  We describe an ensemble of growing scale-free networks in an equilibrium
framework, providing insight into why the exponent of empirical scale-free
networks in nature is typically robust. In an analogy to thermostatistics, to
describe the canonical and microcanonical ensembles, we introduce a functional,
whose maximum corresponds to a scale-free configuration. We then identify the
equivalents to energy, Zeroth-law, entropy and heat capacity for scale-free
networks. Discussing the merging of scale-free networks, we also establish an
exact relation to predict their final "equilibrium" degree exponent. All
analytic results are complemented with Monte Carlo simulations. Our approach
illustrates the possibility to apply the tools of equilibrium statistical
physics to study the properties of growing networks, and it also supports the
recent arguments on the complementarity between equilibrium and nonequilibrium
systems.
