No-one outside of google knows exactly how pagerank is implemented, and it is one of things that google make extremely difficult to reverse engineer, since externally we only see a rounded integer number and one that could be a few months old, we don't get to see the internal realtime number accurate to various decimal points.
We do know that google patented pagerank in
2001, we do know that nofollow as a concept wasn't created until
2005, and we do know that Google changed their handling of pagerank and nofollow links in
2009. But that's about all we can really know, and it is difficult if not impossible to know for sure about the internal implementation of algorithm, and possibly how google might treat some links differently to others (the patent is pretty vague and gives Google a hell of a lot of leeway in terms of what it can do, and what it
has done since the patent).
Which means that some of the information on this thread might be right, some might be chinese whispers in origin perhaps based on original source which is vague, some might provide abstract approximations, some might relate to aspects of the ranking algorithm (not the pagerank algorithm), and some of the information on this thread might sound likely or feasible but be plain wrong, including what I'm going to say next (I think it might be right, but I also think there's a chance it could be wrong) ...
The pagerank algorithm in the patent allows for an iterative and cyclical flow of pagerank with a dampening factor, ie. your home page could pass pagerank onto a section page, but that section page in turn could pass pagerank back to the home page, which in turn passes some of that pagerank back to section page and so on (in an ever-decreasing feedback loop, with less and less pagerank being passed due to a dampening effect/factor).
If such an algorithm is used, then it is possible for a section page to indirectly lose pagerank by linking out and/or linking nofollow too much, because it reduces the share of the pagerank it returns back to the home page, which in turn reduces the pagerank that the homepage can pass back to the section page.
For anyone with the inclination to get into the maths of the pagerank algorithm, there is this book:
Google's Pagerank and Beyond, but even with that book it will only discuss the possible maths theories behind the Google's implementation of the algorithm, not google's final or current implementation of the algorithm.
In simple terms, where possible I would try to avoid too many external links, I'd try to avoid too many links full stop. If you want to litter your pages with social bookmarking links perhaps consider using non-search engine friendly linking methods (some fancy Javascript or Flash which doesn't detract too much from the content for the users). Also question whether you really need to link to that W3 HTML and CSS validator on every page.
As for nofollowing internal links to say a contact us page, why would you link to a contact us page on your own site but essentially say "I cannot vouch for this page".
