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

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

2005-11-07

arxiv.org/abs/cond-mat/0511151v2

Physics

Condensed Matter

Statistical Mechanics

8 pages

Scientific paper

10.1140/epjb/e2006-00051-y

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 $\gamma \geq 3$, they show the crossover behavior for $2 < \gamma < 3$ 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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