  We demonstrate that the normalised localization length $\beta$ of the
eigenfunctions of diluted (sparse) banded random matrices follows the scaling
law $\beta=x^*/(1+x^*)$. The scaling parameter of the model is defined as
$x^*\propto(b_{eff}^2/N)^\delta$, where $b_{eff}$ is the average number of
non-zero elements per matrix row, $N$ is the matrix size, and $\delta\sim 1$.
Additionally, we show that $x^*$ also scales the spectral properties of the
model (up to certain sparsity) characterized by the spacing distribution of
eigenvalues.
