  A novel order parameter $\Phi$ for spin glasses is defined based on
topological criteria and with a clear physical interpretation. $\Phi$ is first
investigated for well known magnetic systems and then applied to the
Edwards-Anderson $\pm J$ model on a square lattice, comparing its properties
with the usual $q$ order parameter. Finite size scaling procedures are
performed. Results and analyses based on $\Phi$ confirm a zero temperature
phase transition and allow to identify the low temperature phase. The
advantages of $\Phi$ are brought out and its physical meaning is established.
