But when you put these properties together you essentially get a single structure representing multiple lists. That is, given items 1 - 5, you could arrange the pointers to traverse them in orders [1, 2, 3, 4, 5] or [1, 3, 5, 4, 2] or [5, 4, 1, 2, 3], but not [1, 5, 2] or [1, 2, 3, 2, 1].
What I don't understand is why anyone would put what is essentially a number of different lists into a single list. I see no advantages either in algorithmic complexity (traversal and addition/insertion/deletion operations are still the same complexity) or implementation. In fact, I can easily see the implementation being a nightmare. It's tricky enough deleting a node from a singly-linked list. I cannot imagine a problem this was invented to solve that could not have been solved more easily with multiple linked lists. Maybe the problem was non-technical, e.g. "get a patent to put on my résumé".
E.g. if you have 1->2 1->4 2->3 3->5 4->5 the lists could be [1,2,4,3,5] and [5,4,3,2,1].