<｜begin▁of▁sentence｜>### Instruction:
Imagine you're charting a course for a thrilling rafting journey along the "River Network," a pathway of interconnected canals that flow from 'Source Springs' (the 'x' node) to the majestic 'Omega Falls' (the 'y' node). Your expedition team consists of various smaller outposts ('a', 'b', 'c', 'd', 'e') located along these canals, each with a limited number of rafts (represented by the capacities) available to propel the adventurers down the network's routes.

Your navigation map outlines the following: From 'Source Springs', you can send 3.0 rafts toward outpost 'a', and 1.0 rafts toward outpost 'b'. Outpost 'a' can dispatch up to 3.0 rafts out to 'c', while 'b' has the capacity to send 5.0 rafts also to 'c' and an additional 4.0 rafts over to outpost 'd'. From 'd', a maximum of 2.0 rafts can plunge onward to outpost 'e'. And from the outposts, both 'c' and 'e' have the capabilities to send 2.0 and 3.0 rafts, respectively, cascading into 'Omega Falls'.

Now, what I'm looking for, as the head guide, is to determine the most rafts we can safely allow to travel through 'River Network' from 'Source Springs' directly to 'Omega Falls' without exceeding the limits of the outposts. This will ensure the maximum adventure for our explorers while maintaining the integrity of our outposts' capacities. Additionally, identifying which outposts and routes form the critical junctures (the minimum cut) where the flow of our rafts is most restricted will be essential to manage and possibly enhance for future expeditions.

I heard about this efficient method called the "Boykov-Kolmogorov algorithm" which might just be the tool we need for this task. Could you harness its capabilities for our adventure map? I believe it will help us achieve a seamless and thrilling rafting experience.
### Response:
import networkx as nx
from networkx.algorithms.flow import boykov_kolmogorov

# Create a directed graph and add weighted edges
G = nx.DiGraph()
G.add_edge('x', 'a', capacity=3.0)
G.add_edge('x', 'b', capacity=1.0)
G.add_edge('a', 'c', capacity=3.0)
G.add_edge('b', 'c', capacity=5.0)
G.add_edge('b', 'd', capacity=4.0)
G.add_edge('d', 'e', capacity=2.0)
G.add_edge('c', 'y', capacity=2.0)
G.add_edge('e', 'y', capacity=3.0)

# Run Boykov-Kolmogorov algorithm to find the maximum single-commodity flow
R = boykov_kolmogorov(G, 'x', 'y')

# Get the value of the maximum flow
flow_value = R.graph['flow_value']

# Print the flow value
print('The maximum flow from node x to node y is:', flow_value)

# Fetch the partition that defines a minimum cut
source_tree, target_tree = R.graph['trees']
partition = (set(source_tree), set(G) - set(source_tree))

# Print the partition sets
print('Partition that defines a minimum cut:', partition)
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