Will the garbage collector be able to identify and clean up objects in cyclic references?

Yes, modern garbage collectors, including those used in Android (for example, the Garbage Collector in JVM/ART), are capable of detecting and cleaning up objects that are in cyclic references if there are no external references to them from root objects.

This is possible thanks to tracing algorithms that start traversal from root objects (such as the stack, static variables) and mark all reachable objects. Objects that are unreachable from the roots are considered garbage, even if they reference each other cyclically.

Thus, cyclic references themselves do not prevent garbage collection if the objects are not used in the program.