Intrinsic degree-correlations in the static model of scale-free networks
School of Physics and Center for Theoretical Physics, Seoul National University, Seoul, 151-747, Korea
Corresponding author: a firstname.lastname@example.org
Published online: 17 February 2006
We calculate the mean neighboring degree function 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.
PACS: 89.75.Da – Systems obeying scaling laws / 89.75.Fb – Structure and organization in complex systems / 05.65.+b – Self-organized systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006