  We introduce a model for growing Cayley trees with thermal noise. The
evolution of these hierarchical networks reduces to the Eden model and the
Invasion Percolation model in the limit $T\to 0$, $T\to \infty$ respectively.
We show that the distribution of the bond strengths (energies) is described by
the Fermi statistics. We discuss the relation of the present results with the
scale-free networks described by Bose statistics.
