There is a lot of incorrect information in this thread, I'll try and alleviate that.
First of all Gravity is a function of mass and the squareroot of the radius from the center of that mass. Its affect diminishes as you move further from the central point.
We can turn this around and consider the 'escape velocity', which is the velocity needed for you to get to infinity (in practice a very very large distance away) and escape the gravitational force of the object:
v2 = 2GM / R , where G is a constant.
Now as the Supermassive Black Hole (SMBH) is at the centre of the galaxy (I'll get to this later in my post) we know that the rest of the galaxy is rotating around it. This SMBH is situated in the galactic bulge, a region within the galaxy which has a significantly higher density of objects and velocity dispersion (the relative velocity between these objects).
Thus the SMBH gravitational influence extends to the radius at which this velocity dispersion can overcome the influence:
R_inf = 2GM / sigma2, where sigma = velocity dispersion
Using average values for M and sigma (108 M_sun and 200kms-1 respectively) R_inf ~ 22pc. A parsec is a standard measurement of distance and is equivalent to 3.26 lightyears (the closest star to the sun is ~ 4.25lyrs.
Sounds pretty big right? Well the galactic bulge is typically on a scale of 450pc, this means that the SMBHs gravity barely affects the galaxy. Gravitationally the galaxy hardly knows the SMBH is there.
But studies show that the SMBH and the galaxy it resides in are intrinsically linked. How can this be so? The answer is accretion feedback. As matter falls towards the SMBH, it gets swept up into an accretion disk orbiting the SMBH at its inner most stable orbit. As this matter falls inwards it releases gravitational energy in the form of (mostly) electromagnetic radiation:
E_acc = GM / R = c2 / 2.
How big is this? Well our Sun uses nuclear fusion to produce energy, the energy that keeps us alive and E_nuc = 0.007c2 or 71 times less than the energy that can be extracted from accreting matter around a SMBH. (Note that in practice E_acc is ~0.05 due to various reasons which are beyond the scope of this ELI5). Running the numbers this accretion energy release is ~1061 erg (the unit is not important). Similarly if you calculate the binding energy of the bulge (the energy that keeps it from blowing apart) you get ~1058 erg.
Thus the galaxy notices the SMBH through its energy release, or 'feedback'. Finally the reason why there is a SMBH at the center of each galaxy is because of dynamical friction. A moving mass is slowed by the gravitational 'wake' of other objects, resulting in a friction and causes the mass to spiral inwards to the centre of the mass density. Going through the equations you can calculate that it will take a SMBH 108 yrs to spiral inwards and arrive at the centre of the galaxy. This is very short compared with the age of the galaxy and hence we see it at the centre.
Source: I've completed a course on SMBHs of whom the lecturer is one of the leading scientific authorities on SMBHs.