  We report theoretical investigations on how edge states are destroyed in
disordered mesoscopic samples by calculating a "phase diagram" in terms of
energy versus disorder strength $(E,W)$, and magnetic field versus disorder
strength $(B,W)$, in the integer quantum Hall regime. It is found that as the
disorder strength $W$ increases, edge states are destroyed one by one if
transmission eigen-channels are used to characterize the edge states. Near the
insulating regime, transmission eigen-channels are closed one by one in the
same order as edges states are destroyed. To identify those edge states which
have survived disorder, we introduce a generalized current density that can be
calculated and visualized.
