Tsallis, C.

The degree distribution of the so-called scale-free networks exhibits, quite often, the form p(k) proportional to 1/(k(0) + k)(gamma) (with gamma > 0 and k(0) > 0), in the limit of large networks. It happens that this form precisely coincides with the q-exponential p(k) proportional to exp(q) (-k/k) (q >= 1 and k > 0), with gamma = 1/(q-1) and k(0) = k/(q-1). It optimises the nonadditive entropy S-q = k(B)/q-1 {1 - Sigma(infinity)(k=1)[p(k)](q)} with mathematically the same constraints that yield the stationary (or quasi-stationary) distribution in nonextensive statistical mechanics. In other words, the most ubiquitous form of the degree distribution of scale-free networks is a realisation of the hypothesis involved within the q-generalisation of Boltzmann-Gibbs statistical mechanics. In addition to this, we show that growth is not a necessary condition for having scale-free networks, in contrast with a widely spread belief.