  One major goal in condensed matter physics is identifying the physical
mechanisms that lead to arrested states of matter, especially gels and glasses.
The complex nature and microscopic details of each particular system are
relevant. However, from both scientific and technological viewpoints, a
general, consistent and unified definition is of paramount importance. Through
Monte Carlo computer simulations of states identified in experiments, we
demonstrate that adhesive hard-sphere dispersions are the result of rigidity
percolation with average number of bonds, $<n_b>$, equals to 2.4. This
corresponds to an established mechanism leading to phase transitions in
network-forming materials. Our findings connect the concept of critical gel
formation in colloidal suspensions with short-range attractive interactions to
the universal concept of rigidity percolation. Furthermore, the bond, angular
and local distributions along the gelation line are explicitly studied in order
to determine the topology of the structure of the critical gel state.
