  Magnetic ordering at low temperature for Ising ferromagnets manifests itself
within the associated Fortuin-Kasteleyn (FK) random cluster representation as
the occurrence of a single positive density percolating network. In this paper
we investigate the percolation signature for Ising spin glass ordering -- both
in short-range (EA) and infinite-range (SK) models -- within a two-replica FK
representation and also within the different Chayes-Machta-Redner two-replica
graphical representation. Based on numerical studies of the $\pm J$ EA model in
three dimensions and on rigorous results for the SK model, we conclude that the
spin glass transition corresponds to the appearance of {\it two} percolating
clusters of {\it unequal} densities.
