quality .edu and .gov backlinks are benefecial. but if they are relevant to your site content and its super powerful. however with constant updates by google a power packed linkwheel strategy becomes essential to rank competitive keywords. pm me for one link strategy.
the one with .gov and .edu are more of quality.Also the one with High PR links.also try to build more do follows links
Relevant, links from pages directly ralated to a keyword. Unrelated links is seen as spam / over-optimatyzation links.
Edu and Gov should be limited as there are not many Edu and Gov sites on the Internet so it would be strange if 40% of edu sites are pointing to your site.
Nowadays best backlinks must be placed on relevant websites and with diversified anchors - that's the recipe
High Page Rank pages that gives you a link back such as footer link or header link will be very beneficial.
backlinks from relevant pages are most beneficial. One relevant quality backlink is better than thousands of spammy links.
On my point of view, do follow link with good PR. This links are most beneficial to every website promotion.