Link categories in Sidebar

At the moment I have the following code in my side bar which pulls all of my links and puts them into a list on my sidebar:

<?php /* If this is the frontpage */ if ( is_home() || is_page() ) { ?>
<?php get_links_list(); }?>

Ideally I would like to split the links into the Link categories as they are displayed in my admin page with the names of these link categories displayed as <h2>.

Can someone please advise me how I can do this?