The cosmic web through the lens of graph entropy
  We explore the information theory entropy of a graph as a scalar to quantify
the cosmic web. We find entropy values in the range between 1.5 and 3.2 bits.
We argue that this entropy can be used as a discrete analogue of scalars used
to quantify the connectivity in continuous density fields. After showing that
the entropy clearly distinguishes between clustered and random points, we use
simulations to gauge the influence of survey geometry, cosmic variance,
redshift space distortions, redshift evolution, cosmological parameters and
spatial number density. Cosmic variance shows the least important influence
while changes from the survey geometry, redshift space distortions,
cosmological parameters and redshift evolution produce larger changes on the
order of $10^{-2}$ bits. The largest influence on the graph entropy comes from
changes in the number density of clustered points. As the number density
decreases, and the cosmic web is less pronounced, the entropy can diminish up
to 0.2 bits. The graph entropy is simple to compute and can be applied both to
simulations and observational data from large galaxy redshift surveys; it is a
new statistic that can be used in a complementary way to other kinds of
topological or clustering measurements.
