  We study the effect of disorder symmetry in a disordered s-wave
superconductor. We begin with an attractive Hubbard model on a two-dimensional
square lattice in the presence of diagonal- and off-diagonal disorder. The
model is studied numerically using Bogoliubov-deGennes mean-field approach. We
find that the off-diagonal disorder is much more efficient in destroying
superconducting order. A detailed analysis brings out very distinct qualitative
pictures in the two cases: diagonal disorder leads to formation of small scale
isolated superconducting islands separated by large region of normal metal,
whereas off-diagonal disorder leads to a connected network of superconducting
region. Naively, it seems that the connected network of superconducting regions
should have a large average value for superconducting order parameter, but this
does not hold true for large disorder, as we demonstrate explicitly. Our
qualititive picture is supported by real-space data on local order parameters.
