  We find that scale-free random networks are excellently modeled by a
deterministic graph. This graph has a discrete degree distribution (degree is
the number of connections of a vertex) which is characterized by a power-law
with exponent $\gamma=1+\ln3/\ln2$. Properties of this simple structure are
surprisingly close to those of growing random scale-free networks with $\gamma$
in the most interesting region, between 2 and 3. We succeed to find exactly and
numerically with high precision all main characteristics of the graph. In
particular, we obtain the exact shortest-path-length distribution. For the
large network ($\ln N \gg 1$) the distribution tends to a Gaussian of width
$\sim \sqrt{\ln N}$ centered at $\bar{\ell} \sim \ln N$. We show that the
eigenvalue spectrum of the adjacency matrix of the graph has a power-law tail
with exponent $2+\gamma$.
