  We evaluate the elasticity of arrested short-ranged attractive colloids by
combining an analytically solvable elastic model with a hierarchical arrest
scheme into a new approach, which allows to discriminate the microscopic
(primary particle-level) from the mesoscopic (cluster-level) contribution to
the macroscopic shear modulus. The results quantitatively predict experimental
data in a wide range of volume fractions and indicate in which cases the
relevant contribution is due to mesoscopic structures. On this basis we propose
that different arrested states of short-ranged attractive colloids can be
meaningfully distinguished as homogeneous or heterogeneous colloidal glasses in
terms of the length-scale which controls their elastic behavior.
