  We study the statistics of the backbone cluster between two sites separated
by distance $r$ in two-dimensional percolation networks subjected to spatial
long-range correlations. We find that the distribution of backbone mass follows
the scaling {\it ansatz}, $P(M_B)\sim M_B^{-(\alpha+1)}f(M_B/M_0)$, where
$f(x)=(\alpha+ \eta x^{\eta}) \exp(-x^{\eta})$ is a cutoff function, and $M_0$
and $\eta$ are cutoff parameters. Our results from extensive computational
simulations indicate that this scaling form is applicable to both correlated
and uncorrelated cases. We show that the exponent $\alpha$ can be directly
related to the fractal dimension of the backbone $d_B$, and should therefore
depend on the imposed degree of long-range correlations.
