Intrinsic degree-correlations in the static model of scale-free networks

We calculate the mean neighboring degree function k̄_nn(k) and the mean clustering function C(k) of vertices with degree k as a function of k in finite scale-free random networks through the static model. While both are independent of k when the degree exponent γ ≥ 3, they show the crossover behavior for 2 < γ< 3 from k-independent behavior for small k to k-dependent behavior for large k. The k-dependent behavior is analytically derived. Such a behavior arises from the prevention of self-loops and multiple edges between each pair of vertices. The analytic results are confirmed by numerical simulations. We also compare our results with those obtained from a growing network model, finding that they behave differently from each other.