The site crawling itself, in your browser
Press the button and this page reads its own sitemap, fetches a sample of the site, parses every document, builds the internal link graph from what it actually finds, and runs PageRank across it. No server, no crawler licence, and nothing leaves your browser.
Live Self Crawl
The crawler reads sitemap.xml, samples URLs from it, fetches each one with a small concurrency limit, parses the returned HTML with DOMParser, and builds the link graph from what it actually finds. PageRank runs for thirty iterations at a damping factor of 0.85. This works only because every request is same origin: the page you are on and the pages it fetches are served from the same host, so the browser permits it. Pointing this at any other domain would be blocked, which is the same reason the skill runner takes pasted source instead of a URL.
Internal linking is the part you fully control
Backlinks are negotiated. Rankings are granted. The distribution of authority inside your own site is the one part of the system where you set the rules, and most sites never look at it.
PageRank did not go away
The public patent is old and the production algorithm has moved on, but link based authority flow is still the mechanism. Running it on your own graph shows where your internal equity actually pools.
Orphans are invisible, not weak
A page with no internal inbound links is not competing badly. It is often not competing at all, and no amount of content work on that page changes it.
Depth is a budget decision
Every extra click from the home page reduces the frequency a crawler returns. If your highest value pages sit at depth four, that is an architecture problem wearing a content problem's clothes.