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

J.-S. Lee, K.-I. Goh, B. Kahng () and D. Kim

The European Physical Journal B: Condensed Matter and Complex Systems, 2006, vol. 49, issue 2, 231-238

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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Date: 2006
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DOI: 10.1140/epjb/e2006-00051-y

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