When viewing the backlinks report in Site Explorer, you will notice that you can filter by "Link Type":
What do they mean?
Here's a quick breakdown:
Dofollow - By default, all links are dofollow links unless modified to become nofollow. Dofollow links are commonly considered to pass "weight" and help a target website or URL to rank better in organic search results. This filter shows all the links that are dofollow.
Redirect - A redirect is a way to send both users and search engines to a different URL from the one they originally requested/want to visit. This filter shows all the links that have been redirected.
Governmental - Governmental links are links from .gov sites. This filter shows all the .gov links.
Educational - Educational links are links from .edu sites. This filter shows all the .edu links.
Nofollow - A nofollow link is link with the attribute rel="nofollow". This tells search engines to not crawl them or count them as votes of quality. This filter shows all the links that are nofollow.
Content - An in-content link (or editorial link) is a link within the body of a piece of content. This filter shows all the links within pieces of content.
With redirect chain - A redirect chain occurs when there are more than one redirect between the initial URL and the destination URL. For example, someone.com redirects to bit.ly, which redirects to yoursite.com. This filter shows all the links with redirect chains.
Without redirect chain - This filter shows all the links without the above stated redirect chains.
So, if I wanted to see all the .gov links linking to my site, I could filter by "Governmental" links, and I'll see all the .gov links: