I am having a number of links in a hierarchial order
IMO if you have it in a Hash of hashes (see perldsc), then the task becomes easy, just walk through the keys and respective values and call appropriate functions, maintain a array and push the values that you are walking through from particular key to print the depth(full link path).

How can I do it with recursion?
Why do you want to specifically go for recursion??, can't you achieve using simple ways unless you want to do something very purposeful inside that depth of link.