<｜begin▁of▁sentence｜>### Instruction:
Imagine we're tracking the spread of medical information within a network of healthcare professionals, where node 1 might be a renowned physician, and nodes 2 through 5 are medical staff in escalating order of hierarchy. The connections, or edges, represent the flow of information from one member to another [(1, 2), (2, 3), (3, 4), (4, 5)]. 

We want to assign a level of influence, or centrality, to each member within this network to understand who could be the most effective in disseminating vital healthcare updates. We're interested in using the Katz centrality measure because it not only considers the immediate connections but also captures the indirect influence a member might have over others in the network.

However, Katz centrality requires setting an attenuation factor—a parameter that diminishes the influence of indirect connections compared to direct ones. To fine-tune this effectively, it's often recommended to choose an attenuation factor just below the reciprocal of the network's largest adjacency matrix eigenvalue. 

Could you, as a Physician Assistant familiar with analyzing patterns of information flow in healthcare settings, translate this graph into an appropriate model and assist with the calculation of Katz centrality, employing that particular attenuation factor? Your insights could crucially inform how to best leverage the existing communication structure to improve the dissemination of medical knowledge within the team.
### Response:
import networkx as nx
import math

# Create a graph
G = nx.Graph()
G.add_edges_from([(1, 2), (2, 3), (3, 4), (4, 5)])

# Calculate the largest eigenvalue for the adjacency matrix of G
eigenvalue = max(nx.adjacency_spectrum(G))
alpha = 1/eigenvalue - 0.01  # Attenuation factor
beta = 1.0  # Weight attributed to the immediate neighborhood
max_iter = 1000  # Maximum iterations

# Compute the Katz centrality
katz_centrality = nx.katz_centrality(G, alpha=alpha, beta=beta, max_iter=max_iter)

# Print the Katz centrality for each node
for node, centrality in sorted(katz_centrality.items()):
    print(f"Node {node}: {centrality:.4f}")
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