The effect of dynamical friction explains why the brightest (more massive) galaxy tends to be found near the center of a galaxy cluster. The effect of the two body collisions slows down the galaxy, and the drag effect is greater the larger the galaxy mass. When the galaxy loses kinetic energy, it moves towards the center of the cluster. However the observed velocity dispersion of galaxies within a galaxy cluster does not depend on the mass of the galaxies. The explanation is that a galaxy cluster relaxes by violent relaxation, which sets the velocity dispersion to a value independent of the galaxy's mass.