Oh yes, I'd say that breathing is of great importance in aikido - in any budo - and in so many ways.
The breathing of air and the "breathing" of
are linked. Training one stimulates the other. So, the use of air breathing in aikido should be similar to that of
"breathing", where the latter is really the main thing.
It should be center (tanden
) breathing, which is belly breathing with a feeling of doing it in your center.
As a basic principle, inhaling equals receiving/accepting, and exhaling is giving/directing. But the ideal is that the difference between the two fades away, at least the turning point between them. Breathing should feel circular, not linear.
Also, meeting an attack while breathing in is risky, since that is when the body is the weakest. Therefore, it is better to shift early between in and out, when the attack approaches, in a feeling of helping the attacker along with the attack.
, static training, though, it is a good exercise to make the initial movement breathing in, and the rest breathing out.
Most aikido techniques can be divided into one step of breathing in, and then two steps of breathing out. So, you breathe out two times in a row. That's good to do, to realize that there is more inside, and to extend your spirit.
Many beginners have difficulties with center breathing. They use chest breathing and don't know how to bring it down. A good way to exercise it, I've found, is to place one's hand on the belly in front of the center, and push it out when inhaling.
When this works out, one should also try to push the hand when exhaling. So, both when breathing in and out, the hand is pushed.
Deep center breathing is very invigorating and inspiring (the word 'inspiration' notes that it is breathing thing). Without it, I would find aikido much less of an attraction.