Backlinks from .edu and .gov domains

When Matt Cutts (Google search quality engineer) was asked about the extra ranking
boost from inbound links originating from .edu and .gov TLDs, he responded as follows:
This is a common misconception—you don’t get any PageRank boost from having
an .edu link or .gov link automatically.

Although Google denies that .edu and .gov links get a PageRank boost, you can easily
construe that the domain extension does matter in some sense. When Google flat out
denies something, it is almost always because it is not true. But when Google is cagey
about something, you need to beware. Most people believe that .edu and .gov links are
more valuable than others because those sites typically have strong PageRank and
therefore more link juice. It is doubtful that Google actually gives these sites greater
weight simply because of the TLD extension. When your site has a link from an .edu
or .gov link, it says a great deal about the site’s trust and authority.
It is very hard to get an .edu or .gov domain. Only one registrar today has permission
to grant .edu domains: EDUCAUSE, a nonprofit organization that won the right to be
the sole registrar of all .edu domains in 2001. Not everyone can get an .edu domain,
and .edu domains are not transferable. Eligibility requirements are very strict (http://net
.educause.edu/edudomain/):

Eligibility for a .edu domain name is limited to U.S. postsecondary institutions that are
institutionally accredited, i.e., the entire institution and not just particular programs, by
agencies on the U.S. Department of Education’s list of Nationally Recognized Accrediting
Agencies. These include both “Regional Institutional Accrediting Agencies” and “National
Institutional and Specialized Accrediting Bodies” recognized by the U.S. Department
of Education.