The algorithm that built Google. A node is important if important nodes point to it — a beautifully circular definition that a little linear algebra makes concrete.
PageRankLive
the algorithm that built Google
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PageRank ranks nodes by importance: a page is important if important pages link to it. It is computed by imagining a random surfer who follows links with probability d and jumps randomly otherwise, then finding where they spend the most time. This eigenvector of the link matrix launched Google and now ranks everything from proteins to social influence.
Reading this result: PageRank is the stationary distribution of a random surfer who follows links with probability d and teleports to a random page with probability 1−d. At d=0.85 link structure dominates but teleport still keeps every node reachable.
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How it works
PageRank models a random surfer who follows a link with probability d (the damping factor) and jumps to a random node otherwise. The long-run fraction of time spent at each node is its rank — the dominant eigenvector of the link matrix, found by power iteration. Beyond web search, it ranks proteins, citations, roads, and social influence.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
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The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.