It's not a generic directed graph either, though - each node only has one outbound link. The sequence of parents for any given node is a linked list, and a cycle in that list is invalid. You certainly don't need to run tortoise and hare for every node path looking for cycles. There are other approaches, clearly - reachability analysis starting from each root node, for example.

But if I were to ask you to write a routine to find the root node for a given node based on that data, then ask you to guard that routine against finding yourself in an infinite loop or stack overflow, tortoise and hare would be a legitimate answer.

Just trying to make it clear that just because the question asks about linked lists, doesn't mean it's always about abstract data structures.