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The origin of scale-free degree distributions in the context of networks isaddressed through an analogous non-network model in which the node degreecorresponds to the number of balls in a box and the rewiring of links to ballsmoving between the boxes. A statistical mechanical formulation is presented andthe corresponding Hamiltonian is derived. The energy, the entropy, as well asthe degree distribution and its fluctuations are investigated at varioustemperatures. The scale-free distribution is shown to correspond to thedegenerate ground state, which has small fluctuations in the degreedistribution and yet a large entropy. We suggest an implication of our resultsfrom the viewpoint of the stability in evolution of networks.Comment: 7 pages, 3 figures. To appear in Europhysics lette

Scale-freeness for networks as a degenerate ground state: A Hamiltonian formulation