There is absolutely no difference for SEO when you create your links as relative or absolute:

 - `<a href="/">Link</a>`
 - `<a href="http://example.com>Link</a>`
 - `<a href="http://example.com/>Link</a>`  (for the home page, the trailing slash doesn't matter.)

Google knows that all of those point to the home page.   It will assign value to them appropriately and list them all the same in Webmaster Tools.

On the other hand these are not equivalent:

 - `<a href="example.com">Link</a>` -- Points to `http://example.com/example.com` because it is interpreted as a relative link (it is missing the `http://` and is a broken link.)
 - `<a href="/index.html">Link</a>`  -- While `index.html` may be the file that contains the home page content, `http://example.com/` and `http://example.com/index.html` are different URLs that could be configured to have different content.   It is better not to use `index.html` in any links on your site.