<｜begin▁of▁sentence｜>### Instruction:
Given an undirected graph where edges have assigned capacities like [(0, 1, 10), (0, 2, 15), (1, 3, 12), (2, 3, 10), (2, 4, 5), (3, 4, 20)], can you generate the Gomory-Hu tree of the graph? Moreover, can you provide a NetworkX API that allows finding the minimum spanning tree in a similar context?
### Response:
from igraph import Graph

# Let's suppose we have an undirected Graph
edges = [(0, 1, 10), (0, 2, 15), (1, 3, 12), (2, 3, 10), (2, 4, 5), (3, 4, 20)]
# Create the graph with edges and edge capacities
graph = Graph(edges=edges)
# Adding edge weights/capacities
graph.es['capacity'] = [10, 15, 12, 10, 5, 20]

# Use the Gomory-Hu tree function
gomory_hu_tree = graph.gomory_hu_tree()

# Print the structure of the tree
print(gomory_hu_tree)

# To compare, here is how you would find the minimum spanning tree in NetworkX
import networkx as nx
G_nx = nx.Graph()
G_nx.add_weighted_edges_from(edges)
min_spanning_tree_nx = nx.minimum_spanning_tree(G_nx)
print(min_spanning_tree_nx.edges(data=True))
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