a blogroll for each category

If a ‘category’ view, display links with same category name

<?php
if ( is_category() ) {
$cat = get_query_var('cat');
$category=get_category($cat);
wp_list_bookmarks('category_name='.$category->cat_name); } ?>
}
?>

This works perfectly for what I need, however, I have one question. I placed this code inside a div. How do I get the div to NOT display if there are not any bookmarks related to the category?

In other words, if a user is on a page about X, but there are no Link/Bookmark/Blogroll categories about X – then do not display the div with wp_list_bookmarks.

Thanks in advance for any and all assistance.