PageRank Simulator: See How Link Juice Flows (Interactive)

INTERACTIVE PAGERANK LAB

See exactly what one link passes

Draw a link and the model recalculates on the spot. In a few minutes you’ll see how a page’s score is shared by its links, what nofollow changes, and why a link from a PR 8 site can be worth more than dozens of small ones.

  • Every link on a page takes a share, so more links means less per link.
  • A nofollow link still takes its share here. It just doesn’t pass it on.
  • Big sites start high, and link schemes show how far bought links can push a page.
Start the first experimentHow the math works
How to use it, in four steps
  1. 1Start with the first experiment. It loads six pages, including a PR 8 news homepage. YOUR PAGE starts at PR 0.
  2. 2Draw a link. With + Link on, tap the Industry blog post, then YOUR PAGE. Or press Do it for me.
  3. 3Read the result. You get the before and after score, the position change and the exact math.
  4. 4Keep going. Follow the next experiment, load a big-site Playground or a link scheme, or share what you built.
Link Graph SimulatorLIVEIllustrative page-level model, not Google’s data

Scenarios

Tools

Illustrative modelOpen webd = 0.856 pagesReady

Experiment result

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Position within this graph

Build a link with the keyboard

Shortcuts when the graph has focus: Space pause, F fit view, Esc cancel a link, Ctrl + Z undo.

Page details

Model assumptions and math Formulas, what nofollow does here, what this can’t tell you, sources

Two ways to run the same graph

Open web (the default) treats every page as part of the much bigger web and shows PR on the 0 to 10 scale. It uses the form from Brin and Page’s 1998 paper, plus two settings for everything that isn’t drawn:

score(i) = (1 − d) + E(i) + d × Σ score(j) ÷ L(j)

  • E(i) comes from the page’s starting PR: the PR it gets from backlinks that aren’t drawn here. A starting PR of p means E = (1 − d) × (6p − 1), so the page scores (1 − d) × 6p before drawn links add anything. Big sites start high (the News homepage is PR 8).
  • L(j) counts every link on page j: the links drawn here plus its links to pages that aren’t drawn (also an assumption you can edit).
  • A page with nothing linking to it sits at a raw 0.15, which is PR 0. Open web scores don’t add up to a fixed total.

Pure PageRank drops the outside assumptions and runs the normalized version with a uniform random jump, so every score is a share and they all add up to 100%:

p(i) = (1 − d) ÷ N + d × Σ p(j) ÷ L(j) + d × R ÷ N

  • N is the number of pages drawn, L(j) is the number of links drawn on page j.
  • R is the score sitting on pages with no links out, plus the unpassed share of nofollow links. It goes back into the random jump and is spread evenly over every page.
  • There’s no PR 0 to 10 in Pure mode. Six pages sharing 100% between them can’t produce a PR 8 site: that scale only means something for a page inside the whole web.
  • d is the damping factor, 0.85 by default, the value the original paper suggests. You can change it above the graph.

Both modes are solved by power iteration until the scores stop changing (to about 13 decimal places).

What one followed link passes

passes = d × score(source) ÷ L(source)

In the first experiment the Industry blog post is PR 4.1 (a raw 252.9) and, once it links to YOUR PAGE, has 12 links (2 drawn here, 10 to pages not drawn). So the link passes 0.85 × 252.9 ÷ 12 = 17.9, and YOUR PAGE goes from a raw 0.15 (PR 0) to 18.1 (PR 2.7).

The PR 8 News homepage has 120 links, so its link passes 0.85 × 251,942 ÷ 120 = 1,785 and takes YOUR PAGE to about PR 5.2. One rule of thumb falls out of the math: a link is worth roughly the source’s PR minus log₆ of (its links ÷ 0.85).

Adding a link adds 1 to L, so every other link on that page carries a little less.

Followed vs. nofollow links

One assumption, used in both modes: a nofollow link (or sponsored or ugc) still counts as one of the page’s links, but passes nothing. In Pure mode its share goes back to the random jump so the total stays 1. In Open web it simply leaves the model.

That’s a simplification. Since 2019 Google treats nofollow, sponsored and ugc as hints, so in real Search a nofollow link might be used or might not.

A short history of PageRank sculpting

For a few years some SEOs nofollowed their own low-value internal links (login, terms, cart) on the theory that the saved share would flow to the links that mattered. In 2009 Google’s Matt Cutts confirmed it doesn’t work that way any more: a nofollowed link’s share isn’t handed to the other links on the page, it just doesn’t flow. This model follows that behavior, which is why the Followed vs. nofollow scenario shows almost nothing gained by nofollowing utility links, while removing them does change the split.

Parasite pages are a different lesson

A third-party page placed on a big site to borrow its reputation falls under Google’s site reputation abuse policy. That’s enforced against the page itself, with manual actions and with systems that, over time, rank that section on its own. It isn’t a change to link math, so the manual action demo in the Parasite scenario marks the page as demoted in Search and leaves every PR alone.

Google said in November 2024 that first-party involvement doesn’t change the third-party nature of this content. Since late August 2026, Google says these manual actions no longer affect results for searchers in the European Economic Area.

The PR 0 to 10 scale

PR = log₆(score ÷ 0.15), capped at 10

0.15 is the raw score of a page with nothing linking to it (1 − d at the default damping), so PR 0 means no link value and each point is worth 6 times the one below it. PR 8 carries about 1,300 times the raw score of PR 4. Google never published how its old toolbar scale worked and retired it years ago, so base 6 is this model’s assumption. Turn on Raw scores to see the numbers the math actually uses.

How the math is checked

The engine was tested against an independent linear solve of both equations and against NetworkX’s PageRank on 137 graphs: cycles, chains, pages with no links out, nofollow links, single pages, different damping values and 120 random graphs. Pure scores always total 1, Open web accounting always adds up (base + starting PR + drawn links), adding a link always thins the others, and removing it restores the original scores. 623 checks, 0 failures.

What this model can’t tell you

  • Google says PageRank still matters as one of its core ranking systems, but it has evolved a lot since 1998 and works alongside many other signals. These scores are not Google’s and they are not rankings.
  • Every page name and starting PR here is an example, not a measurement of a real site. Positions only compare pages inside this graph.
  • It treats every link on a page the same. Real systems weigh things like where a link sits, its anchor text, topical relevance and the quality of the site.
  • It works page by page. Real sites also carry site-level signals that a page graph can’t show.

Sources

A teaching model by Jourdan Rombough at Optimization Theory. Page names and numbers are illustrative inputs, not measurements of real sites, and scores are not Google’s.