There was always connection (maintaining your alignment and structure while taking their balance) and turning their center with your center. These seem to be pretty basic instructions in Aikido, but I seldom see them mindfully practiced and applied.
There's a great difference between "making a connection" and doing it with kokyu; there a great difference between "alignment and structure" and using kokyu. Ikeda Sensei uses kokyu, but since it's a way of rearranging the body with mind-intent it can't really be seen. So most people copying the appearance and thinking "structure", etc., will usually do it wrongly. A lot of it needs to be learned by feel.