  The hierarchical structure of scale-free networks has been investigated
focusing on the scaling of the number $N_h(t)$ of loops of size h as a function
of the system size. In particular we have found the analytic expression for the
scaling of $N_h(t)$ in the Barab\'asi-Albert (BA) scale-free network. We have
performed numerical simulations on the scaling law for $N_h(t)$ in the BA
network and in other growing scale free networks, such as the bosonic network
(BN) and the aging nodes (AN) network. We show that in the bosonic network and
in the aging node network the phase transitions in the topology of the network
are accompained by a change in the scaling of the number of loops with the
system size.
