PageRank as a Monte Carlo random walk. A surfer at node i follows a uniformly chosen outgoing edge with probability α=0.85, else teleports to a uniformly random node — exactly the process whose stationary distribution is PR(i)=N1−α+αj→i∑out(j)PR(j).
Thousands of phantom hops per frame fill a visit histogram while one prototypical surfer is animated on top with a glowing trail; node radii and the numbers under each label show the live visit fraction. The true PageRank is computed once by power iteration so a green ring lights up around every node whose Monte Carlo estimate is within 0.005 of the truth, and the bottom bar tracks the ℓ1 error ∥MC−PR∥1 collapsing toward zero — the law of large numbers doing PageRank in real time.