13. The polar equation of a circle is $\rho=\sqrt{2}(\cos \theta+\sin \theta)$, then the polar coordinates of the center of the circle are
13. $\left(1, \frac{\pi}{4}\right)$. From $\rho=2 \cos \left(\theta-\frac{\pi}{4}\right)$, we get the center of the circle as $\left(1, \frac{\pi}{4}\right)$, or convert it to Cartesian coordinates to find it.