Abstract.
We calculate the mean neighboring degree function \(\bar k_{\rm{nn}}(k)\) 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.
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Lee, JS., Goh, KI., Kahng, B. et al. Intrinsic degree-correlations in the static model of scale-free networks. Eur. Phys. J. B 49, 231–238 (2006). https://doi.org/10.1140/epjb/e2006-00051-y
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DOI: https://doi.org/10.1140/epjb/e2006-00051-y