If <pre>Profile: <a href=<?php echo $logbook_graph; ?> > <?php echo $logbook_graph; ?> </a></pre> doesn’t work, can you post the code that is generating $logbook_graph, and where it’s called from (helper, page, or template). Also the fieldtype that it is being pulled from, as I have experienced differences between handling of single vs para vs code fieldtypes.
In my code suggestion I’ve deliberately omitted the quotes surrounding the url to avoid further confusing the quotes issue, but it should still parse correctly in a browser. If you post the results of that back here, please can you insert some dashes or something between h-t-t-p, as urls get changed when posted here.