A link checker is a fantastic tool to be able to look into the types of links that your site has received as well as the types of links that your competitors has. The search engines are pretty much determined by who has the most links, as if it is a popularity contest, so finding out how many you have, vs how many your competition has is important, as well as being able to see what kinds of links your competitors have been able to receive. That way, you can often contact those resources your competitors use, and try and request a link from them also since you are writing on a similar subject matter.
If you are brand new, do not get caught up on how many links the Yahoo site: operator is showing (or not showing). Google's link tools don't show you everything, so do not get worried that they aren't finding all of your links. The Yahoo tool is good, but it shows nofollow and dofollow links, and since the nofollow links don't really pass any value, it can make searching through the tool a bit cumbersome. And remember, just because Yahoo sees a link (or doesn't see a link) doesn't really matter when it comes to Google (who has the highest number of searchers) because they really are two separate companies in how they operate. When checking links, it is important to know all of those pitfalls, since it can lead to frustration that really isn't needed at all.
When checking out different link sources, you'll want to keep a few things in mind for consideration when evaluation whether or not a link source is good. If there are already tons of links on the page you're wanting a link on, then the link juice that will flow your site will probably be minimal, but every link does help. It all comes down to how much work is involved in getting that link.
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