  We use the first Betti number of a complex to characterize the morphological
structure of granular samples in mechanical equilibrium. We analyze
two-dimensional granular packings after a tapping process by means of both
simulations and experiments. States with equal packing fraction obtained with
different tapping intensities are distinguished after the introduction of a
filtration parameter which determines the particles (nodes in the network) that
are joined by an edge. We first use numerical simulations to characterize the
effect of the precision in the particles localization by artificially adding
different levels of noise in this magnitude. The outcomes obtained for the
simulations are then compared with the experimental results allowing a clear
distinction of experimental packings that have the same density. This is
accomplished by just using the position of the particles and no other
information about the possible contacts, or magnitude of forces.
