Page Rank Case Study using Markov Modelling

Author: T.G. Barker | How Google Evaluates Websites | Last reviewed: 12/07/2026.
Markov chains, first introduced by Russian mathematician Andrey Markov in 1906, provide a way to model sequences of dependent events — a method I’ve adapted here to explain the mathematical SEO framework of how PageRank flows in SEO.

Website User Navigation Example

In this graphic we have used tgBarker’s website as our example for this case study showing how we used a Markov chain process (which is used by Google’s PageRank modelling). The model is a simplified diagram displaying the major nodes as it gives an easier understanding of the flow of travel to a node and from a node..

From Website Navigation to Search System Understanding

This graph gives you a strategic map of how users interact with your site—perfect for guiding internal linking, CTA placement, and content updates. A Markov chain models user navigation as a stochastic process where the next page visited depends only on the current page—not the full history. This is ideal for estimating transition probabilities across your site. This review only makes sense once you understand how search systems actually evaluate structure, authority and intent across a website.

The Markov Chain Mathematics Behind PageRank

Google’s original PageRank algorithm, introduced in the late 1990s, was built on Markov modelling principles—treating the web as a graph of interconnected pages where a “random surfer” follows links with certain probabilities. Each step in this Markov chain represented the likelihood of moving from one page to another, and the stationary distribution of this process produced the PageRank score, a measure of authority and importance. While Google has since layered hundreds of other ranking signals on top, PageRank has always remained a core part of their system, continuously refined to handle scale, spam, and modern search needs. Even today, authority flow across links and the underlying Markov chain mathematics still influence how Google evaluates websites and how pages are interpreted. This flow of authority is more fully understood through structural authority flow and internal linking relationships.

Using AI to See Your Website Differently

While many SEO companies are busy speculating about the complexities of search and AI merging in the future, we take a different approach. Instead of only writing about AI and Search merging, we are practically using AI — to help visualize websites. In this example, we show how AI assists in examining your current site by working alongside Google Analytics to provide clearer insights.

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How introducing a new page (like “Case Studies” or “AI Packages”) might redistribute flow:

New Page Simulation: Case Studies & AI Packages
🆕 Expanded Page Set
• Home
• Blog
• Services
• About
• Contact
• Pricing
• Case Studies
• AI Packages

🔁 Updated Transition Matrix (Simplified)

From / To	Home	Blog	Services	About	Contact	Pricing	Case Studies	AI Packages
Home	0.04	0.30	0.20	0.08	0.08	0.15	0.10	0.05
Blog	0.10	0.35	0.15	0.08	0.08	0.10	0.10	0.04
Services	0.08	0.20	0.20	0.08	0.08	0.15	0.15	0.06
About	0.08	0.15	0.15	0.20	0.08	0.10	0.14	0.10
Contact	0.15	0.10	0.08	0.10	0.20	0.15	0.12	0.10
Pricing	0.20	0.08	0.15	0.08	0.10	0.20	0.10	0.09
Case Studies	0.10	0.10	0.20	0.10	0.10	0.15	0.15	0.10
AI Packages	0.08	0.08	0.18	0.10	0.10	0.20	0.16	0.10

📈 Simulated Steady-State Distribution

Page	Long-Term Probability
Blog	22.6%
Case Studies	16.8%
Pricing	15.2%
Services	14.3%
AI Packages	10.7%
Home	8.9%
About	6.3%
Contact	5.2%

 Strategic Insights

🧠 Case Studies = Trust Magnet

• Strong long-term retention suggests users value proof and real-world results.
• Use this page to reinforce credibility and link back to Services and Pricing.

🤖AI Packages = Conversion Catalyst

• High flow from Services and Pricing implies users are exploring solutions.
• Optimize this page for clarity, tiered offerings, and direct CTAs.

🔗Internal Linking Strategy

• Link Blog posts to Case Studies and AI Packages to guide users deeper into the funnel.
• Consider dynamic modules like “Related Solutions” or “Success Stories” on high-traffic pages.

If you want to understand how your own website is currently being interpreted, the Strategic Search Authority Review explains how this analysis is applied in practice.

Conclusion

This case study demonstrates that a website can be examined as a connected probability system rather than simply a collection of individual pages. By applying Markov modelling principles, we can observe how changes to navigation, internal linking and page structure may redistribute long-term probability across the site.

The purpose is not to claim that we can reproduce Google’s PageRank calculations, but to use established mathematical principles to visualise structural relationships, identify where authority and attention may concentrate, and test how introducing new pages could alter the wider website model.

In practical terms, it provides a different way of asking an important question: if search systems evaluate websites through links, relationships and repeated structural signals, what does the structure of your website encourage them to understand as most important?

The next step is to examine how structural authority flows through internal links across a website and how those relationships can reinforce the relative importance of individual pages.

To see how these principles can be applied to a large commercial website, read our Pharmacy UK Markov Chain SEO case study, where graph analysis and Markov modelling were used to identify how an unusually flat authority structure may have limited ranking progress.