  Short Gamma-Ray Burst (SGRB) progenitors have long been thought to be
coalescing binary systems of two Neutron Stars (NSNS) or a Neutron Star and a
Black Hole (NSBH). The August 17$^{\rm th}$, 2017 detection of the GW170817
gravitational-wave signal by Advanced LIGO and Advanced Virgo in coincidence
with the electromagnetic observation of the SGRB GRB 170817A confirmed this
scenario and provided new physical information on the nature of these
astronomical events. We use SGRB observations by the Neil Gehrels Swift
Observatory Burst Alert Telescope and GW170817/GRB 170817A observational data
to estimate the detection rate of coincident gravitational-wave and
electromagnetic observations by a gravitational-wave detector network and
constrain the physical parameters of the SGRB jet structure. We estimate the
rate of gravitational-wave detections coincident with SGRB electromagnetic
detections by the Fermi Gamma-ray Burst Monitor to be between $\sim$ 0.1 and
$\sim$ 0.6 yr$^{-1}$ in the third LIGO-Virgo observing run and between $\sim$
0.3 and $\sim$ 1.8 yr$^{-1}$ for the LIGO-Virgo-KAGRA network at design
sensitivity. Assuming a structured model with a uniform ultra-relativistic jet
surrounded by a region with power-law decay emission, we find the jet
half-opening angle and the power-law decay exponent to be $\theta_c\sim
7\,{}^\circ$ -- $22\,{}^\circ$ and $s\sim 5$ -- $30$ at 1$\sigma$ confidence
level, respectively.
