  We investigate the correlation between nine different dark matter halo
properties using a rank correlation analysis and a Principal Component Analysis
for a sample of haloes spanning five orders of magnitude in mass. We consider
mass and dimensionless measures of concentration, age, relaxedness, sphericity,
triaxiality, substructure, spin, and environment, where the latter is defined
in a way that makes it insensitive to mass. We find that concentration is the
most fundamental property. Except for environment, all parameters are strongly
correlated with concentration. Concentration, age, substructure, mass,
sphericity and relaxedness can be considered a single family of parameters,
albeit with substantial scatter. In contrast, spin, environment, and
triaxiality are more independent, although spin does correlate strongly with
substructure and both spin and triaxiality correlate substantially with
concentration. Although mass sets the scale of a halo, all other properties are
more sensitive to concentration.
