  The Andromeda galaxy (M\,31) hosts one of the nearest and most quiescent
super-massive black holes, which provides a rare, but promising opportunity for
studying the physics of black hole accretion at the lowest state. We have
conducted a multi-frequency, multi-epoch observing campaign, using the Karl G.
Jansky Very Large Array (VLA) in its extended configurations in 2011-2012, to
advance our knowledge of the still poorly known radio properties of M\,31*. For
the first time, we detect M\,31* at 10, 15 and 20 GHz, and measure its spectral
index, $\alpha \approx -0.45\pm0.08$ (S$_{\nu}$ $\varpropto$ $\nu^{\alpha}$),
over the frequency range of 5-20 GHz. The relatively steep spectrum suggests
that the observed radio flux is dominated by the optically-thin part of a
putative jet, which is located at no more than a few thousand Schwarzschild
radii from the black hole. On the other hand, our sensitive radio images show
little evidence for an extended component, perhaps except for several
parsec-scale "plumes", the nature of which remains unclear. Our data also
reveal significant (a few tens of percent) flux variation of M\,31* at 6 GHz,
on timescales of hours to days. Furthermore, a curious decrease of the mean
flux density, by $\sim$50\%, is found between VLA observations taken during
2002-2005 and our new observations, which might be associated with a
substantial increase in the mean X-ray flux of M\,31* starting in 2006.
