Get the name an the description of a link category

I have a link category with the id $id=23; and the slug $slug=friends;. I managed to read all links from that category using get_bookmarks($id).

Now I also want to use the name and the description ob the link category. How geht I get these values? I tried for example:

$cat = get_the_category($id);
$output .= "<p>Description: ".$cat[0]->category_description."</p>";

unfortunately this (and other things) did not work.

So how can I receive the name and the description ob the link category with the id=23? Is it also possible to recieve this via the slug of the link category? I tried get_category_by_slug($slug), but this always gave an empty result,…