Yes, galaxies can be considered to revolve around a common center. In the case of most galaxies, including our own Milky Way, the center is believed to be dominated by a supermassive black hole. This central black hole exerts a gravitational force on the stars and other objects within the galaxy, causing them to orbit around it.
The concept of centripetal force comes into play here. In order for an object to move in a curved path, there must be a force acting towards the center of that path. In the case of a galaxy, the gravitational force from the central black hole provides the necessary centripetal force to keep the stars in orbit.
The distribution of mass within a galaxy, including the stars, gas, dust, and dark matter, affects the overall gravitational field within the galaxy. This distribution determines the orbital speeds of objects within the galaxy, with objects closer to the center generally moving faster due to the stronger gravitational force.
It's worth noting that the gravitational interactions between the stars and other objects within the galaxy also play a role in the dynamics of galactic rotation. Additionally, the presence of dark matter, a mysterious form of matter that does not emit or interact with light but exerts a gravitational pull, contributes significantly to the overall mass and rotational dynamics of galaxies.