We use 47 gravitational wave sources from the Third LIGO–Virgo–Kamioka Gravitational Wave Detector Gravitational Wave Transient Catalog (GWTC–3) to estimate the Hubble parameter H(z), including its current value, the Hubble constant H₀. Each gravitational wave (GW) signal provides the luminosity distance to the source, and we estimate the corresponding redshift using two methods: the redshifted masses and a galaxy catalog. Using the binary black hole (BBH) redshifted masses, we simultaneously infer the source mass distribution and H(z). The source mass distribution displays a peak around 34 M_⊙, followed by a drop-off. Assuming this mass scale does not evolve with the redshift results in a H(z) measurement, yielding  (68% credible interval) when combined with the H₀ measurement from GW170817 and its electromagnetic counterpart. This represents an improvement of 17% with respect to the H₀ estimate from GWTC–1. The second method associates each GW event with its probable host galaxy in the catalog GLADE+, statistically marginalizing over the redshifts of each event’s potential hosts. Assuming a fixed BBH population, we estimate a value of  with the galaxy catalog method, an improvement of 42% with respect to our GWTC–1 result and 20% with respect to recent H₀ studies using GWTC–2 events. However, we show that this result is strongly impacted by assumptions about the BBH source mass distribution; the only event which is not strongly impacted by such assumptions (and is thus informative about H₀) is the well-localized event GW190814.