An interactive model of link equity propagation, authority accumulation and algorithmic link devaluation, built on the damped random-surfer math behind PageRank.
An upgraded, fully interactive way to see how link juice flows between pages. Read the guide here, then take it for a spin.
1What the Link Graph Simulator models
A deterministic, browser-based model of link authority that you can inspect, edit and stress-test.
The Link Graph Simulator is an educational model of how link equity moves through the web and accumulates as authority. It represents a miniature web as a directed graph G = (V, E): every vertex is a URL or domain, every edge is a hyperlink, and every followed edge transfers a share of its source vertex's PageRank to its target.PageRank is computed as the stationary distribution of a damped random-surfer Markov chain, solved by power iteration with a
damping factor of 0.85. Each followed edge carries d × PR(source) ÷ outdegree(source) per iteration, and the simulator renders that throughput as animated particles, so a quantity you normally only read about becomes something you can watch.
Then it lets you break things on purpose. Load a private blog network, a link wheel, a link farm or a parasite page, flip links to nofollow, and run a footprint sweep that devalues the outbound edges of suspicious nodes. Every change triggers a full recompute, and the event log records the money site's value before and after.
The ranking value a hyperlink transfers. In PageRank terms, the share of a page's score that leaves through one followed outbound edge.
The equity a node holds once the graph converges. Here it's the node's PageRank, scaled so the whole graph starts with 100 units.
A link that still exists but no longer passes equity. Search engines neutralize manipulative links instead of always penalizing the site.
2What you can measure
Four mechanics that decide how much authority a page actually receives.
Equity propagation
Mass flows along followed edges and pools on nodes with strong inbound profiles. Node radius grows with PageRank, and particle density tracks each edge's throughput.
Damping and teleportation
Every iteration, 15% of each node's mass teleports back to the seed pages. That's why a closed link wheel recycles a baseline share instead of creating authority from nothing.
Nofollow evaporation
Compare the 2009+ model, where a nofollowed edge still counts in the outdegree and its share is lost, with the pre-2009 model that made PageRank sculpting work.
Algorithmic devaluation
A footprint sweep flags nodes that share hosting, registrars, templates or tracking IDs. Flagged nodes stay in the graph, but their outbound links stop passing equity.
3Run your first experiment
Three steps, about two minutes, and you'll see why footprints matter more than link count.
Pick a scenario from the scenarios panel. Start with pbn: five expired domains, each inheriting equity from its own legacy backlinks, all pointing at one money site. Read the briefing, then hover each pink node to inspect its footprint profile.
Change the topology with the tools. + node drops any of seven node types, + link draws a followed edge (click a source, then a target), nofollow toggles an edge's attribute and delete removes nodes or edges. PageRank recomputes instantly and the log reports the change on the target node.
Press spambrain sweep. A classifier beam crosses the graph, flags every node whose footprint score clears the threshold and devalues its outbound edges. In the PBN scenario the money site drops from 41.1 to 14.2 , a 66% loss, while the one domain with a genuinely independent profile keeps passing equity.
Keyboard controls
Shortcuts only work while your mouse is over the simulator or it has keyboard focus, so they never interfere with the rest of the page.
| Key | Control | What it does |
|---|---|---|
| Tip: click the graph once so it has keyboard focus | ||
| 1 | move | Drag nodes to rearrange the layout | 2 | + node | Drop a new node of the selected type | 3 | + link | Click a source node, then a target node | 4 | nofollow | Click an edge to toggle nofollow on it | 5 | delete | Remove a node or an edge | S | spambrain sweep | Run the footprint classifier across the graph | M | nofollow model | Switch between the 2009+ and pre-2009 models | R | reset | Reload the current scenario | Space | pause flow | Freeze the particles while the graph has focus |
The embed below is the original v1. Version 2 lets you watch link juice flow through a graph you control.
4Launch the simulator
Hover or tap a node for its profile, click the graph to enable keyboard shortcuts, and keep an eye on the event log.
Link Graph Simulator: an interactive PageRank sandbox that shows how link equity flows between pages, and how search engines devalue manipulative link structures. It needs JavaScript to run.
Rebuild the scheme you just tested in the new PageRank simulator and see where the juice really lands.
5How to read the graph
Every visual property in the simulator maps to a quantity in the model.
Node types
Visual encodings
6The PageRank algorithm
Where the numbers come from, in the exact form the simulator computes.
PageRank models a random surfer who starts on some page, follows an outbound link chosen uniformly at random with probability d, and with probability 1 − d gets bored and jumps to a new starting page. A page's PageRank is the long-run probability of finding the surfer there. Formally it's the principal eigenvector of the Google matrix. Because damping makes that matrix stochastic, irreducible and aperiodic, the vector exists, is unique, and can be found by repeated multiplication.
u, wNodes in the graph. w→u means w links to u.
d = 0.85Damping factor: the share of mass that follows links each iteration.
L(w)Outdegree of w. In the 2009+ model, nofollowed links count here too.
vuTeleportation vector. Classic PageRank uses 1/N; the simulator weights seeds 5 (authority), 4 (legacy links) and 1 (everything else), normalized to sum to 1.
z danglingNodes with no outbound links. Their mass is redistributed through v so none is lost.
The surfer interpretation explains why links behave like votes weighted by the voter. A page the surfer visits often sends more probability mass through each of its links than a page almost nobody reaches. That's why one link from a strong page can outweigh dozens from weak ones.
Without damping, the surfer could get trapped in a closed loop and rank would pile up there forever. The 1 − d teleport term guarantees every node a baseline share and makes the chain ergodic. It also sets convergence speed: the error shrinks by roughly a factor of d each iteration.
A page with no outbound links is a sink. Mass flows in and has nowhere to go. The simulator uses the standard fix and redistributes dangling mass through the teleportation vector every iteration, so total probability is conserved unless links are nofollowed or devalued.
Start with PageRank proportional to the seed vector, apply the update to every node, and repeat. Because the error contracts by about d per round, the built-in graphs converge in roughly 60 to 140 iterations. The solver meter under the PageRank table shows the exact count.
Worked example: link dilution
Take a page holding 10 units of PageRank. With d = 0.85 it passes 8.5 units per iteration in total, split evenly across its followed outbound links. Every link you add dilutes every other link on the page:
That's why one editorial link from a focused page can outweigh a sitewide footer link on a page with 200 outbound links. In the natural web scenario, adding a single link from big-news.com lifts your-site.com from 34.7 to 38.3 .
Recreate the worked example in PageRank Simulator v2 and watch every link's share change as you add or remove links.
7Nofollow, PageRank sculpting and the hint model
The same attribute has meant three different things since 2005.
Load the nofollow sculpting scenario and switch models. Under pre-2009 rules, /product holds 14.1. Under 2009+ rules it falls to 2.3, about 9.8 units evaporate every iteration, and the graph keeps only 34.7 of its 100 units. Deleting the junk links instead of nofollowing them restores /product to 14.1, which is the modern lesson: prune or consolidate low-value internal links rather than nofollowing them.
Google, Yahoo and MSN adopt it to fight blog comment spam.
Google's Matt Cutts confirms nofollowed links still count in the divisor and the PageRank they would have passed evaporates.
Google adds rel="sponsored" and rel="ugc" and treats all three attributes as hints for ranking.
Nofollow no longer guarantees a URL stays out of the crawl or the index.
The simulator's 2009+ model treats nofollow as a strict directive. Since 2019 Google may choose to count a nofollowed link, so read the evaporation meter as the worst case for sculpting, not a guarantee.
8What each scenario demonstrates
Results from the simulator itself, using each scenario's default graph and a single sweep.
| Scenario | Topology | Money site before | After sweep | Change |
|---|---|---|---|---|
| Money-site PageRank × 100 on each default graph, before and after one sweep | ||||
| Natural web | Mixed organic graph | 34.7 | 34.7 | No footprints | Private blog network | 5 expired domains into 1 site | 41.1 | 14.2 | −66% | Web 2.0 link wheel | 6-node ring plus spokes | 34.2 | 2.4 | −93% | Link farm | 6-node all-to-all cluster | 20.7 | 5.4 | −74% | Parasite page | Rented page on a trusted host | 19.2 | 7.1 | −63% |
Money-site PageRank retained after the sweep
Scenario deep dives
A mixed graph of reciprocal and one-way links with one authority seed. Nothing here carries a footprint, so the sweep passes it untouched. The lesson is the base mechanic: a link is worth the linking page's rank divided by its followed outbound links, so placement on strong, focused pages beats volume.
Five expired domains each inherit equity from legacy backlinks seeded at 4×. Four share infrastructure: an IP block, a registrar with WHOIS privacy, an identical theme, one Cloudflare account and shared Analytics and AdSense IDs. The sweep flags them and the money site falls from 41.1 to 14.2. hiking-log.com survives because it has its own host, real topical content and links out to other sites. Networks get caught by what their members have in common, not by the links themselves.
Six hosted properties each link to the next one and to your site. Deleting a single spoke only costs about 3.3 units (34.2 to 30.9) because the ring mostly circulates the teleportation baseline each member already receives. A perfect ring is also a trivially detectable shape, and the sweep takes the money site from 34.2 to 2.4.
One homepage links to three money pages and seven nofollowed utility pages. Switch between the pre-2009 and 2009+ models to watch /product move between 14.1 and 2.3 while the leak meter fills. Then delete the junk links instead: /product returns to 14.1 with nothing evaporating.
Six members link to all five others and to the paying site, 30 edges inside a cluster of six. Rank loops around the cluster and inflates every member, but all-to-all reciprocal linking with no links to real sites is a textbook footprint. After the sweep the money site drops from 20.7 to 5.4.
big-publisher.com, seeded at 8×, passes internal equity to a rented page that exists to rank and link out. The page inherits the host's authority without earning any of its own, which is exactly what Google's site reputation abuse policy targets. The sweep applies that policy and the money site falls from 19.2 to 7.1.
Start from a money site and one authority node. Nodes you add as PBN, Web 2.0 or link farm carry default footprint scores of 0.8, 0.7 and 0.85, above the 0.5 threshold, so the sweep will catch them. Plain pages, authority sites and legacy backlinks carry no footprint.
Load your own PBNs, wheels and farms into the PageRank tool v2 and see how much equity actually reaches the money site.
9How search engines devalue manipulative link structures
Modern link-spam systems mostly neutralize links instead of penalizing whole sites.
Infrastructure footprints
Shared IP blocks and hosting, one registrar with WHOIS privacy, a single CDN account, identical Analytics or AdSense IDs, cloned themes and plugin stacks.
Graph footprints
Closed rings, complete clusters, all-to-all reciprocal linking and networks whose members link to one target and almost nothing else.
Content and anchor footprints
Thin or spun posts, off-topic placements, exact-match anchor text at unnatural ratios and templated author bios across unrelated domains.
Temporal footprints
Domains registered or revived in the same week, sudden link velocity spikes and posts that all publish on the same schedule.
How Google's link-spam systems evolved
Targets manipulative link profiles, applied in periodic refreshes that could hold sites down for months.
Penguin joins the core algorithm, becomes more granular and "devalues spam by adjusting ranking based on spam signals, rather than affecting ranking of the whole site."
Google uses its AI spam-prevention system to neutralize unnatural links. As Google put it, "any credit passed by these unnatural links are lost."
New spam policies target third-party pages that exploit a host's ranking signals (enforced from May 5, 2024) and expired domains repurposed to manipulate rankings.
10Beyond classic PageRank
The 1998 formula is the foundation, not the finished system.
Personalized PageRank and TrustRank Paper 2004
Replace the uniform teleport vector with a seed set of trusted pages, and trust decays with link distance from those seeds. The simulator's 5× authority and 4× legacy weights are a small personalized PageRank.
Reasonable surfer Patent 2010
Google's US 7,716,225 describes weighting each link by how likely a user is to click it, using features like position, anchor text and styling. Links stop being equal votes: a prominent in-content link can carry far more than a footer link.
Distance from seed sites Patent 2015
US 9,165,040 ranks pages by their shortest link distance from a set of trusted seed pages, which leaves networks with no path from trusted seeds with very little to pass.
PageRank today Status
Toolbar PageRank stopped updating in late 2013 and was removed in 2016, and the last PageRank patents expired in 2019. The signal itself stayed: in 2017 Google's Gary Illyes wrote that "after 18 years we're still using PageRank (and 100s of other signals) in ranking."
Model limits
What this simulator deliberately leaves out.
PageRank Simulator v2 is the interactive follow-up to everything on this page.
?Frequently asked questions
Quick answers to what people ask most after running the simulator.
No. It's the original 1998 PageRank formulation running on a toy graph. Google still uses PageRank-derived signals, but alongside hundreds of others and with link weighting this simulator doesn't model.
PageRank is a probability distribution that sums to 1. Multiplying by 100 makes the numbers readable as percentages of the graph's total authority. When nofollowed or devalued links leak mass, the total drops below 100, and the juice-kept meter shows how far.
They stand in for backlink profiles outside the sandbox. Mathematically it's a personalized teleportation vector: those seeds get 5× (authority) or 4× (legacy backlinks) the random-jump probability of an ordinary page.
A closed ring only redistributes the teleportation mass its members already receive. With no inbound links from outside, the wheel is circulating its own baseline, and a perfect ring is an easy pattern to detect.
Since September 2019 Google treats nofollow, sponsored and ugc as hints, so it may count some of them. The simulator uses the strict interpretation to show the worst case for sculpting. Nofollowed links can still send referral traffic and help discovery.
A simplified footprint classifier. Each suspicious node carries a score, and anything at 0.5 or higher is flagged and has its outbound links devalued. It illustrates the outcome of link neutralization, not how SpamBrain works internally.
Sources and further reading
- Brin, S. and Page, L. (1998). The Anatomy of a Large-Scale Hypertextual Web Search Engine. Stanford InfoLab.
- Gyöngyi, Z., Garcia-Molina, H. and Pedersen, J. (2004). Combating Web Spam with TrustRank. VLDB 2004.
- Cutts, M. (2009). PageRank sculpting.
- Google Search Central (2016). Penguin is now part of our core algorithm.
- Google Search Central (2019). Evolving nofollow: new ways to identify the nature of links.
- Google Search Central (2022). December 2022 link spam update.
- Google Search Central (2024). March 2024 core update and new spam policies.
- US Patent 7,716,225 (2010). Ranking documents based on user behavior and/or feature data.
- US Patent 9,165,040 (2015). Producing a ranking for pages using distances in a web-link graph.
Keep exploring
Go back and build a scheme that survives the sweep, or read how each technique works and how it gets caught in the full guide.
Link Graph Simulator by Jourdan Rombough, Optimization Theory.
More Writing & Research by Jourdan Rombough
View all research
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