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

J. -S. Lee·K. -I. Goh·B. Kahng·D. Kim
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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 $γ\geq 3$, 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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J. -S. Lee, K. -I. Goh, B. Kahng, D. Kim. 2006-01-04. Intrinsic degree-correlations in static model of scale-free networks. https://doi.org/10.1140/epjb%2Fe2006-00051-y

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