  Context: Gravitational redshift is a classical effect of Einstein's General
Relativity, already measured in stars, quasars and clusters of galaxies. Aims:
We here aim to identify the signature of gravitational redshift in the emission
lines of active galaxies due to supermassive black holes, and compare to what
is found for inactive galaxies. Methods: Using the virial theorem, we estimate
gravitational redshifts for quasars from the 14th data release of the Sloan
Digital Sky Survey, and compare these with measured ones from the difference
between the redshifts of emission lines of Sydney Australian Astronomical
Observatory Multi-object Integral Field (SAMI) galaxies in central and outer
annuli of their integral field spectra. Results: Firstly, from the full width
at half maximum of $H_\beta$ lines of 57 Seyfert type I galaxies of the AGN
Black Hole Mass Database, we derive a median gravitational redshift $z_g = 1.18
\times 10^{-4}$. Expanding this analysis to 86755 quasars from DR14 of SDSS we
have a median value $z_g = 1.52 \times 10^{-4}$. Then, by comparing the
redshifts of $34$ lines measured at central and outer regions of LINER galaxies
in the SAMI survey we obtain $z_g = (0.68 \pm 0.09) \times 10^{-4}$, which
increases to $z_g = (1.0 \pm 0.1) \times 10^{-4}$ when using $H_\alpha$ and
$H_\beta$ lines. These numbers are compatible with central black holes of
$\approx 10^9$ solar masses and broad line regions of $\approx 1$pc. For
non-AGN galaxies the gravitational redshift is compatible with zero.
