Python: Mathematical PageRank Vector Convergence

Implement the core Google PageRank power-iteration algorithm over a web graph using damping factors.

The Mathematics of PageRank

PageRank models a random web surfer navigating through hyperlinks:
$$\text{PR}(A) = \frac{1 - d}{N} + d \sum_{i \in M(A)} \frac{\text{PR}(i)}{L(i)}$$

Where:
- $d = 0.85$ is the damping factor (85% probability of following a link, 15% probability of jumping to a random page).
- $N$ is the total number of pages in the graph.
- $L(i)$ is the number of outbound links from page $i$.

The algorithm runs iterative vector updates until the rank delta drops below an epsilon threshold (e.g. $10^{-6}$).

Target Output

{'A': 0.3878, 'B': 0.2148, 'C': 0.3974}

Need a Hint?

Initialize each node rank to (1 - d) / N
Distribute d * ranks[node] / len(out_links) to each destination
Update ranks dictionary at the end of each iteration

solution.py

Terminal Output Ready

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