<｜begin▁of▁sentence｜>### Instruction:
Given a directed graph with 4 vertices and 3 directed edges forming a simple hierarchy, can you calculate Kleinberg's authority scores for the vertices of the graph?
### Response:
```python
import igraph as ig

# Create a graph with 4 vertices and 3 directed edges forming a hierarchy
graph = ig.Graph(4, [(0, 1), (1, 2), (2, 3)], directed=True)

# Calculate authority scores with default settings
authority_scores = graph.authority_score()

# Print the authority scores for each vertex
for index, score in enumerate(authority_scores):
    print(f'Vertex {index}: Authority score = {score}')
```
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