<｜begin▁of▁sentence｜>### Instruction:
Imagine you're at an orthodontic conference, where the presenters are discussing the referral network between professionals within a local dental community. This network is composed of four major dental offices, labeled 'A', 'B', 'C', and 'D'. These offices refer patients to one another, and the pattern of referrals is directed, with each referral having a different 'weight' based on the volume or value of the referrals made.

The offices have the following referral pattern:
- Office 'A' refers 2 patients to 'B' and 3 patients to 'C'.
- Office 'B' refers 1 patient to 'C' and 1 patient to 'D'.
- Office 'C' refers 4 patients to 'D'.
- Office 'D' refers 5 patients back to 'A'.

In this professional network model, you are intrigued by the idea of utilizing the PageRank algorithm to determine the influence or popularity of each dental office. The PageRank algorithm will take into account the referral pattern and the 'damping factor', which we can liken to the likelihood that a patient will continue to be referred within the network rather than seeking services outside.

Your task is to calculate the PageRank values for each office using a damping factor of 0.85, which reflects a realistic scenario where 85% of patients are likely to follow through on a referral within this network, while 15% may choose an external option. This calculation will enable you to assess the prominence of each office within the local dental referral network.

To set this up in a more technical format, you would simulate this network and its referral pattern on a computer, typically using a graph representation file, though no specific file name has been mentioned here. The outcome will highlight which dental office holds the greatest importance in the eyes of the referred patients, which is crucial information for understanding the dynamics of the local dental community and, potentially, for making strategic business decisions.
### Response:
import networkx as nx

# Create a directed graph
G = nx.DiGraph()

# Add edges (directed)
G.add_edge('A', 'B', weight=2)
G.add_edge('A', 'C', weight=3)
G.add_edge('B', 'C', weight=1)
G.add_edge('B', 'D', weight=1)
G.add_edge('C', 'D', weight=4)
G.add_edge('D', 'A', weight=5)

# Compute PageRank
pagerank = nx.pagerank(G, alpha=0.85)

print(pagerank)
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