Google PageRank

Graph Theory · Axiom Academy

How Graph Theory Revolutionized Web Search and Built a Trillion-Dollar Company The Problem That Changed Everything In 1998, the internet had a massive problem: finding information was nearly impossible. Early search engines ranked pages by counting keywords, which meant spam-filled pages with "cheap! buy now! best deal!" repeated hundreds of times would rank at the top. Then two Stanford graduate students, Larry Page and Sergey Brin, had a revolutionary insight: what if we treated the web as a giant directed graph? The Brilliant Idea: Instead of just counting words on a page, count the links pointing to that page. A page linked to by many important pages is probably more important than a page with no links - just like how an academic paper cited by many important papers is probably influential. This graph theory approach became G o o g l e , now worth over 1.5 trillion. Let's understand the mathematics behind it! The World Wide Web is naturally a directed graph : Directed Edges (E): Hyperlinks from one page to another Why Directed? A link from page A to page B doesn't mean B links back to A Graph G = (V, E): The entire World Wide Web! A Small Web Graph - Click on pages to see their connections! Scale of the Web Graph (2024): Vertices: ~1.8 billion websites (5+ billion pages indexed by Google) Edges: Trillions of hyperlinks Average In-Degree: ~10-15 links per page Diameter: Approximately 19 clicks between any two pages!

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