Add a trust metric and chains of provenance. Bad ring link -> bad trust percolating up that chain. Little trust, your site isn't always shown as part of the ring. Too much loss of trust, you're out.
(Ultimately, this is a bad facsimile of human group behavior - all the way up to shunning people who deeply violate group norms. And I don't think it'll scale super-well. )
Except there's no provenance or root of trust. There is (IIUC) no back-propagation of a penalty if sites violate trust, just an overall observational measure.
And I'd still say pagerank did work really well in an Internet where there was overwhelmingly trust. But in a world where default-trust is a bad stance, I believe there needs to be an equivalent of what "You can trust X" does in small in-person groups. (Or, alternatively "Sheesh, X went off and just destroyed all trust")
I do think it'll need to be more than a single metric, too. Trust is multidimensional by topic(E.g. "I trust the NYTs data science folks, I have zero trust for the OpEds"), and it is somewhat personal. (E.g. I might have experienced X lying to me, while they've been 100% honest to you - maybe in/outgroup, maybe political alignment, maybe differing beliefs, etc. Ultimately, what we call trust in an indirect situation is "most of my directly trusted folk vouch for that person)
(Ultimately, this is a bad facsimile of human group behavior - all the way up to shunning people who deeply violate group norms. And I don't think it'll scale super-well. )