>but that none of them are the three that are mentioned up-thread.

Not sure if cosmology is some exception (I guess one could find specialist universities in all kinds of subjects), but overall those three as exactly ranked as the top three, ranked by papers, quality, citations, patents, etc, here, across all kinds of fields:

"To compile the 2017 ranking of the world’s most innovative universities, Clarivate Analytics (formerly the Intellectual Property & Science business of Thomson Reuters) began by identifying more than 600 global organizations – including educational institutions, nonprofit charities and government-funded labs – that publish the most academic research. Then they evaluated each candidate on 10 different metrics, focusing on academic papers (which indicate basic research) and patent filings (which point to an institution’s ability to apply research and commercialize its discoveries), and ranked them based on their performance."

1 Stanford University

2 Massachusetts Institute of Technology (MIT)

3 Harvard University

https://www.reuters.com/article/us-amers-reuters-ranking-inn...

this is exactly what I wanted to criticise by my comment. I don't think these rankings are that important because they don't capture what the (original) article wanted to measure. There's only one stanford, which might be better than every other university out there. But there are a lot, often way smaller, universities out there that produce fantastic research. You have to add them together.

I'm curious, in your experience, (and I am curious - not being argumentative), how socially connected do you find the citation graph to be?

A while back, I was mapping innovation diffusion, as indicated by papers and patents and hiring company's R&D budgets and ROI on said investment and the like, and I was surprised at how much innovation spreads through folks that know one another, as opposed to papers that anyone could (in theory) read. I have to guess that people would similarly cite papers of people they know (maybe even of the same lab?). Do you think that has any effect on the score that you are pointing me towards?

Oh come on, everybody can churn out papers and patent filings.

If you go by Nobel prizes, the ranking is different (leaving out non-US contestants):

Physics:

1. MIT

2. Harvard

3. Berkeley

4. Chicago

5. Columbia

Chemistry:

1. Harvard

2. Berkeley

3. Chicago

4. Caltech

5. MIT

Medicine:

1. Harvard

2. Rockefeller

3. Columbia

4. Caltech

5. WashU

Conclusion: Stanford is overrated.