  The detection of gravitational waves by Advanced LIGO and Advanced Virgo
provides an opportunity to test general relativity in a regime that is
inaccessible to traditional astronomical observations and laboratory tests. We
present four tests of the consistency of the data with binary black hole
gravitational waveforms predicted by general relativity. One test subtracts the
best-fit waveform from the data and checks the consistency of the residual with
detector noise. The second test checks the consistency of the low- and
high-frequency parts of the observed signals. The third test checks that
phenomenological deviations introduced in the waveform model (including in the
post-Newtonian coefficients) are consistent with zero. The fourth test
constrains modifications to the propagation of gravitational waves due to a
modified dispersion relation, including that from a massive graviton. We
present results both for individual events and also results obtained by
combining together particularly strong events from the first and second
observing runs of Advanced LIGO and Advanced Virgo, as collected in the catalog
GWTC-1. We do not find any inconsistency of the data with the predictions of
general relativity and improve our previously presented combined constraints by
factors of 1.1 to 2.5. In particular, we bound the mass of the graviton to be
$m_g \leq 4.7 \times 10^{-23} \text{eV}/c^2$ ($90\%$ credible level), an
improvement of a factor of 1.6 over our previously presented results.
Additionally, we check that the four gravitational-wave events published for
the first time in GWTC-1 do not lead to stronger constraints on alternative
polarizations than those published previously.
