  The origin of scale-free degree distributions in the context of networks is
addressed through an analogous non-network model in which the node degree
corresponds to the number of balls in a box and the rewiring of links to balls
moving between the boxes. A statistical mechanical formulation is presented and
the corresponding Hamiltonian is derived. The energy, the entropy, as well as
the degree distribution and its fluctuations are investigated at various
temperatures. The scale-free distribution is shown to correspond to the
degenerate ground state, which has small fluctuations in the degree
distribution and yet a large entropy. We suggest an implication of our results
from the viewpoint of the stability in evolution of networks.
