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.
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