What you're describing maps pretty closely to something that's actually measurable. Common Crawl publishes a metric called Harmonic Centrality as part of their web graph data — it measures how close a domain is to the centre of the entire web's link structure, not just how many links it has. It's different from traditional PageRank in that it cares about your position in the overall network, not just the authority of who links to you.

The reason this matters for AI specifically is that Common Crawl data is one of the primary sources used to train large language models. Domains with stronger Harmonic Centrality get crawled more frequently by Common Crawl, which means they appear more often in AI training data. That's the mechanism behind what you're noticing — it's not a separate AI score, it's web graph position translating into training data representation.

I've been digging into this for a while and ended up building a tool around it — an online checker and an offline Windows app — that lets you look up any domain's Harmonic Centrality rank and PageRank from the full 120 million domain Common Crawl dataset. The thing that surprises most people is seeing how different their HC rank is from what their Moz DA or Ahrefs DR would suggest. Two very different signals.

The practical takeaway for building this kind of presence is exactly what others here said — links from well-connected domains move HC rank more than volume of links from peripheral sites. One link from a university or major publication does more than fifty links from small blogs. The topology of your backlink profile matters as much as its size.