  We present an updated catalog of X-ray point sources in the inner
500$\arcsec$ ($\sim$20 parsec) of the Galactic Center (GC), where the {\it
nuclear star cluster} (NSC) stands, based on a total of $\sim$4.5 Ms of {\it
Chandra} observations taken from September 1999 to April 2013. This ultra-deep
dataset offers unprecedented sensitivity for detecting X-ray sources in the GC,
down to an intrinsic 2--10 keV luminosity of
$1.0\times10^{31}{\rm~erg~s^{-1}}$. A total of 3619 sources are detected in the
2--8 keV band, among which $\sim$3500 are probable GC sources and $\sim$1300
are new identifications. The GC sources collectively account for $\sim$20\% of
the total 2--8 keV flux from the inner 250$\arcsec$ region where detection
sensitivity is the greatest. Taking advantage of this unprecedented sample of
faint X-ray sources that primarily traces the old stellar populations in the
NSC, we revisit global source properties, including long-term variability,
cumulative spectra, luminosity function and spatial distribution. Based on the
equivalent width and relative strength of the iron lines, we suggest that in
addition to the arguably predominant population of magnetic cataclysmic
variables (CVs), non-magnetic CVs contribute substantially to the detected
sources, especially in the lower-luminosity group. On the other hand, the X-ray
sources have a radial distribution closely following the stellar mass
distribution in the NSC, but much flatter than that of the known X-ray
transients, which are presumably low-mass X-ray binaries (LMXBs) caught in
outburst. This, together with the very modest long-term variability of the
detected sources, strongly suggests that quiescent LMXBs are a minor
($\lesssim$ a few percent) population.
