  We investigate equal spheres packings generated from several experiments and
from a large number of different numerical simulations. The structural
organization of these disordered packings is studied in terms of the network of
common neighbours. This geometrical analysis reveals sharp changes in the
network's clustering occurring at the packing fractions (fraction of volume
occupied by the spheres respect to the total volume, $\rho$) corresponding to
the so called Random Loose Packing limit (RLP, $\rho \sim 0.555$) and Random
Close Packing limit (RCP, $\rho \sim 0.645$). At these packing fractions we
also observe abrupt changes in the fluctuations of the portion of free volume
around each sphere. We analyze such fluctuations by means of a statistical
mechanics approach and we show that these anomalies are associated to sharp
variations in a generalized thermodynamical variable which is the analogous for
these a-thermal systems to the specific heat in thermal systems.
