<｜begin▁of▁sentence｜>### Instruction:
Imagine you are consulting on a case where you have a network of three primary ENT departments within a hospital, each with varying referral load capacities and pathways, symbolized by weighted directed connections. We have recorded the referral pathways and capacities in the following manner: The ENT department at node 0 refers patients to department 1 with a capacity of 5, department 1 refers to department 2 with a capacity of 4, department 2 loops back to department 0 with a capacity of 3, and additionally, there is a direct route from department 0 to department 2 with a capacity of 3.

In assessing the optimal and least burdensome referral flow within this hospital network to ensure patient care efficiency and departmental load balance, could you deduce the most substantial and slenderest referral arborescences utilizing Edmonds' algorithm within the NetworkX framework? This inquiry would involve applying the method to these directed pathways and capacities to understand the best and worst-case scenarios for patient referrals.
### Response:
import networkx as nx
from networkx.algorithms.tree.branchings import Edmonds

# Create a directed graph
G = nx.DiGraph()
# Add weighted edges
G.add_weighted_edges_from([(0, 1, 5), (1, 2, 4), (2, 0, 3), (0, 2, 3)])
# Initialize Edmonds' algorithm object
ed = Edmonds(G)
# Find the maximum branching (arborescence)
max_branching = ed.find_optimum(attr='weight', default=0, kind='max', preserve_attrs=True)
# Find the minimum branching (arborescence)
min_branching = ed.find_optimum(attr='weight', default=0, kind='min', preserve_attrs=True)

# Print the results
print('Maximum Spanning Arborescence:', max_branching.edges(data=True))
print('Minimum Spanning Arborescence:', min_branching.edges(data=True))
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