  Context. In September 2017 the largest X-class flare of Solar Cycle 24
occurred from the most active region (AR) of this cycle, AR 12673. The AR
attracted much interest because of its unique morphological and evolution
characteristics. Among the parameters examined in the AR was magnetic helicity,
but either only approximately, and/or intermittently. Aims. This work is
interested in studying the evolution of the relative magnetic helicity and of
the two components of its decomposition, the non-potential, and the
volume-threading one, in the time interval around the highest activity of AR
12673. Special emphasis is given on the study of the ratio of the non-potential
to total helicity, that was recently proposed as an indicator of ARs
eruptivity. Methods. For these, we first approximate the coronal magnetic field
of the AR with two different optimization-based extrapolation procedures, and
choose the one that produces the most reliable helicity value at each instant.
Moreover, in one of these methods, we weight the optimization by the
uncertainty estimates derived from the Helioseismic and Magnetic Imager (HMI)
instrument, for the first time. We then follow an accurate method to compute
all quantities of interest. Results. The first observational determination of
the evolution of the non-potential to total helicity ratio seems to confirm the
quality it has in indicating eruptivity. This ratio increases before the major
flares of AR 12673, and afterwards it relaxes to smaller values. Additionally,
the evolution patterns of the various helicity, and energy budgets of AR 12673
are discussed and compared with other works.
