When you create an admin, there are two ways to create the admin.  The first is that you can simply create an admin record.  When you do that, the admin record will not have a "Link to Constituent" link.  The other is that you can take an existing constituent record and "Create As Admin" to create an admin record that is basically a duplicate of the existing constituent record.  When you do that, a link is formed between the admin and the constituent record.  That link can be found on the admin record as a "Link to Constituent" link and on the constituent record as a "Link to Admin" link.