodes and validate this with the output of the `nx.minimum_cut_value` function?
### Response:
import networkx as nx

# Create a graph
G = nx.karate_club_graph()

# Set all edges to have a 'capacity' of 1
nx.set_edge_attributes(G, 1, "capacity")

# Compute the Gomory-Hu tree of the graph
T = nx.gomory_hu_tree(G)

# Function to find the minimum edge weight in the shortest path
# between two nodes in the Gomory-Hu tree
def minimum_edge_weight_in_shortest_path(T, u, v):
    path = nx.shortest_path(T, u, v, weight="weight")
    return min((T[u][v]["weight"], (u, v)) for (u, v) in zip(path, path[1:]))

# Example usage of the function
u, v = 0, 33
cut_value, edge = minimum_edge_weight_in_shortest_path(T, u, v)
print(f'Minimum cut value between node {u} and node {v}:', cut_value)

# Compare with nx.minimum_cut_value
print('Validation with nx.minimum_cut_value:', nx.minimum_cut_value(G, u, v))
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