  In this paper the question about statistical properties of
block--hierarchical random matrices is raised for the first time in connection
with structural characteristics of random hierarchical networks obtained by
mipmapping procedure. In particular, we compute numerically the spectral
density of large random adjacency matrices defined by a hierarchy of the
Bernoulli distributions $\{q_1,q_2,...\}$ on matrix elements, where
$q_{\gamma}$ depends on hierarchy level $\gamma$ as $q_{\gamma}=p^{-\mu
\gamma}$ ($\mu>0$). For the spectral density we clearly see the free--scale
behavior. We show also that for the Gaussian distributions on matrix elements
with zero mean and variances $\sigma_{\gamma}=p^{-\nu \gamma}$, the tail of the
spectral density, $\rho_G(\lambda)$, behaves as $\rho_G(\lambda) \sim
|\lambda|^{-(2-\nu)/(1-\nu)}$ for $|\lambda|\to\infty$ and $0<\nu<1$, while for
$\nu\ge 1$ the power--law behavior is terminated. We also find that the vertex
degree distribution of such hierarchical networks has a poly--scale fractal
behavior extended to a very broad range of scales.
