Seeing patterns in noise: Gigaparsec-scale `structures' that do not
  violate homogeneity
  Clowes et al. (2013) have recently reported the discovery of a Large Quasar
Group (LQG), dubbed the Huge-LQG, at redshift z~1.3 in the DR7 quasar catalogue
of the Sloan Digital Sky Survey. On the basis of its characteristic size ~500
Mpc and longest dimension >1 Gpc, it is claimed that this structure is
incompatible with large-scale homogeneity and the cosmological principle. If
true, this would represent a serious challenge to the standard cosmological
model. However, the homogeneity scale is an average property which is not
necessarily affected by the discovery of a single large structure. I clarify
this point and provide the first fractal dimension analysis of the DR7 quasar
catalogue to demonstrate that it is in fact homogeneous above scales of at most
130 Mpc/h, which is much less than the upper limit for \Lambda CDM. In
addition, I show that the algorithm used to identify the Huge-LQG regularly
finds even larger clusters of points, extending over Gpc scales, in explicitly
homogeneous simulations of a Poisson point process with the same density as the
quasar catalogue. This provides a simple null test to be applied to any cluster
thus found in a real catalogue, and suggests that the interpretation of LQGs as
`structures' is misleading.
