Should tables or classes be bidirectional in all cases?

Question

Database

There is a connection:

Here both aggregation and composition. Do all the given classes have to store back references to the enclosing class (doubly linked list)?
A professor can exist without a Department and a University, but a Department cannot exist without a University.

Answer 1

Do all the given classes have to store back references to the enclosing class (doubly linked list)?

No, in many cases one-sided is sufficient.
The most popular type of communication is just one-way many-to-one.