  We use a new algorithm to find the stress-carrying backbone of ``generic''
site-diluted triangular lattices of up to 10^6 sites. Generic lattices can be
made by randomly displacing the sites of a regular lattice. The percolation
threshold is Pc=0.6975 +/- 0.0003, the correlation length exponent \nu =1.16
+/- 0.03 and the fractal dimension of the backbone Db=1.78 +/- 0.02. The number
of ``critical bonds'' (if you remove them rigidity is lost) on the backbone
scales as L^{x}, with x=0.85 +/- 0.05. The Young's modulus is also calculated.
