WRONG!!! So many people confuse lack of air with lack of gravity probably because in deep space where there is no air there is also negligible gravity.
However gravity and vacuum are not related at all. You can have a container and pump out all the air, but gravity still acts there. (pupils at school see a famous experiment of ringing an electric bell in a vacuum inside a glass jar the bell does NOT float around….see "bangs in space") You can be in deep space and have air (in a space ship) so they are not related.
There is a link in extra terrestrial terms though..it is the gravity of Earth which holds our atmosphere in place. If a planet is much smaller there is less gravity and it will not be so good at holding an atmosphere, which is why there is no atmosphere on Mercury and is why the atmosphere on Mars is not so dense as ours.