PageRank Simulator
Construct custom link graphs by creating pages and drawing directed links, then watch PageRank scores converge iteration by iteration using the standard damping formula and dangling node redistribution.
Link Graph Visualization
Click or drag nodes. Use arrow keys on focused nodes to move.Score Distribution
Live scores updated per iteration| Page | In / Out | Score (PR) | Change (Δ) |
|---|---|---|---|
| Total Probability Mass | 1.0000 | ||
Initial state: 6 pages initialized with uniform rank 0.1667 (1/N). Click "Step once" or "Run to convergence".
PageRank Iteration Formula (With Dangling Node Redistribution)
PR(u)Calculated PageRank score for target page udDamping factor (default 0.85, probability of following outbound links)NTotal number of pages currently in the graphBuSet of pages linking directly into page u (inbound linkers)L(v)Total number of outbound links on linking page vDSet of dangling nodes (pages with zero outbound links, redistributed equally)How PageRank Computes Link Authority
The damping factor models the behavior of a hypothetical web surfer who randomly clicks links on pages. With a damping factor of 0.85, the surfer has an 85 percent chance of clicking an outbound link on the current page and a 15 percent chance of abandoning the sequence to jump directly to any random page in the index. This teleportation mechanism prevents search engines from getting trapped in infinite loops or rank sinks where equity circulates indefinitely.
PageRank scores converge because the link graph forms a mathematical Markov chain with a stationary probability distribution. During power iteration, each round transfers equity through directed links until the amount of score flowing into every node exactly balances the amount flowing out. According to the Perron-Frobenius theorem, a connected, damped transition matrix is guaranteed to reach an equilibrium where additional iterations produce changes smaller than any chosen threshold.
A dangling node is any page that contains no outbound hyperlinks, such as a PDF document, a thank-you page, or a media asset. In a naive PageRank calculation, authority entering a dangling node cannot escape, which drains equity out of the entire network. Production search engines solve this leakage by redistributing the accumulated score of all dangling nodes equally across every page in the index, preserving the total probability mass.
Manipulative link farms rely on creating dozens of artificial websites that all point to a single target URL. However, PageRank operates on the conservation of link equity. If the satellite booster pages have no external links from real websites, they possess only the base teleportation score. Circulating authority within a closed network cannot manufacture new PageRank out of nothing, which is why isolated link clusters consistently fail to generate significant ranking authority. To understand how modern search engines evaluate link graphs alongside content relevance, explore our comprehensive ranking hub or read our detailed PageRank formula guide.