01.05 · Concept
Links as Votes: PageRank and What It Became
Explain PageRank as an eigenvector over a link graph, and say honestly which parts of that idea still operate and which were replaced.
PageRank is a fixed-point ranking over a directed link graph: pages pass authority through outgoing links until the scores stabilise. Its core insight was that links from authoritative pages count more than raw link totals. Modern search still uses graph authority signals, but ranking now combines them with relevance, intent, spam handling, freshness and learned systems.
What this lesson answers
- how does PageRank work as an eigenvector
- why is PageRank not just counting links
- does Google still use PageRank for ranking
Notes
PageRank’s original idea is to treat the web as a graph: pages are nodes, links are directed edges, and a link is a kind of recommendation. A page is important if important pages link to it, so rank is not just a count of incoming links. The rank of each page depends on the ranks of the pages pointing to it, which makes the whole problem recursive.
The eigenvector mental model is “keep passing importance along links until the scores stop changing.” Imagine a random web surfer who repeatedly follows links, with a small chance of jumping to a random page instead of getting trapped.
References
Common questions
- What does it mean to call PageRank an eigenvector?
- Build a transition matrix from the link graph, then repeatedly distribute score from each page through its outgoing links. When further iterations no longer change the relative scores, the stable vector is an eigenvector of that matrix. In practical terms, it is the long-run authority distribution implied by the graph.
- Why did PageRank need a random jump or damping factor?
- Without damping, a surfer following links can get stuck in dead ends, closed clusters or disconnected parts of the web. A small chance of jumping elsewhere makes the process well behaved across the whole graph. It also turns PageRank from a brittle link-following simulation into a stable global scoring method.
- Is PageRank still how search engines rank pages?
- Not by itself. The link graph remains useful because citations and references can signal authority, but modern ranking uses many other inputs. Search engines also evaluate the query, page content, freshness, location, structured data, spam patterns and learned relevance signals. PageRank’s idea survived as one ingredient, not the full recipe.
Short definition: what is Links as Votes: PageRank and What It Became?