Nonextensive aspects of the degree distribution in Watts–Strogatz (WS) small-world networks, P SW ( k ) , have been discussed in terms of a generalized Gaussian (referred to as Q-Gaussian) which is derived by the three approaches: the maximum-entropy method (MEM), stochastic differential equation (SDE), and hidden-variable distribution (HVD). In MEM, the degree distribution P Q ( k ) in complex networks has been obtained from Q-Gaussian by maximizing the nonextensive information entropy with constraints on averages of k and k 2 in addition to the normalization condition. In SDE, Q-Gaussian is derived from Langevin equations subject to additive and multiplicative noises. In HVD, Q-Gaussian is made by a superposition of Gaussians for random networks with fluctuating variances, in analogy to superstatistics. Interestingly, a single P Q ( k ) may describe, with an accuracy of | P SW ( k ) - P Q ( k ) | ≲ 10 - 2 , main parts of degree distributions of SW networks, within which about 96–99% of all k states are included. It has been demonstrated that the overall behavior of P SW ( k ) including its tails may be well accounted for if the k-dependence is incorporated into the entropic index in MEM, which is realized in microscopic Langevin equations with generalized multiplicative noises.