PageRank
A spaceship surfs the warp lanes of a made-up galaxy and the busiest stars rise to the top.
The numbers
This site, ranked
The same maths on aldus.nexus itself. Every project is a star in its own colour. Two projects are linked both ways when they share a tag, more strongly the more tags they share, and every project links to and from the landing page and the How it works page. The surfer's long-run share of time on each page is its PageRank. Click a star to open that page.
every project as a link
How it works
Picture a bored pilot who keeps jumping along random one-way lanes. Most of the time they follow a lane out of the current system; now and then, with chance 1 - d, they warp to any system at random. Over a long flight, the share of time spent at each system is its PageRank. Systems are important if important systems point to them.
Power iteration gets the same answer without the ship. Every system starts with equal rank, then hands its rank out evenly along its lanes, plus a small even share from the warps. Repeat, and the numbers settle, usually within a few dozen rounds. Lower damping settles faster.
A dead end has no lanes out, so its rank leaks away like a black hole unless it is shared out again. A spider trap is a group that only links to itself: without warps it would swallow everything.
The site section runs the same thing on this website. Links there have weights: two projects that share two tags are joined twice as strongly as projects that share one, so the surfer follows a link with chance proportional to its weight. The landing page and How it works link to everything and everything links back, so they rank well, but a project that shares two or three tags with many others can pull in even more.
one simple rule about a random walk ranks a whole web, and the answer is a fixed point that the walk and the arithmetic both find.