  We have carried out optical spectroscopy with the Anglo-Australian Telescope
for 24,726 objects surrounding a sample of 19 Giant Radio Galaxies (GRGs)
selected to have redshifts in the range 0.05 to 0.15 and projected linear sizes
from 0.8 to 3.2 Mpc. Such radio galaxies are ideal candidates to study the
Warm-Hot Intergalactic Medium (WHIM) because their radio lobes extend beyond
the ISM and halos of their host galaxies, and into the tenuous IGM. We were
able to measure redshifts for 9,076 galaxies. Radio imaging of each GRG,
including high-sensitivity, wideband radio observations from the Australia
Telescope Compact Array for 12 GRGs and host optical spectra (presented in a
previous paper, Malarecki et al. 2013), is used in conjunction with the
surrounding galaxy redshifts to trace large-scale structure.
  We find that the mean galaxy number overdensity in volumes of ~700 Mpc$^3$
near the GRG host galaxies is ~70 indicating an overdense but non-virialized
environment. A Fourier component analysis is used to quantify the anisotropy in
the surrounding galaxy distribution. For GRGs with radio components offset from
the radio axis, there is a clear influence of the environment with lobes
appearing to be deflected away from overdensities in the surrounding medium.
Furthermore, the GRG lobes tend to be normal to the plane defined by the galaxy
neighbourhood close to the host. This indicates the tendency for lobes to grow
to giant sizes in directions that avoid dense regions on both small and large
scales.
