For the root of this site, WPMU returns a list of blogs in an array, which contains the blog_id, domain, and path. I also inserted the blogname into the array which I retrieved with get_blog_option().
The array was not in alphabetical order, and I wanted to sort it by the $blogs[$i]['blogname'] property. After a bit of Googling, I found I could make use of the usort function, which allows you to perform sorting with a user function.
This is what I ended up with:
function cmp($a, $b) {
return strcmp($a['blogname'], $b['blogname']);
}
usort($blogs, 'cmp');
Which is surprisingly simple, and works. Now, on the root, the blogs are displayed in alphabetical order.

