Growing Cayley trees described by a Fermi distribution

In growing Cayley trees with thermal noise we show that the distribution of the bond strengths (energies) is described by the Fermi statistics. The evolution of these hierarchical networks reduces to the Eden model and the invasion percolation model in the limits T-->0 and T-->infinity, respectively. We discuss the relation of the present results with the scale-free networks described by Bose statistics.