<｜begin▁of▁sentence｜>### Instruction:
As a fitness instructor, I'd like to analyze the performance of my clients during their workout sessions. Imagine a scenario where I have a group of clients performing a sequence of exercises (clients 1 -> 2 -> 3 -> 4 -> 2 and client 5 -> 4). Using the analogy of authority scores in network theory, I'm interested in calculating the authority scores for each client based on their workout performance. I also need to normalize these scores so that the client with the highest score receives a rating of 1. Additionally, I want to determine the largest eigenvalue associated with these scores to understand the overall influence of the workout routines on the clients' progress.
### Response:
from igraph import Graph

# Create a directed graph
g = Graph([(0, 1), (1, 2), (2, 3), (3, 1), (4, 3)], directed=True)

# Calculate the authority scores with normalization
auth_scores, largest_eigenvalue = g.authority_score(scale=True, return_eigenvalue=True)

# Print the authority scores and the largest eigenvalue
print('Authority scores:', auth_scores)
print('Largest eigenvalue:', largest_eigenvalue)
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