A galaxy is just a very large collection of stars (and interstellar matter such as dark matter, gas and dust) held together by gravity. Galaxies are classified mainly as elliptical, spiral, and irregular. There is not a specific criterion other than the fact that the stars all all bound by theretheir mutual gravitational attraction. It is speculated that most galaxies have a black hole at its center. This is not necessary however for a collection of stars to be considered as a galaxy.