<｜begin▁of▁sentence｜>### Instruction:
Certainly! Let's rephrase the scenario through the lens of a Tax Accountant profession:

Imagine you're working with a company's transaction network, where each department is represented by a node, and the directed edges reveal the flow of financial information or dependencies between these departments. We have a simplified ledger showcasing the relationships as follows: Transactions originate from department 0 and move to 1, from 1 to 2, from 2 to 3, and there's a feedback loop where transactions flow from 3 back to 1.

In this scenario, we are interested in assessing the influence of each department on the overall financial network. To do this, we'll employ a method akin to calculating tax liabilities but for network influence, known as Katz centrality. Now, to ensure our influence scores are not exaggerated, we need them to be tempered by a consistent factor, which should be below a certain threshold determined by the financial network's structure; specifically, less than the inverse of the largest value we could assign to the transactions based on the ledger's interdependencies.

As your tax advisor, I'd like to obtain the Katz centrality scores for each department to advise you on which department holds the most significant influence over your financial network, ensuring that our calculation respects the constraint mentioned above. Could you provide me with these centrality measures, taking into account our specified limit for the tempering factor?
### Response:
import networkx as nx
import math

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

# Add edges to the graph (nodes are added automatically)
G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 1)])

# Compute the largest eigenvalue of the adjacency matrix
eigenvalue = max(nx.adjacency_spectrum(G))
alpha = 1 / eigenvalue - 0.01

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

# Print Katz centrality of each node
for n, c in sorted(katz_centrality.items()):
    print(f"Node {n} has Katz centrality: {c:.2f}")
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