<｜begin▁of▁sentence｜>### Instruction:
In the context of evaluating the environmental impact of a product distribution network, imagine we're examining a system that encompasses seven key stages, designated by nodes 1 through 7, each representing a phase in the product's lifecycle or a transition point in the supply chain. The connections between these nodes are characterized not only by the capacity of each link to handle the flow of goods and information but also by the cost associated with these transfers, potentially reflective of energy consumption, emissions, or financial expenditures. 

Our objective is to identify a logistics strategy where the movement of goods from the initial stage (node 1) to the final stage (node 7) is executed in such a manner that the overall system operates at peak efficiency—that is, we aim to maximize the throughput while simultaneously minimizing the associated costs.

If we were to model this distribution network using NetworkX, how would we determine the pathway from the origin (node 1) to the endpoint (node 7) that supports the greatest flow volume without incurring excessive environmental or economic costs? This is essential for recommending the most sustainable logistics strategy. Assume we have encapsulated this network's structural and attribute data within a GML file titled "distribution_network.gml." How do we extract this optimal flow strategy from the file using NetworkX algorithms?
### Response:
import networkx as nx

# Create a directed graph
G = nx.DiGraph()
# Add edges with capacities and costs
G.add_edges_from(
    [
        (1, 2, {'capacity': 12, 'weight': 4}),
        (1, 3, {'capacity': 20, 'weight': 6}),
        (2, 3, {'capacity': 6, 'weight': -3}),
        (2, 6, {'capacity': 14, 'weight': 1}),
        (3, 4, {'weight': 9}),  # Implied infinite capacity
        (3, 5, {'capacity': 10, 'weight': 5}),
        (4, 2, {'capacity': 19, 'weight': 13}),
        (4, 5, {'capacity': 4, 'weight': 0}),
        (5, 7, {'capacity': 28, 'weight': 2}),
        (6, 5, {'capacity': 11, 'weight': 1}),
        (6, 7, {'weight': 8}),  # Implied infinite capacity
        (7, 4, {'capacity': 6, 'weight': 6})
    ]
)
# Compute the maximum flow with the minimum cost
flowDict = nx.max_flow_min_cost(G, 1, 7)
# Calculate the cost of the flow
mincost = nx.cost_of_flow(G, flowDict)

print('Minimum cost:', mincost)
print('Flow dictionary:', flowDict)
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