Did LIGO measurements prove that the speed of gravity equals the speed of light? This question about the speed of light prompted my own question. In the linked question it is asked if there is experimental proof that the speed of gravity equals the speed of light. I was surprised not to see the LIGO measurements mentioned.
The experiment uncovered the arrival of a spacetime distortion coming from fast-spinning binary systems of black holes or neutron stars. Due to LIGO's extensive Nature (there is one observatory in Livingston and one in Hanford) it seems that upon arrival the gravitational wave (if it hits the Earth at a sharp angle) will hit one of both observatories first (which one depends obviously from the origin of the wave). So it should be possible to measure the speed of gravity. Or, at least, to measure if the speed is finite (or not).
Has this been done?
 A: Yes. In principle, the speed of gravitational waves can be measured using the data of LIGO. In fact, using a Bayesian approach, the first measurement of the speed of gravitational waves using time delay among the GW detectors was suggested/performed by Cornish, Blas and Nardini. By applying the Bayesian method, they found that the speed of gravitational waves is constrained to 90% confidence interval between $0.55c$ and $1.42c$ by use of the data of binary black hole mergers GW150914, GW151226, and GW170104.
After that, a more precise measurement of the speed of gravitational waves was
performed by the measurement of the time delay between GW and electromagnetic observations of the same astrophysical source, as @Andrew nicely mentioned, by use of a binary neutron star inspiral GW170817. They found the speed of gravitational wave signal is the same as the speed of the gamma rays to approximately one part in $10^{15}$. Note that this study is primarily based on the difference between the speed of gravity and the speed of light.
Recently, a new method has been introduced using a geographically separated network of detectors. As the authors mentioned, while this method is far less
precise, it provides an independent measurement of the speed of gravitational waves by combining ten binary black hole events and the binary neutron star event from the first and second observing runs of Advanced LIGO and Advanced Virgo. By combining the measurements of LIGO and Virgo, and assuming isotropic propagation, the authors have constrained the speed of gravitational waves to ($0.97c$, $1.01c$) which is within 3% of the speed of light in a vacuum.
In my opinion, the best study is the second one (that @Andrew nicely mentioned), in which multiple measurements can be measured to produce a more accurate result, but the later (the third study) has its scientific significance. This is because the later method is an independent method of directly measuring the speed of gravity which is based solely on GW observations and so not reliant on multi-messenger observations, as the authors mentioned.
Besides these achievements, there are other interesting results that one can extract from LIGO's data. For example, observations of LIGO have constrained a lower bound on the graviton Compton wavelength as
$${{\lambda _{{\rm{graviton}}}} > 1.6 \times {{10}^{13}}{\rm{km}}},$$
which is really interesting. In fact, assuming that gravitons are dispersed in vacuum like massive particles, i.e. ${\lambda _{graviton}} = \frac{h}{{{m_{graviton}}\,c}}$, one can find an upper bound for graviton's mass as ${{m_{{\rm{graviton}}}} \le 7.7 \times {{10}^{ - 23}}eV/{c^2} \sim {{10}^{ - 38}}g}$, which is extremely small, beyond the technology of our detectors.
A: Yes, the multi-messenger observation of GW170817 (a binary neutron star merger) allows for a measurement of the speed of gravitational waves. One can compare the arrival times of the gamma ray burst (which travels from the source to Earth at the speed of light), with the arrival time of the gravitational waves (which of course travel at the speed of gravitational waves).
The test is described in detail in this paper published in The Astrophysical Journal Letters:
Abbott et al. (2017), Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A, https://doi.org/10.3847/2041-8213/aa920c.
In particular, LIGO, Virgo, and the Fermi Gamma-ray Burst Monitor found that
\begin{equation}
-3 \times 10^{-15} \leq \frac{\Delta v}{v_{\rm EM}} \leq +7 \times 10^{-16}
\end{equation}
where $\Delta v=v_{\rm GW}-v_{\rm EM}$ is the difference between the speed of gravitational waves and the speed of light, $v_{\rm GW}$ is the speed of gravitational waves, and $v_{\rm EM}$ is the speed of light.
A: Time differences in the detection of a gravitational wave event at two or even three detectors can only give an upper bound on the speed of gravitational waves. This is because there is a line of points that are equidistant from all three detectors. You would need to detect an event at at least four sites to establish the speed of gravitational waves from time differences in the gravitational wave detection alone. So far, only one event (GW170814) has been detected at three different sites, and no events have been detected at four sites.
However, this is not a major problem because, as mentioned in another answer, comparing arrival times of gravitational waves and electromagnetic waves from GM170817 has already provided very tight upper and lower bounds on the speed of gravitational waves.
A: The time delay between LIGO detections doesn’t so much verify the speed of gravity to equal $c$; rather, this fact is taken as a given to help determine the direction of  origin of the wave. For example, if the two detectors register a blip at the same time, then the wave must have come from some direction perpendicular to the line connecting the two. A measurement of the delay restricts the possible originating directions, but only if the speed of gravity is known a priori (which LIGO can help to determine by other means, as discussed in another answer).
