PageRank

Lesson notes

Overview

A page is important if important pages link to it — found by repeatedly passing rank along links. This topic is rated beginner and is number 16 of 117 in Computer Science. Core ideas and first intuitions. No prior knowledge needed.

What you are seeing

The panel above shows an interactive animation of the idea. Every slider changes one quantity so you can see its effect on the outcome. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.

In depth

PageRank, the idea behind early Google search, ranks pages by the principle that a page is important if important pages link to it. Each page divides its rank among the pages it links to, and a damping factor d models a random surfer who occasionally jumps to a random page. Iterating PR = (1 − d)/N + d·ΣPR(u)/L(u) converges to the steady state, which is the leading eigenvector of the link matrix. It counters link spam by weighting links by importance.

Reading the relationship

The expression "PR = (1−d)/N + d·Σ PR(u)/L(u)" is a compact summary of the idea. It uses the symbols P, R, d, N, Σ, u; name what each one stands for before you start. Notice that it contains a ratio, so increasing the denominator makes the result smaller, and a sum, so many small contributions are added together. Then use the sliders to see how changing one quantity changes the others.

A guided exploration

1. Run the animation once with the default settings and describe in words what happens. 2. Change one slider at a time and note which quantity responds most. 3. Push each slider to its extreme and decide whether the result still makes sense.

Try this

Start by only moving one slider at a time. Say aloud what you expect, then check.

Common pitfalls

Test small inputs by hand and then the largest ones. Off-by-one errors and forgetting how cost grows with input size are the most common traps.

How it connects

It builds on “Minimum Spanning Tree (Prim)”, the topic before it in Computer Science. Once you are comfortable, continue with “Recursion: Tower of Hanoi”.

Why it matters

Computing ideas decide how fast, how safely and how well software can solve problems.