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On 17 August 2017, the LIGO and Virgo observatories made the first directdetection of gravitational waves from the coalescence of a neutron star binarysystem. The detection of this gravitational-wave signal, GW170817, offers anovel opportunity to directly probe the properties of matter at the extremeconditions found in the interior of these stars. The initial,minimal-assumption analysis of the LIGO and Virgo data placed constraints onthe tidal effects of the coalescing bodies, which were then translated toconstraints on neutron star radii. Here, we expand upon previous analyses byworking under the hypothesis that both bodies were neutron stars that aredescribed by the same equation of state and have spins within the rangeobserved in Galactic binary neutron stars. Our analysis employs two methods:the use of equation-of-state-insensitive relations between various macroscopicproperties of the neutron stars and the use of an efficient parametrization ofthe defining function $p(\rho)$ of the equation of state itself. From the LIGOand Virgo data alone and the first method, we measure the two neutron starradii as $R_1=10.8^{+2.0}_{-1.7}$ km for the heavier star and $R_2=10.7^{+2.1}_{-1.5}$ km for the lighter star at the 90% credible level. If weadditionally require that the equation of state supports neutron stars withmasses larger than $1.97 \,M_\odot$ as required from electromagneticobservations and employ the equation-of-state parametrization, we furtherconstrain $R_1= 11.9^{+1.4}_{-1.4}$ km and $R_2= 11.9^{+1.4}_{-1.4}$ km at the90% credible level. Finally, we obtain constraints on $p(\rho)$ at supranucleardensities, with pressure at twice nuclear saturation density measured at$3.5^{+2.7}_{-1.7}\times 10^{34} \,\mathrm{dyn}/\mathrm{cm}^{2}$ at the 90%level.

GW170817: Measurements of Neutron Star Radii and Equation of State