  Color quadrupoles have been found to be important in the proper description
of observables sensitive to the small-x regime in nuclei as well as in the
operator definition of the Weizs\"acker-Williams gluon distribution. In this
paper, we derive the small-x evolution equation of the quadrupole and the
Weizs\"acker-Williams gluon distribution without taking large N_c limit and
study the properties of the equation in both dilute and saturation regime. We
find that the quadrupole evolution follows the BFKL evolution in the dilute
regime and then saturates in the dense region due to nonlinear terms. This
leads us to conclude that the Weizs\"acker-Williams gluon distribution should
obey the same geometrical behavior as the dipole gluon distribution as found in
the inclusive DIS measurement.
